2215 The following copied from Internet see Reference " They don't accelerate. Photons travel at the speed of light. The fact is that the photons coming out of the other side of the glass are not the same ones that went in to the glass.
As photons hit the glass, they scatter off the atoms in the glass  or rather, they are absorbed by the glass atoms, inducing a vibration of the atom, and then the vibration causes a new photon to be emitted in a random direction. There's a delay between when the photon is absorbed and when the new one is emitted."
2315 The question above in blue on Quora Digest answered by Jacob VanWagoner at the 2415 date poses for me in a thought experiment, the following:
2715 The photon see page Control Panel +Aether Physics Model Figure 4 .
The above My concept is similar except for J_Wave Strings to Bohr Radius section copied here from page Control Panel +Aether Physics Model:
Bohr Atom:
Perhaps the foremost scientists of the 20th century was Niels Bohr, the first to apply Planck's quantum idea to problems in atomic physics. In the early 1900's, Bohr proposed a quantum mechanical description of the atom to replace the early model of Rutherford.
The Bohr model basically assigned discrete orbits for the electron, multiples of Planck's constant, rather than allowing a continuum of energies as allowed by classical physics.
The power in the Bohr model was its ability to predict the spectra of light emitted by atoms. In particular, its ability to explain the spectral lines of atoms as the absorption and emission of photons by the electrons in quantized orbits.
Our current understanding of atomic structure was formalized by Heisenberg and Schroedinger in the mid1920's where the discreteness of the allowed energy states emerges from more general aspects, rather than imposed as in Bohr's model. The Heisenberg/Schroedinger quantum mechanics have consistent fundamental principles, such as the wave character of matter and the incorporation of the uncertainty principle.
In principle, all of atomic and molecular physics, including the structure of atoms and their dynamics, the periodic table of elements and their chemical behavior, as well as the spectroscopic, electrical, and other physical properties of atoms and molecules, can be accounted for by quantum mechanics => fundamental science.
de Broglie Matter Waves:
Perhaps one of the key questions when Bohr offered his quantized orbits as an explanation to the UV catastrophe and spectral lines is, why does an electron follow quantized orbits? The response to this question arrived from the Ph.D. thesis of Louis de Broglie in 1923. de Broglie argued that since light can display wave and particle properties, then perhaps matter can also be a particle and a wave too.
One way of thinking of a matter wave (or a photon) is to think of a wave packet. Normal waves look with this:
having no beginning and no end. A composition of several waves of different wavelength can produce a wave packet that looks like this:
So a photon, or a free moving electron, can be thought of as a wave packet, having both wavelike properties and also the single position and size we associate with a particle. There are some slight problems, such as the wave packet doesn't really stop at a finite distance from its peak, it also goes on for every and every. Does this mean an electron exists at all places in its trajectory?
de Broglie also produced a simple formula that the wavelength of a matter particle is related to the momentum of the particle. So energy is also connected to the wave property of matter.
Lastly, the wave nature of the electron makes for an elegant explanation to quantized orbits around the atom. Consider what a wave looks like around an orbit, as shown below.
The electron matter wave is both finite and unbounded (remember the 1st lecture on math). But only certain wavelengths will `fit' into an orbit. If the wavelength is longer or shorter, then the ends do not connect. Thus, de Broglie explains the Bohr atom in that on certain orbits can exist to match the natural wavelength of the electron. If an electron is in some sense a wave, then in order to fit into an orbit around a nucleus, the size of the orbit must correspond to a whole number of wavelengths.
Notice also that this means the electron does not exist at one single spot in its orbit, it has a wave nature and exists at all places in the allowed orbit. Thus, a physicist speaks of allowed orbits and allowed transitions to produce particular photons (that make up the fingerprint pattern of spectral lines). And the Bohr atom really looks like the following diagram:
While de Broglie waves were difficult to accept after centuries of thinking of particles are solid things with definite size and positions, electron waves were confirmed in the laboratory by running electron beams through slits and demonstrating that interference patterns formed.
How does the de Broglie idea fit into the macroscopic world? The length of the wave diminishes in proportion to the momentum of the object. So the greater the mass of the object involved, the shorter the waves. The wavelength of a person, for example, is only one millionth of a centimeter, much to short to be measured. This is why people don't `tunnel' through chairs when they sit down.
Young TwoSlit Experiment:
The wavelike properties of light were demonstrated by the famous experiment first performed by Thomas Young in the early nineteenth century. In original experiment, a point source of light illuminates two narrow adjacent slits in a screen, and the image of the light that passes through the slits is observed on a second screen.
click here to interference movieclick here to see a wave experimentThe dark and light regions are called interference fringes, the constructive and destructive interference of light waves. So the question is will matter also produce interference patterns. The answer is yes, tested by firing a stream of electrons.
However, notice that electrons do act as particles, as do photons. For example, they make a single strike on a cathode ray tube screen. So if we lower the number of electrons in the beam to, say, one per second. Does the interference pattern disappear?
The answer is no, we do see the individual electrons (and photons) strike the screen, and with time the interference pattern builds up. Notice that with such a slow rate, each photon (or electron) is not interacting with other photons to produce the interference pattern. In fact, the photons are interacting with themselves, within their own wave packets to produce interference.
But wait, what if we do this so slow that only one electron or one photon passes through the slits at a time, then what is interfering with what? i.e. there are not two waves to destructively and constructively interfere. It appears, in some strange way, that each photon or electron is interfering with itself. That its wave nature is interfering with its own wave (!).
The formation of the interference pattern requires the existence of two slits, but how can a single photon passing through one slit `know' about the existence of the other slit? We are stuck going back to thinking of each photon as a wave that hits both slits. Or we have to think of the photon as splitting and going through each slit separately (but how does the photon know a pair of slits is coming?). The only solution is to give up the idea of a photon or an electron having location. The location of a subatomic particle is not defined until it is observed (such as striking a screen).
2915 I copied this reference on Internet:
The photoelectric effect says that photons strike a metal surface and are absorbed by outer electrons, giving them enough energy to break free and escape. So, what do we have left? Does that mean that, if we left a light shining on a piece of metal long enough, that eventually there would be a hole burned in the metal? Are these electrons replaced? What happened to the atom? It has absorbed a photon and lost an electron. Is the total energy of the system lower or higher?
Reference https://www.physicsforums.com/threads/electronvsphoton.76316/
The cardioid torus J_Waves in a closed loop J_Tubular bulges at wavelength and frequency that determines the color of this J_Photon. The J_Electron 137 J_Waves in the first level shell would be a color that no photon is created from. A Photon is created when an J_Electron escapes from 2nd shell level or falls to first shell level, a lower level. The frequency and wave length of this color will be determined by that of the J_Electron J_Waves at the second level shell. The frequency and wave length will be determined for J_Waves in this circumference of this J_Electron in the second level shell. Also this will be determined for Shell levels 3 through 6. The J_Electrons color determined by the frequency that its wave length that its quantizing shells circumference. The charges, gravity, momentum, inertia and electromagnetic forces in the J_Electrons' Atom's fields inverse square rule in its shells.
Outside of the atom's shells when a electron falls to an inner shell and gives up the radiation of J_Photon cardioid J_Torus' J_Electromagnetic field interaction with J_Aether accelerates this J_Photon to near the speed of light as the atoms force fields diminish. The speed a J_Photon's J_Packet travels in nearly a straight line through J_Aether depends on J_Waves color frequency and mass. The J_Aether's J_Waves mass interact with the J_Electromagnetic cardioid's field maintaining its instant velocity near the speed of light.
21215 With the 137 J_Waves in the J_Photon cardioid J_Torus' J_Electromagnetic field created similar to J_Electron 137 J_Waves moving around in J_Atom's shells moving in a loop of wire. The J_Photon cardioid is very hard to measure the size of it. What can be detected is its J_Torus. The J_Electromagnetic cardioid's field J_Photon being composed of J_Waves can be split into two J_Photons. This is how it can as a wave pass through the two slit experiment and cause the interference pattern on a screen.
_________________________________________________________________________

21415 I made an entry and Debian Linux on 21315 couldn't save this blog update. This also happened on my concrete 5 blog spacetime and the whole blog except the spacetime heading was lost a week ago. I am now using Mint on Ubuntu Linux on virtual Oracle instead Oracle virtualbox on windows7 on this same DELL laptop.
21515 The response is to slow. I will use my widows 7 on Desktop.
21815 I have had a Apple Tech in town update my MacPro to snowlion version which works faster. I will be able to load Ubuntu into a partition the tech set up address for it.
The photon 1/2 spin over 2 imaginary spheres green double loxodrom is wrapped around 1 imaginary sphere 2 times to create a 1 spin cardioid shape closed loop J_String traveling through spacetime.
31115 Continued from Blog page Equations I will now explore how Black Holes has developed and stars to galaxies could be composed of J_Waves.
31315 Reference NATIONAL GEOGRAPHIC  APRIL 2014 page 85 start of foldout :
COSMIC QUESTIONS ; "In the 20th century the universe became a storya scientific one. It had always been seen as static and eternal. Tnehn astronomers observed other galaxies flying away from ours, and Einstein's general relativity theory implied space itself was expandingwhich meant the universe had once been denser. What had seemed eternal now had a beginning and an end. But what beginning? What end? Those questions are still open."
My paradigm J_Waves concept answers those questions which I will disclose.
Continuing the above reference quote "what is our universe made of ? Stars, dust and gasthe stuff we can discernmake up less than 5 percent of the universe. Their gravity can't account for how galaxies hold together. scientists figure about 24 percent of the universe is a mysterious dark matterperhaps exotic particles formed right after inflation. The rest is dark energy: an unknown energy field or property of space that counteracts gravity, providing an explanation for observations that the expansion of space is accelerating."
I will now Disclose My new and unique concept of how the above referenced phenomena in my new and unique paradigm takes place. "The universe composed 24% Dark matter 4% gas 0.5% Planets and stars with the rest 71.5% Dark energy."
My concept explains this with J_Aether being an integral part with the J_Waves mass and J_Energy making up the 24% Dark mater 71.5 % Dark energy equals 95.5% of J_Universe. The J_Spiraling J_Strings J_Mass moving near the speed of light gives J_Visible+J_Dark Energy equals J_Mass times the speed of light squared.
31415 I will now continue My Disclosure on 11315 which I entered with an afternoon's work on my desktop Dell PC which was knocked out by Windows 7 update just as I finished entering the end of disclosure before I was going to save it. My GFI Backup on an exterior hard drive also failed its backup when I got knocked of Windows7 up date of this blog hosted by Concrete 5. They might have a backup but don't know how to check and see. So now I will now try to renter the rest of that disclosure on my MacPro laptop.
31415 Disclosure using my unique notation (J_) that indicates My New Paradigm unique concept which is a deeper meaning to the words common usage:
The paramount concept is that J_Aether J_Spiraling away from high J_Density J_3Dimension Volume to lower J_3Dimension Volume sub micro J_Waves in J_Tours J_Cosmic Strings. This sub micro tube like J_Cosmic J_String that J_Waves bulges like crest moves in this J_String at the speed of Light carrying in each a minuscule amount of J_Mass. The ( J_Visible J_Energy + the J_Dark J_Energy ) = ( J_Visible J_Mass + J_Dark J_Mass ) * ( speed of light )^2 . The J_Spiraling of J_Waves J_Strings is Paramount to Creating J_Gravity. J_Constant constant is also created by this J_Spiraling invisible J_Strings. J_Inertia, J_Momentum are Paramount J_Creation results of J_Strings J_Space J_Spiraling J_Fabric of J_Universe where the J_Relative motion of separate units of J_Wave J_Particles through J_Space. My comprehension of how a smaller body of J_Waves moving J_Relative to large body of J_Waves i Works as follows: The J_Strings J_Spiraling from all bodies of J_Waves push on each systems J_String by the action of any 2 J_Waves can't occupy the same J_Space at the same instance of J_Time. The J_Waves J_Mass in pushing on opposing system of J_Waves J_Mass body. This causes the J_Waves moving near the speed of light to alter their speed slightly this creates the J_Force involved in J_Momentum, J_Inertia, J_Gravity and J_Cosmic constant. The J_Force J_Vectors are created by J_Acceleration of J_Mass.The J_Acceleration of J_Gravity is determined by the angle of J_String averaged out J_Vector from all the J_Strings in the J_Fabric of J_Space. From the crest of J_Waves J_Photons are J_Radiated through the J_String J_Fabric of J_Space in the J_Universe. In this Disclosure all the effects of this new and unique J_Paradigm will be Disclosed later as I live with it.
31515 The J_Strings come from every directions from their J_Mass source inversely J_Gravity strength in relation to their distance. This effect would be J_Strong force at distance in the Planck Range. It would take a minima of three J_Wave lengths of planck length to exert a J_Strong force binding action.
31615 J_Mass equals conventual mass plus Higgs particle. Particle Physicist end their conventional description of microscopic composition at quark particle level. In the sub microscopic domain the J_Waves in a J_Proton J_String J_Body could bond with a J_Neutron J_Waves J_String J_Body by J_Strong force.
J_Gravity acceleration force on J_Mass in J_Waves J_Body is on each and not dependent on the number of J_Waves in a J_Body. Albert Einstein,s concept of a 2 dimensional plane like, a rubber sheet, deformed in the 3 dimensional direction by 2 bodies of mass forming gravitational acceleration. Whereas My concept of 4 dimensional J_Space where J_Strings of J_Fabric J_Gravitational acceleration on 2 J_Bodies of J_Mass. The 2 J_Bodies are pushed by the J_Strings of each J_Body by the force of J_Gravity inversely Proportional to the distance between them. All J_Bodies in J_Space are acted on by their J_Gravitational force and acceleration inversely Proportionally to the distance between each of them.
31715 First J_Mass = J_Dark J_Mass + J_Visible J_Mass. Next 2 seperate volums of J_Masses that are equal one J_Toroidal J_Volume with outside surface simular to Sine Wave iside surface a cylinder nearly a Planck Length long.
31815 The first J_String 1 J_Wave Length long nearly 1 Planck Length. The other = J_Mass with = volume is a rod nearly 1 Planck Length. The first moving at nearly the speed of light along J_Spiral in the direction from higher density of mass to lower density of mass the other = J_Mass is moving in the oposite direction along the same segment of J_Spiral. For every action in J_Aether there is an = and opposite reaction.
J_Quarks are the reorganization of derbus from neuculer particle's of J_Waves that particle physicists have smashed together at near the speed of light. J_Quarks are the different organized derbus parts J_Strings observed by particle physicists. J_Up Quark, J_Down Quark, J_Top Quark, J_Bottom Quark & J_Strange Quark are the reorganizations of neuculer particles parts. Latter I will calculate the number of J_waves in each comepared the 137 J_Waves perJ_Electron or J_Photon. From the outside Crest of
J_wave the J_Photon the same number of J_waves 137 that J_Electron J_Radiates when an J_Electron leaves an outer higher energy level for the next orbit in for this number of J_Waves 137. This J_Photon J_String moves in nearly a straight line curve through J_Aether fabric of J_Space composed of J_Spiraling J_Cosmic J_Strings.
My Disclosure language is complex to cover whats new and unique in My J_Paradigm J_Aether's Cosmic J_String with one half of J_Mass J_Toroidal moveing in a J_Spiraling direction out to lower density area of J_Mass. This is for J_Aether and for the creation off elementary units and what particle physit call elementary particles. One of current science physicist J. RRichard Gott follows:
Cosmic String
We've blown through black holes and wormholes, but there's yet another possible means of time traveling via theoretic cosmic phenomena. For this scheme, we turn to physicist J. Richard Gott, who introduced the idea of cosmic string back in 1991. As the name suggests, these are stringlike objects that some scientists believe were formed in the early universe.
These strings may weave throughout the entire universe, thinner than an atom and under immense pressure. Naturally, this means they'd pack quite a gravitational pull on anything that passes near them, enabling objects attached to a cosmic string to travel at incredible speeds and benefit from time dilation. By pulling two cosmic strings close together or stretching one string close to a black hole, it might be possible to warp spacetime enough to create what's called a closed timelike curve.
32515 I am not studying time travel but the above article continues on this subject:
Using the gravity produced by the two cosmic strings (or the string and black hole), a spaceship theoretically could propel itself into the past. To do this, it would loop around the cosmic strings.
Quantum strings are highly speculative, however. Gott himself said that in order to travel back in time even one year, it would take a loop of string that contained half the massenergy of an entire galaxy. In other words, you'd have to split half the atoms in the galaxy to power your time machine. And, as with any time machine, you couldn't go back farther than the point at which the time machine was created.
Oh yes, and then there are the time paradoxes.
5715 Copied My today's Email Quora Digest's:
The great thing about an "atom" is in the name. It comes from a Greek word meaning "cannot be broken". That's not quite correct, but it's actually pretty close.
It doesn't take any energy for an atom to sit there being an atom. You're probably drawing an analogy to living things, but an atom isn't a living thing. Living things are arrangements of atoms that are characterized by a bunch of dynamic properties, and go from living to nonliving when those properties are interrupted. Atoms are vastly, vastly simpler things, and don't really analogize well.
So an atom doesn't need any energy to go on doing its thing. It is (at least at this level of talking about it) a fundamental thing in the universe that just sits there. Energy can move it around and connect it to other atoms, but the fundamental beinganatom part is constant and requires no maintenance. Quite the opposite: the energy that it has is conserved and it would take an input of more energy to change it.
Radioactivity does alter this for some atoms, but that's kind of a separate topic. The atoms you're thinking about here are nonradioactive and will just sit there for pretty much all of history.
You mention "3.3 billion years", which is puzzling, since most atoms are a good deal older than that. I think you may be thinking about life on earth, which is about that old. But life doesn't "use" atoms in that way. Life "uses" energy, which comes from the sun. (Which is, slowly, running out, but it's got several billion more years to go. The sun is really, really, REALLY big.)
Atoms themselves are just building blocks: life moves them around but doesn't really affect them as atoms. Electrons come and go from an individual atom, but there are lots of them, and there are always more around. The earth has a pretty much fixed supply of them, and they just move, not disappear.
What "3.3 billion years of use"? The energy is locked up as potential energy in various forms, nobody is draining it. Except in the rare case of unstable nuclei, which lose small amounts as they decay to stable nuclei. But then they stop losing energy, too.
To be more clear: all I said above applies to the nuclear energy. Chemical energy is gained and lost all the time. But the inevitable entropy from these changes is found in the state of aggregations of atoms, not in the individual atoms themselves. The latter can gain and lose chemical (electromagnetic) energy all the time without any wear. Even for 14 billion years of 'use'.
Atoms don't get 'used up', unless you do nuclear fission. Fusion is different, it combines atoms.
Non excited atoms are in their ground state, unless their nuclei are unstable (e.g., radioactive Uranium, or Plutonium, or Tritium). They can't really lose more energy. Think of throwing a grain of sand into space. It isn't going to deteriorate either, unless it just gets hit by a cosmic ray which can happen sometimes.
Unless quite extreme amounts of energy are applied to an atom (i.e., in the core of a star or a supernova, or a hydrogen bomb, or impact from another high energy particle), it will stay the way it is effectively forever.
Excited atoms can change their chemical and electrical behavior temporarily, due to changes in their electron shells. But, these are generally temporary, and don't affect the inner atomic nuclei at all.
Most of the hydrogen that composes the water in your body, as well as much of the lithium in your cell phone's lithium ion batteries, was create a few minutes after the Big Bang, 13.8 billion years ago. Most of the rest of the atoms that are you and everything else you know were created over subsequent billions of years in a sequence of stars that formed, fused for millions or billions of years and exploded, sending their fused guts into space. Most of your atoms heavier than carbon were fused in a set of supernovae explosions a few tens to hundreds of millions before the formation of our solar system 4.6 billion years ago.
References:
Big Bang nucleosynthesisSolar SystemNebular hypothesisFormation and evolution of the Solar SystemInterestingly, the
Nebular hypothesis, that the solar system formed from a large interstellar gas cloud was first proposed by Immanuel Kant of all people in 1755 in his book
General History of Nature and Theory of the Heavens.
The 18th century was a pretty amazing time for theories about the solar system.
Short answer:
Energy is conserved, and (bio)chemical cycles don't cause any net change in the atoms themselves. The increase in
entropy over time involves the arrangement and energy distribution (mostly kinetic) of the atoms, and not any changes within the atoms themselves.
Long answer:
The atomic nucleus is pretty much indestructible by chemical processes, including the (bio)chemical processes of organisms. (It is possible to change a nucleus, but it takes a
lot of energy (e.g., particle accelerators, cosmic rays), more energy than nontechnological living things can manipulate.)
Now the electrons of the atom are another story: chemical and biochemical processes often involve transfer of electrons from one atom to another. But the electrons are all
identical, so if you lose an electron and gain one back later, you end up with an atom which is identical to what you started with.
Let's suppose a simplified biochemical cycle:
1. photosynthesis: 6 CO2 + 6 H2O > C6H12O6 + 6 O2.
2. respiration: C6H12O6 + 6 O2 > 6 CO2 + 6 H2O.
First, if you "follow" the nuclei in the reaction, nothing happens to them. Second, note that these two reactions are opposites. It follows from the
conservation of energy that the energy absorbed in photosynthesis is equal to the energy released in respiration. Third, there is a net increase in
entropy, but that does not involve the deterioration of the atoms involved. Remember, the atomic nuclei and the electrons are "indestructible". Instead, entropy has to do with the arrangement and energy distribution of the particles making up the universe. The net result of the cycle is that a few visiblelight photons are absorbed and that their energy is converted to kinetic energy of the atoms and perhaps a few lowerenergy infrared photons (both the kinetic energy and the infrared photons are colloquially considered to be heat energy).
I add one more thought. According to grand unification theories protons will decay, I think at a half life of E(32) (1 with 32 zeroes) years. Even stable isotopes will thus not be forever. But they decay is taking longer than the estimated age of the universe. Such reasoning would also be consistent with the 2nd law of thermodynamics that postulates an ever increasing entropy (I recognize that I mix a classical law of physics with a quantum effect).
Hats off to Joshua Engel, who, although not a physicist, did talk very nicely about this subject.
You wrote about atoms. The simplest atom is made up of a proton and electron. These have been found to be nondecaying. After extensive testing, no decay of the electron or proton has ever been documented and recorded. It is estimated they live over 10^42 years. A neutron does decay when alone (15 seconds is the halflife), but does not appear to decay when in a nucleus with a proton following the QCD (quantum chromodynamics, see Wikipedia link below) model. So stable isotopes of atoms do not decay.
"It doesn't take any energy for an atom to sit there being an atom." An atom is... So, what is this chemistry? Chemistry is the study of the reactions of different atoms exchanging different electron configurations. The
nucleus is unaffected by chemical reactions. The elementary particle of the
electron is unaffected by chemical reactions, but the electrons' quantum states (ie, clouds) are changed when an atom undergoes a chemical reaction.
What drives chemical reactions, this continually changing flux of electron clouds and quantum states? The driver of chemical reactions is the need for atoms to find a state of low energy, specifically low Gibbs energy, in its localized space. So, a low Gibbs energy may occur on the inside of a living cell (allowing the reaction to occur) and, on the outside of the cell, the Gibbs energy would higher, preventing the reaction to occur. The endless supply of energy needed to power life (these localized areas of differing Gibbs energy states, the driver of life's activities) is ultimately provided by the sun.
I hope that helps.
Wikipedia:
Quantum chromodynamics
Joshua Engel, gave a really good answer. The best way that I came up to think about this is to write 1. That 1 will forever be a one. It doesn't lose anything to go to 0. It doesn't gain anything to go to 2.
We can do many things to that 1. Add 5 to it to make 6. then multiply to make 36. Square root to get +/ 6.That 1 can be part of = anything you like. It won't change in the same way that an atom does't change.
Atoms do acquire energy by being bombarded by photon which kick the electrons up into a more energetic orbit. Later on the electrons decline to lower energy orbits giving up photons to keep "the books balanced".
So the energy of atoms is variable, but the ground state or lowest energy state is constant over time.
Energy can't be destroyed. Mass is energy (E=mc2), protons and neutrons have mass.
In a nuclear reactor, atoms are smashed apart to form two smaller atoms (fission). The cumulative mass of these two atoms is slightly less than the original atom, releasing an enormous amount of energy in the form of electromagnetic radiation. This heats water into steam, which spins a turbine, which rotates magnets and induces electricity into wire.
Physics 101, my friend. Energy is neither created, nor destroyed. Every single joule of energy that you have used, are using, or will ever use has been here since the time of the BigBang. It just keeps changing form  from thermal to mechanical and there onwards to electrical in power plants; from chemical in gunpowder, to the light, heat and sound of the explosion  the total energy of the universe, including the energy that keeps atoms going, has been constant since the beginning of time,
Atoms don't consume energy. Just like every process or object in the world, they merely convert it,
Momentum, inertia, gravity and entropy are the four fundamental "forces" that enliven all atomic matter. The so called "Big Bang" happened 13.8 billion years ago, and it was so energetic that it is still unfolding to this day and will do so for about another estimated
googol years before it finally runs out of steam. (See:
Heat death of the universe)
Its simple, energy can neither be created nor be destroyed, but only can be transformed from one form to another.
That's why atoms still have energy.
61915 J_Paradigm extends Einstein's definitions to include the J_Wave J_ Mechanizes needed to facilitate those definitions. J_WaveJ_SpiralJ_String 2 J_PlanckLength Diameter mutually pushes 2 similar bodies toward eachother in J_Gravity. J_Acceleration of a body's J_Strings pushes on the similar J_Strings of another with a force inversely proportional to the square of their distance. J_Inertia and J_Momentum of this body are similarly created. These similar effects take place in the acceleration of J_Gravity between 2 bodies.
The J_AetherJ_WaveJ_Spiral goes out from J_Atom's nucus through electron shells where once in a long while a J_Spiarl curls into an J_Electron orbit, while the other J_Spirals proceed on out forming a J_Quantum of space time J_WaveLength, J_PlanckLength.
62015 J_SpiralJ_tringsJ_Aether form a J_Unified J_Field throughout the J_Universe. In the case of J_GravityJ_Field J_MassJ_CrestJ_SpinJ_OuterJ_WaveJ_AetherJ_ForceJ_FieldJ_DarkJ_Energycreats. J_ElectronJ_SpiralJ_String after filling its orbit creates J_Electromagnetic J_Field in J_AetherJ_Field. Any change in J_Electron will to some degree effect another J_Electron in the J_Electromagnetic J_UnifiedJ_Field.This Phehysics label Entanglement.
62115 when a J_Quantum 137 J_WaveLengths in an inner shell of a J_Atom has an increase of another J_Quantum of J_WaveLength the nex outer J_ElectrunShell is moved to when ths J_Atom asorbs J_Photon 1 J_QuantumJ_WaveLengths required for this J_Shell No. 2. level. The reverse would be the case if a J_QuantumJ_Ph0ton was J_Radiated so onley the next inner J_Shell energy level was requirred. J_Radiated is the one of many J_Function of J_Field for J_ElectromagneticJ_UnifiedJ_FieilddJ_Funcnction. When the J_PhotonJ_Quantum of 137 J_WaveLengths of cumulative J_Mass moving at the speed of light impinges on another body of J_Atoms a J_Reaction will occur. The Quote sunlight J_MassJ_Photons J_Reaction J_Force on a solar sail is copied from above "exerts a force of 1–6 nPa (1–6×10−9 N/m2), on average." which is stronger than ordinary light J_Photons moving at the speed of light with a smaller term than ( 10^9 ) Like ( 10^<1010 ).
61715 Continued from My Email
EarthSky // Science Wire, Space Release Date: Jun 16, 2015
Astronomers see cavities – like giant bubbles – in hot gas around galaxy cluster NGC 5813, caused by multiple eruptions over millions of years of a black hole.
Chandra XRay Observatory image of the galaxy group NGC 5813.
NASA astronomers using the Chandra Xray Observatory probe have discovered a unique group of galaxies that appear to have undergone substantial restructuring due to multiple eruptions from a supermassive black hole. The eruptions took place over 50 million years, astronomers say. These eruptive bursts of energy caused shockwaves and pushed surrounding gas in the galaxy cluster away from the black hole’s center, causing visible cavities much like giant bubbles. Researchers were able to determine the length of the black hole’s eruption period by studying these cavities. The Astrophysical Journal published this study in its June, 2015 issue.
This galactic group, called NGC 5813, lies 105 million light years from Earth and is comprised of no more than 50 different galaxies all enveloped in large amounts of hot, Xray emitting gas.
The erupting supermassive black hole is located in the central galaxy of the group. According to a June 10 statement from the Chandra mission, the black hole’s spin, and the large amount of heated gas spiraling toward its center, cause:
… a rotating, tightly wound vertical tower of magnetic field that flings a large fraction of the inflowing gas away from the vicinity of the black hole in an energetic, highspeed jet.
NGC 5813 with location of cavities indicated. Image via NASA Chandra Observatory
Chandra’s most recent observations revealed a third pair of cavities, separate from the two that had previously been discovered in this group. The three cavities represent three distinct eruptions – the highest number ever observed in any galaxy group.
In order to discover more about the black hole’s volatile past, researchers focused on the appearance, energy, and location of the three cavity pairs. Surprisingly researchers determined that the energy required to create the cavities closest to the black hole’s center is lower than the energy required to make the older pair, which is further way from the center.
Researchers then determined that the rate of energy production from the supermassive black hole has remained constant, which indicates that the eruption associated with the inner cavities is actually still occurring.
Each of the three pairs of cavities is associated with a shock front, which is a visible sharp edge in the Xray image.
These shock fronts, similar to a sonic boom from a supersonic jet, heat the surrounding gas and prevent it from cooling and coalescing into new stars.
Closer scrutiny of the shock fronts revealed they are blurred and broad, rather than sharp. this blurriness is now believed to result from turbulence in the heated gas. With this new insight, researchers have found an average speed of the random motions of the gas in NGC 5813. This turbulent velocity was determined to be 160,000 miles per hour, which is consistent with predictions in theoretical models.
The Chandra observations of NGC 5813 are the longest ever obtained of any galaxy group, lasting over a week. These observations demonstrate the ongoing story of supermassive black holes.
Still much of a mystery, the galactic group NGC 5813 continues to reveal how these massive forces help shape the landscape of our universe.
NGC 5813 as seen in visible light. Image via NASA Chandra Observatory
Bottom line: NASA astronomers announced in June, 2015 that they used the Chandra XRay Observatory to discover cavities – like giant bubbles – in the hot gas inundating galaxy cluster NGC 5813. A supermassive black hole in a galaxy at the cluster’s core is thought to have made these cavities via multiple eruptions over 50 million years, which caused shockwaves and pushed surrounding gas outwar!
Via NASA
61715 Continued from Page Badquality Copied the above from EarthSky in my Email:
9815 Copy Quora Digest below:
Nathan Kane, I've spend 100's of hours taking and teaching the SAT/ACT and run a tutoring co.
17.7k Views
I think this is about the hardest SAT math question I've ever seen on the exam, partially because of it's just a tough problem and partially because it takes significantly longer than most (even challenging) questions.
Source: Official SAT Study Guide– sharing under fair use permissions (education) as per the Copyright Act of 1976.
Well... "energy cannot be created or destroyed" is a very naive way of expressing energy conservation (physicists will tell you that the naive concept of energy is not even relativistic as differen... (more)
Joshua Engel, not a physicist
The energy of splitting a single atom isn't that great. For a single uranium atom, you get about 10^11 Joules of energy. That's about a trillionth as much as that apple falling on your head.
Atom... (more)
Depends on what you mean by recent, and depends on what you mean by calculus. Typically, when saying 'calculus' mathematicians either mean something more fancy like the lambda calculus (which is ve... (more)
Energy is conserved whenever the equations describing the system are unchanging (invariant) under time translations. This is a consequence of Noether's theorem.
Most systems we usually deal with, ... (more)
Originally Answered: What is the theory of relativity?
Classical physics, built upon the work of people like Isaac Newton, seemed to cover all the bases for everyday life. But people like Einstein realized that it didn't work so well at the extremes –... (more)
After 15+ years as a Windows user, I purchased a Macbook Retina 15" about three months ago. After using it for the first couple of weeks, I asked myself this same question. I liked the Macbook bett... (more)
It's quite amazing, isn't it, that the rolling one circle around another circle turns turns the rolling two full turns.
You can check it yourself with two coins. Fix one, like the one with Lincol... (more)
Not overrated but oversold and misunderstood. People want to get into it because they see the results of the profession itself. Not many fields out there where you don't need a college degree to ... (more)
91715 I am going to give up on using Planck Length as J_WaveLength. See Spacetime Page:
Planck length
From Wikipedia, the free encyclopedia
(Redirected from Planck volume)
In physics, the Planck length, denoted ℓ_{P}, is a unit of length, equal to 1.616199(97)×10^{−35} metres. It is a base unit in the system of Planck units, developed by physicist Max Planck. The Planck length can be defined from three fundamental physical constants: the speed of light in a vacuum, the Planck constant, and the gravitational constant.
Value
The Planck length ℓ_{P} is defined as
where is the speed of light in a vacuum, G is the gravitational constant, and ħ is the reduced Planck constant. The two digits enclosed by parentheses are the estimated standard error associated with the reported numerical value.^{[1]}^{[2]}
The Planck length is about 10^{−20} times the diameter of a proton, and thus is exceedingly small.
Theoretical significance
There is currently no proven physical significance of the Planck length; it is, however, a topic of theoretical research. Since the Planck length is so many orders of magnitude smaller than any current instrument could possibly measure, there is no way of examining it directly. According to the generalized uncertainty principle (a concept from speculative models of quantum gravity), the Planck length is, in principle, within a factor of 10, the shortest measurable length – and no theoretically known improvement in measurement instruments could change that.^{[citation needed]}
In some forms of quantum gravity, the Planck length is the length scale at which the structure of spacetime becomes dominated by quantum effects, and it is impossible to determine the difference between two locations less than one Planck length apart. The precise effects of quantum gravity are unknown; it is often guessed that spacetime might have a discrete or foamy structure at a Planck length scale.^{[citation needed]}
The Planck area, equal to the square of the Planck length, plays a role in black hole entropy. The value of this entropy, in units of the Boltzmann constant, is known to be given by , where A is the area of the event horizon. The Planck area is the area by which the surface of a spherical black hole increases when the black hole swallows one bit of information, as was proven by Jacob Bekenstein.^{[3]}
If large extra dimensions exist, the measured strength of gravity may be much smaller than its true (smallscale) value. In this case the Planck length would have no fundamental physical significance, and quantum gravitational effects would appear at other scales.
In string theory, the Planck length is the order of magnitude of the oscillating strings that form elementary particles, and shorter lengths do not make physical sense.^{[4]} The string scale l_{s} is related to the Planck scale by ℓ_{P} = g_{s}^{1/4}l_{s}, where g_{s} is the string coupling constant. Contrary to what the name suggests, the string coupling constant is not constant, but depends on the value of a scalar field known as the dilaton.
In loop quantum gravity, area is quantized, and the Planck area is, within a factor of 10, the smallest possible area value.
In doubly special relativity, the Planck length is observerinvariant.
The search for the laws of physics valid at the Planck length is a part of the search for the theory of everything.^{[clarification needed]}
Visualization
The size of the Planck length can be visualized as follows: if a particle or dot about 0.1 mm in size (which is approximately the smallest the unaided human eye can see) were magnified in size to be as large as the observable universe, then inside that universesized "dot", the Planck length would be roughly the size of an actual 0.1 mm dot. In other words, a 0.1 mm dot is halfway between the Planck length and the size of the observable universe on a logarithmic scale.
See also
Notes and references
Bibliography
External links
[hide]




Base Planck units 


Derived Planck units 


92115 Copied from Today's My Email which I will put a copy here:

From Your Quora Digest •
Physics
String Theory: What is AdS/CFT?
Jared Kaplan, Professor of Physics at Johns Hopkins University, Ph.D. from Harvard University
2.4k Views • Upvoted by David SimmonsDuffin, Physicist • Vladimir Novakovski, US IPhO team 2001 • Frank Heile, PhD in Physics from Stanford University
I agree with what Jay Wacker said... but here's some of my own personal perspective.
First of all, the problems of Quantum Gravity are qualitatively different from those associated with the Standard Model of particle physics; the latter include the Hierarchy Problem, the nature of Dark Matter, Baryogenesis, the Strong CP Problem, Grand Unification, etc. With all of these questions the issue is to find a new description of nature at short(er) distances that explains some thusfar unexplained effect or parameter. I'd claim that we basically have the theoretical tools to do this already, in the form of quantum field theory (QFT)... in most cases the problem is that we do not have enough experimental data to distinguish between the various explanations that have already been put forward. In some (fewer) cases the theoretical calculations involved are hard enough that we can't get sufficient precision to test our theories.
However, with quantum gravity there can be no shorter distance description. Because of the uncertainty principle, to resolve shorter distances we must use higher and higher energies. If we try to continue this past the Planck scale (the characteristic lengthscale of quantum gravity), we start making black holes, and cranking up the energy further just leads to larger and larger black holes. The naive reductionist program ends at quantum gravity. There are many other reasons why this should be the case  the most famous is Black Hole thermodynamics, which also provides the useful hint that the fundamental degrees of freedom in gravity are associated with areas, not volumes. Other more technical reasoning leads to the expectation that gravity should emerge as the approximate description of an exact theory that lives at infinity, on the `boundary of spacetime'... and therefore has fewer dimensions. This is Holography.
AdS/CFT is a concrete, working realization of holography. It is the statement that any complete theory of quantum gravity in d+1 dimensional AntideSitter spacetime is identical to a CFT in d dimensions. This means that you can study (or even solve) quantum gravity by studying and solving CFTs. This is exciting because we know a lot of examples of CFTs... we even know algorithms that would allow us (in principle) to program a computer to calculate anything we want to know about the behavior of many CFTs.
Let's try to define some of these terms:
Quantum Gravity: By this I just mean any theory that reduces to classical General Relativity coupled to matter when you zoom out and look at it at large distances. By "matter" I mean stuff like the particles in the Standard Model, e.g. quarks, photons, the Higgs boson, etc.
AntideSitter Space: Imagine a universe like a trash compactor, with a force that's constantly squeezing everything together. That's (very roughly) AntideSitter space (AdS). This force means that AdS behaves like a cavity or a "box"... it allows us to put quantum gravity in a convenient box.
Conformal Field Theories (CFTs) are (roughly) quantum field theories that are scale invariant  they look the same when you zoom in and out. The strong force is described by a theory that's very similar to the sorts of CFTs that arise in the bestknown examples of AdS/CFT. It's worth noting that a contemporary understanding of fundamental physics suggests that all welldefined QFTs can be regarded as perturbations of CFTs. A major task for contemporary theoretical physicists is to understand the space of CFTs.
Written 8 Sep, 2013 • View Upvotes
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If the Higgs Boson is responsible for giving mass, then how is it, itself, massive?
4.3k Views • David has 210+ answers in Quantum Mechanics.
The Higgs boson gets its mass by the exact same process as all the other particles in the Standard Model: the Higgs mechanism.
The Higgs field couples to all fields in the standard model, and it also has a quartic selfcoupling which is unstable at a zero value of the Higgs field  so in the vacuum it takes on a nonzero expectation value. This expectation value breaks the SU(2)R×U(1)Y symmetry of the standard model which exists in the absence of a vacuum expectation value of the Higgs field. This is called spontaneous symmetry breaking. So the property of the Higgs field which makes it produce mass is that it has a symmetric potential, but its minimum allows for there to be an asymmetry in the vacuum state of the theory.
The observable Higgs boson is found by expanding the Higgs field around the nontrivial minimum of the Higgs potential. This gives a quadratic term with a positive definite mass squared for the Higgs boson.
The Goldstone modes of the Higgs field associated with the symmetric directions along the nontrivial minimum are absorbed into the gauge boson fields  which gives these just the right number of degrees of freedom to be massive vector bosons. The massive vector bosons are required to make the weak interactions work theoretically.
It is all very neat and tidy, but it does not explain the origin of mass: not really.
For that you need an explanation of the values of the couplings of the Higgs to all the other fields.
Now, if you are trying to suggest that the existence of the Higgs boson proves the existence of a deity or other supernatural force, then no: the theory doesn't allow for that interpretation.
Sorry.
Updated 24 May • View Upvotes • Asked to answer by Roosevelt Wallace
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#IStandWithAhmed (Sept 2015)
Why is Ahmed being offered internships by MIT, NASA, Twitter etc?
Stan Baranowski, Actor and director from New York City, now living and working in Richmond, Vi...
30k Views • Upvoted by Paul Alfred, Social Media Recruiter & Social Media Strategy Consultant w…
Put yourself in his shoes: you build a digital clock as a science project for school. Whether you built it from scratch or you used parts of another clock to do it doesn't matter. You proudly bring... (more)
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How many dimensions are there in our universe?
Barak Shoshany, Graduate Student at Perimeter Institute for Theoretical Physics
29.4k Views • Upvoted by Deep Sarkar, Ph.D. Research Scholar in Physics at TIFR
Barak has 38 endorsements in Physics.
Let us begin by defining what is meant by "dimension" when one says "our universe has n dimensions". The number of dimensions in spacetime is, roughly speaking, the number of coordinates required to... (more)
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A source of light in a closed room with spherical, perfectly reflecting wall all around was turned on for a while and then turned off. Will the light particles be continuously reflecting and would we be able to detect light for eternity?
Frank Heile, Physicist, SW Eng, Consciousness Theory
2.4k Views • Frank has 30+ answers in Speed of Light.
First of all, there is no such thing as a perfect mirror in the real world. For example, if the mirror reflected 99.9999% of the light that hit it and if your sphere had a diameter of 1000 meters,... (more)
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Once again, is the Universe young?
Joseph Wang, Ph.D. Astrophysics
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Yes the universe is quite young. It's only 13 billion years old, when we'd expect stars to last for another several trillion years. The sun is only a third generation star, which means that our u... (more)
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Hypothetical Scenarios
Why has nobody tried to dig a hole to the other side of the world? What would happen if this is done successfully?
Franklin Veaux, Decidedly nonhypothetical.
17.8k Views • Franklin has 370+ answers in Philosophy of Everyday Life.
The earth is not solid. It has a thin solid crust, under which is liquid magmasuperheated molten rock. Think of a volcano; that's what happens when you bore a hole through the crust.
Under thous... (more)
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Physics
For someone who has neither a physics nor math background, what sequence of books I would have to read to actually understand string theory?
Dan Piponi, PhD in Mathematics
21.5k Views • Upvoted by Inna Vishik, Postdoctoral fellow @ MIT physics department
Dan has 13 endorsements in Mathematics.
The specific choice of books doesn't really matter IMO and lecture notes may serve better than a book in many cases.
 A linear algebra course.
 An advanced calculus course including multivariate cal...
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Can a wavefunction spread faster than the speed of light?
David SimmonsDuffin, Physicist
3k Views • Upvoted by Hongwan Liu, FirstYear Graduate Student in Physics, MIT • Hadayat Seddiqi, quantum computing @ ORNL
David has 30+ answers in Quantum Mechanics.
Yes, a wavepacket spreads faster than the speed of light, even in QFT. This is actually a very familiar phenomenon that has nothing to do with quantum mechanics: with properly chosen initial condit... (more)
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 101015 Copied today’s Quora column from my email:

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101715 Copied from Quora:
(I don't know when the below was copied from Quora)
It is not true. It was an old law of science overturned by Einstein when he deduced E = mc^2.
Energy, if you include mass energy, can not be created or destroyed.
102815 Screen Shot from LEXE months ago:
This is actually backwards. Photons do not have mass, and sources emitting light do lose mass! However, I assume that situation would prompt a similar question, so here we go.
In the earlier days of special relativity, physicists used to talk about the mass of a particle "increasing" as its speed increased. There was nothing wrong with this convention / definition of "mass", but it wound up being inconvenient. So, being a humandefined term, the physics community decided to talk about it differently: "mass is mass," and it doesn't change depending on who's measuring it and from what reference frame.
Most people are familiar with the famous equation relating mass and energy, E=mc2, but fewer people actually understand what it means. In particular, it refers to the energy that a massive particle at rest has, just by virtue of its mass. A more complete and inclusive formula relating a particle's energy E, mass m, momentum p, and the speed of light c, is
E2=(mc2)2+(pc)2.
Note that, for a particle at rest, p=0, and we just get E=mc2. Also note that, for a massless particle (like a photon), you get E=pc.
So, what about the object giving off light? Consider the situation from a reference frame where the object starts at rest. It then gives off some light. That light has both energy and momentum, and so, by conservation of both, the object must have less energy, but must also have gained momentum (in the direction opposite the light). Looking back at
E2=(mc2)2+(pc)2,
this means the mass must have gone down! (However, the numbers here are generally very, very small.)
111915 The Mass of a Photon in relation to the above I will address Later
But I will now enter here the Email Quora Digest to me prior art most source:
Why did Einstein say 'Sometimes one pays most for the things one gets for nothing'?
Shockingly, the quote is actually authentic. And, as usual with authentic quotes, it's incredibly obvious when you add the context:
Some friends and admirers learned that he had decided to build a summer house with his hardearned savings. They offered him a princely gift of land. But Einstein shook his head. "No," he said; "I could accept a gift from a community. I cannot accept such a gift from an individual. Every gift we accept is a tie. Sometimes," he added with Talmudic wisdom, " one pays most for the thing one gets for nothing."
To put it even more obviously: you "pay the most" in the sense that an obligation you feel, but can't put a value or price on, can cause you to keep paying more than what any reasonable valuation might have been.
Source: Page on saturdayeveningpost.com
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Now as to the 102815 and 111915 inputs above I copy again: Richard Muller's:
"Most people are familiar with the famous equation relating mass and energy, E=mc2, but fewer people actually understand what it means. In particular, it refers to the energy that a massive particle at rest has, just by virtue of its mass. A more complete and inclusive formula relating a particle's energy E, mass m, momentum p, and the speed of light c, is
E2=(mc2)2+(pc)2.
Note that, for a particle at rest, p=0, and we just get E=mc2. Also note that, for a massless particle (like a photon), you get E=pc.
So, what about the object giving off light? Consider the situation from a reference frame where the object starts at rest. It then gives off some light. That light has both energy and momentum, and so, by conservation of both, the object must have less energy, but must also have gained momentum (in the direction opposite the light). Looking back at
E2=(mc2)2+(pc)2,
this means the mass must have gone down! (However, the numbers here are generally very, very small.)"
I will review J_PhotonJ_Mass in my Blog's Equations and Spacetime Pages and above.
On the above Top of this Page down to the two lines ____ over  pertaining to the Photons to be reviewed in relation to J_Photon.
112015 As I evaluate the J_PhotonJ_Mass relative to J_ElectronJ_Mass per 137 J_Waves. I will also evaluate the J_Cosmicneutrino J_Mass per 137 J_Waves of the J_Electron. The J_Mass of (One J_WaveLength is 6.64918460583942E033kg)
112115 Not finding Photon Mass review yet I go to the intrenet Physics Stack and copy:
Photon
Composition 
Elementary particle 
Statistics 
Bosonic 
Interactions 
Electromagnetic 
Symbol 
γ 
Theorized 
Albert Einstein 
Mass 
Photon From Wikipedia, the free encyclopedia This article is about the elementary particle of light. For other uses, see Photon (disambiguation). Photon Composition Elementary particle Statistics Bosonic Interactions Electromagnetic Symbol γ Theorized Albert Einstein Mass 0 <1×10−18 eV/c2[1] Mean lifetime Stable[1] Electric charge 0 <1×10−35 e[1] Spin 1 Parity −1[1] C parity −1[1] Condensed I(JPC)=0,1(1−−)[1]
A photon is an elementary particle, the quantum of light and all other forms of electromagnetic radiation. It is the force carrier for the electromagnetic force, even when static via virtual photons. The effects of this force are easily observable at the microscopic and at the macroscopic level, because the photon has zero rest mass; this allows long distance interactions. Like all elementary particles, photons are currently best explained by quantum mechanics and exhibit wave–particle duality, exhibiting properties of waves and of particles. For example, a single photon may be refracted by a lens or exhibit wave interference with itself, but also act as a particle giving a definite result when its position is measured. Waves and quanta, being two observable aspects of a single phenomenon cannot have their true nature described in terms of any mechanical model. [2] A representation of this dual property of light, which assumes certain points on the wave front to be the seat of the energy is also impossible. Thus, the quanta in a light wave cannot be spatially localized. Some defined physical parameters of a photon are listed.
The modern photon concept was developed gradually by Albert Einstein in the first years of the 20th century to explain experimental observations that did not fit the classical wave model of light. In particular, the photon model accounted for the frequency dependence of light's energy, and explained the ability of matter and radiation to be in thermal equilibrium. It also accounted for anomalous observations, including the properties of blackbody radiation, that other physicists, most notably Max Planck, had sought to explain using semiclassical models, in which light is still described by Maxwell's equations, but the material objects that emit and absorb light do so in amounts of energy that are quantized (i.e., they change energy only by certain particular discrete amounts and cannot change energy in any arbitrary way). Although these semiclassical models contributed to the development of quantum mechanics, many further experiments[3][4] starting with Compton scattering of single photons by electrons, first observed in 1923, validated Einstein's hypothesis that light itself is quantized. In 1926 the optical physicist Frithiof Wolfers and the chemist Gilbert N. Lewis coined the name photon for these particles, and after 1927, when Arthur H. Compton won the Nobel Prize for his scattering studies, most scientists accepted the validity that quanta of light have an independent existence, and the term photon for light quanta was accepted.
In the Standard Model of particle physics, photons and other elementary particles are described as a necessary consequence of physical laws having a certain symmetry at every point in spacetime. The intrinsic properties of particles, such as charge, mass and spin, are determined by the properties of this gauge symmetry. The photon concept has led to momentous advances in experimental and theoretical physics, such as lasers, Bose–Einstein condensation, quantum field theory, and the probabilistic interpretation of quantum mechanics. It has been applied to photochemistry, highresolution microscopy, and measurements of molecular distances. Recently, photons have been studied as elements of quantum computers and for applications in optical imaging and optical communication such as quantum cryptography.
Contents
1 Nomenclature 2 Physical properties 2.1 Experimental checks on photon mass 3 Historical development 4 Einstein's light quantum 5 Early objections 6 Wave–particle duality and uncertainty principles 7 Bose–Einstein model of a photon gas 8 Stimulated and spontaneous emission 9 Second quantization and high energy photon interactions 10 The hadronic properties of the photon 11 The photon as a gauge boson 12 Contributions to the mass of a system 13 Photons in matter 14 Technological applications 15 Recent research 16 See also 17 Notes 18 References 19 Additional references 20 External links
Nomenclature Standard Model of particle physics CERN LHC Tunnel1.jpg Large Hadron Collider tunnel at CERN Background [show] Constituents [show] Limitations [show] Scientists [show]
v t e
In 1900, the German physicist Max Planck was working on blackbody radiation and suggested that the energy in electromagnetic waves could only be released in "packets" of energy. In his 1901 article [5] in Annalen der Physik he called these packets "energy elements". The word quanta (singular quantum) was used even before 1900 to mean particles or amounts of different quantities, including electricity. Later, in 1905, Albert Einstein went further by suggesting that electromagnetic waves could only exist in these discrete wavepackets.[6] He called such a wavepacket the light quantum (German: das Lichtquant).[Note 1] The name photon derives from the Greek word for light, φῶς (transliterated phôs). Arthur Compton used photon in 1928, referring to Gilbert N. Lewis.[7] The same name was used earlier, by the American physicist and psychologist Leonard T. Troland, who coined the word in 1916, in 1921 by the Irish physicist John Joly, in 1924 by the French physiologist René Wurmser (18901993) and in 1926 by the French physicist Frithiof Wolfers (18911971).[8] The name was suggested initially as a unit related to the illumination of the eye and the resulting sensation of light and was used later on in a physiological context. Although Wolfers's and Lewis's theories were never accepted, as they were contradicted by many experiments, the new name was adopted very soon by most physicists after Compton used it.[8][Note 2]
In physics, a photon is usually denoted by the symbol γ (the Greek letter gamma). This symbol for the photon probably derives from gamma rays, which were discovered in 1900 by Paul Villard,[9][10] named by Ernest Rutherford in 1903, and shown to be a form of electromagnetic radiation in 1914 by Rutherford and Edward Andrade.[11] In chemistry and optical engineering, photons are usually symbolized by hν, the energy of a photon, where h is Planck's constant and the Greek letter ν (nu) is the photon's frequency. Much less commonly, the photon can be symbolized by hf, where its frequency is denoted by f. Physical properties See also: Special relativity and Photonic molecule The cone shows possible values of wave 4vector of a photon. The "time" axis gives the angular frequency (rad⋅s−1) and the "space" axes represent the angular wavenumber (rad⋅m−1). Green and indigo represent left and right polarization
A photon is massless,[Note 3] has no electric charge,[12] and is stable. A photon has two possible polarization states. In the momentum representation, which is preferred in quantum field theory, a photon is described by its wave vector, which determines its wavelength λ and its direction of propagation. A photon's wave vector may not be zero and can be represented either as a spatial 3vector or as a (relativistic) fourvector; in the latter case it belongs to the light cone (pictured). Different signs of the fourvector denote different circular polarizations, but in the 3vector representation one should account for the polarization state separately; it actually is a spin quantum number. In both cases the space of possible wave vectors is threedimensional.
The photon is the gauge boson for electromagnetism,[13]:2930 and therefore all other quantum numbers of the photon (such as lepton number, baryon number, and flavour quantum numbers) are zero.[14] Also, the photon does not obey the Pauli exclusion principle.[15]:1221
Photons are emitted in many natural processes. For example, when a charge is accelerated it emits synchrotron radiation. During a molecular, atomic or nuclear transition to a lower energy level, photons of various energy will be emitted, from radio waves to gamma rays. A photon can also be emitted when a particle and its corresponding antiparticle are annihilated (for example, electron–positron annihilation).[15]:572, 1114, 1172
In empty space, the photon moves at c (the speed of light) and its energy and momentum are related by E = pc, where p is the magnitude of the momentum vector p. This derives from the following relativistic relation, with m = 0:[16]
E^{2}=p^{2} c^{2} + m^{2} c^{4}.
The energy and momentum of a photon depend only on its frequency (ν) or inversely, its wavelength (λ):
E=\hbar\omega=h\nu=\frac{hc}{\lambda}
\boldsymbol{p}=\hbar\boldsymbol{k},
where k is the wave vector (where the wave number k = k = 2π/λ), ω = 2πν is the angular frequency, and ħ = h/2π is the reduced Planck constant.[17]
Since p points in the direction of the photon's propagation, the magnitude of the momentum is
p=\hbar k=\frac{h\nu}{c}=\frac{h}{\lambda}.
The photon also carries spin angular momentum that does not depend on its frequency.[18] The magnitude of its spin is \scriptstyle{\sqrt{2} \hbar} and the component measured along its direction of motion, its helicity, must be ±ħ. These two possible helicities, called righthanded and lefthanded, correspond to the two possible circular polarization states of the photon.[19]
To illustrate the significance of these formulae, the annihilation of a particle with its antiparticle in free space must result in the creation of at least two photons for the following reason. In the center of momentum frame, the colliding antiparticles have no net momentum, whereas a single photon always has momentum (since, as we have seen, it is determined by the photon's frequency or wavelength, which cannot be zero). Hence, conservation of momentum (or equivalently, translational invariance) requires that at least two photons are created, with zero net momentum. (However, it is possible if the system interacts with another particle or field for annihilation to produce one photon, as when a positron annihilates with a bound atomic electron, it is possible for only one photon to be emitted, as the nuclear Coulomb field breaks translational symmetry.)[20]:6465 The energy of the two photons, or, equivalently, their frequency, may be determined from conservation of fourmomentum. Seen another way, the photon can be considered as its own antiparticle. The reverse process, pair production, is the dominant mechanism by which highenergy photons such as gamma rays lose energy while passing through matter.[21] That process is the reverse of "annihilation to one photon" allowed in the electric field of an atomic nucleus.
The classical formulae for the energy and momentum of electromagnetic radiation can be reexpressed in terms of photon events. For example, the pressure of electromagnetic radiation on an object derives from the transfer of photon momentum per unit time and unit area to that object, since pressure is force per unit area and force is the change in momentum per unit time.[22] Experimental checks on photon mass
Current commonly accepted physical theories imply or assume the photon to be strictly massless. If the photon is not a strictly massless particle, it would not move at the exact speed of light in vacuum, c. Its speed would be lower and depend on its frequency. Relativity would be unaffected by this; the socalled speed of light, c, would then not be the actual speed at which light moves, but a constant of nature which is the maximum speed that any object could theoretically attain in spacetime.[23] Thus, it would still be the speed of spacetime ripples (gravitational waves and gravitons), but it would not be the speed of photons.
If a photon did have nonzero mass, there would be other effects as well. Coulomb's law would be modified and the electromagnetic field would have an extra physical degree of freedom. These effects yield more sensitive experimental probes of the photon mass than the frequency dependence of the speed of light. If Coulomb's law is not exactly valid, then that would cause the presence of an electric field inside a hollow conductor when it is subjected to an external electric field. This thus allows one to test Coulomb's law to very high precision.[24] A null result of such an experiment has set a limit of m ≲ 10−14 eV/c2.[25]
Sharper upper limits have been obtained in experiments designed to detect effects caused by the galactic vector potential. Although the galactic vector potential is very large because the galactic magnetic field exists on very long length scales, only the magnetic field is observable if the photon is massless. In case of a massive photon, the mass term \scriptstyle\frac{1}{2} m^2 A_{\mu}A^{\mu} would affect the galactic plasma. The fact that no such effects are seen implies an upper bound on the photon mass of m < 3×10−27 eV/c2.[26] The galactic vector potential can also be probed directly by measuring the torque exerted on a magnetized ring.[27] Such methods were used to obtain the sharper upper limit of 10−18eV/c2 (the equivalent of 1.07×10−27 atomic mass units) given by the Particle Data Group.[28]
These sharp limits from the nonobservation of the effects caused by the galactic vector potential have been shown to be model dependent.[29] If the photon mass is generated via the Higgs mechanism then the upper limit of m≲10−14 eV/c2 from the test of Coulomb's law is valid.
Photons inside superconductors do develop a nonzero effective rest mass; as a result, electromagnetic forces become shortrange inside superconductors.[30] See also: Supernova/Acceleration Probe Historical development Main article: Light Thomas Young's doubleslit experiment in 1801 showed that light can act as a wave, helping to invalidate early particle theories of light.[15]:964
In most theories up to the eighteenth century, light was pictured as being made up of particles. Since particle models cannot easily account for the refraction, diffraction and birefringence of light, wave theories of light were proposed by René Descartes (1637),[31] Robert Hooke (1665),[32] and Christiaan Huygens (1678);[33] however, particle models remained dominant, chiefly due to the influence of Isaac Newton.[34] In the early nineteenth century, Thomas Young and August Fresnel clearly demonstrated the interference and diffraction of light and by 1850 wave models were generally accepted.[35] In 1865, James Clerk Maxwell's prediction[36] that light was an electromagnetic wave—which was confirmed experimentally in 1888 by Heinrich Hertz's detection of radio waves[37]—seemed to be the final blow to particle models of light. In 1900, Maxwell's theoretical model of light as oscillating electric and magnetic fields seemed complete. However, several observations could not be explained by any wave model of electromagnetic radiation, leading to the idea that lightenergy was packaged into quanta described by E=hν. Later experiments showed that these lightquanta also carry momentum and, thus, can be considered particles: the photon concept was born, leading to a deeper understanding of the electric and magnetic fields themselves.
The Maxwell wave theory, however, does not account for all properties of light. The Maxwell theory predicts that the energy of a light wave depends only on its intensity, not on its frequency; nevertheless, several independent types of experiments show that the energy imparted by light to atoms depends only on the light's frequency, not on its intensity. For example, some chemical reactions are provoked only by light of frequency higher than a certain threshold; light of frequency lower than the threshold, no matter how intense, does not initiate the reaction. Similarly, electrons can be ejected from a metal plate by shining light of sufficiently high frequency on it (the photoelectric effect); the energy of the ejected electron is related only to the light's frequency, not to its intensity.[38][Note 4]
At the same time, investigations of blackbody radiation carried out over four decades (1860–1900) by various researchers[39] culminated in Max Planck's hypothesis[5][40] that the energy of any system that absorbs or emits electromagnetic radiation of frequency ν is an integer multiple of an energy quantum E = hν. As shown by Albert Einstein,[6][41] some form of energy quantization must be assumed to account for the thermal equilibrium observed between matter and electromagnetic radiation; for this explanation of the photoelectric effect, Einstein received the 1921 Nobel Prize in physics.[42]
Since the Maxwell theory of light allows for all possible energies of electromagnetic radiation, most physicists assumed initially that the energy quantization resulted from some unknown constraint on the matter that absorbs or emits the radiation. In 1905, Einstein was the first to propose that energy quantization was a property of electromagnetic radiation itself.[6] Although he accepted the validity of Maxwell's theory, Einstein pointed out that many anomalous experiments could be explained if the energy of a Maxwellian light wave were localized into pointlike quanta that move independently of one another, even if the wave itself is spread continuously over space.[6] In 1909[41] and 1916,[43] Einstein showed that, if Planck's law of blackbody radiation is accepted, the energy quanta must also carry momentum p = h/λ, making them fullfledged particles. This photon momentum was observed experimentally[44] by Arthur Compton, for which he received the Nobel Prize in 1927. The pivotal question was then: how to unify Maxwell's wave theory of light with its experimentally observed particle nature? The answer to this question occupied Albert Einstein for the rest of his life,[45] and was solved in quantum electrodynamics and its successor, the Standard Model (see Second quantization and The photon as a gauge boson, below). Einstein's light quantum
Unlike Planck, Einstein entertained the possibility that there might be actual physical quanta of light—what we now call photons. He noticed that a light quantum with energy proportional to its frequency would explain a number of troubling puzzles and paradoxes, including an unpublished law by Stokes, the ultraviolet catastrophe, and of course the photoelectric effect. Stokes's law said simply that the frequency of fluorescent light cannot be greater than the frequency of the light (usually ultraviolet) inducing it. Einstein eliminated the ultraviolet catastrophe by imagining a gas of photons behaving like a gas of electrons that he had previously considered. He was advised by a colleague to be careful how he wrote up this paper, in order to not challenge Planck too directly, as he was a powerful figure, and indeed the warning was justified, as Planck never forgave him for writing it.[46] Early objections Up to 1923, most physicists were reluctant to accept that light itself was quantized. Instead, they tried to explain photon behavior by quantizing only matter, as in the Bohr model of the hydrogen atom (shown here). Even though these semiclassical models were only a first approximation, they were accurate for simple systems and they led to quantum mechanics.
Einstein's 1905 predictions were verified experimentally in several ways in the first two decades of the 20th century, as recounted in Robert Millikan's Nobel lecture.[47] However, before Compton's experiment[44] showing that photons carried momentum proportional to their wave number (or frequency) (1922), most physicists were reluctant to believe that electromagnetic radiation itself might be particulate. (See, for example, the Nobel lectures of Wien,[39] Planck[40] and Millikan.[47]) Instead, there was a widespread belief that energy quantization resulted from some unknown constraint on the matter that absorbs or emits radiation. Attitudes changed over time. In part, the change can be traced to experiments such as Compton scattering, where it was much more difficult not to ascribe quantization to light itself to explain the observed results.[48]
Even after Compton's experiment, Niels Bohr, Hendrik Kramers and John Slater made one last attempt to preserve the Maxwellian continuous electromagnetic field model of light, the socalled BKS model.[49] To account for the data then available, two drastic hypotheses had to be made:
Energy and momentum are conserved only on the average in interactions between matter and radiation, not in elementary processes such as absorption and emission. This allows one to reconcile the discontinuously changing energy of the atom (jump between energy states) with the continuous release of energy into radiation. Causality is abandoned. For example, spontaneous emissions are merely emissions induced by a "virtual" electromagnetic field.
However, refined Compton experiments showed that energy–momentum is conserved extraordinarily well in elementary processes; and also that the jolting of the electron and the generation of a new photon in Compton scattering obey causality to within 10 ps. Accordingly, Bohr and his coworkers gave their model "as honorable a funeral as possible".[45] Nevertheless, the failures of the BKS model inspired Werner Heisenberg in his development of matrix mechanics.[50]
A few physicists persisted[51] in developing semiclassical models in which electromagnetic radiation is not quantized, but matter appears to obey the laws of quantum mechanics. Although the evidence for photons from chemical and physical experiments was overwhelming by the 1970s, this evidence could not be considered as absolutely definitive; since it relied on the interaction of light with matter, a sufficiently complicated theory of matter could in principle account for the evidence. Nevertheless, all semiclassical theories were refuted definitively in the 1970s and 1980s by photoncorrelation experiments.[Note 5] Hence, Einstein's hypothesis that quantization is a property of light itself is considered to be proven. Wave–particle duality and uncertainty principles See also: Wave–particle duality, Squeezed coherent state, Uncertainty principle and De Broglie–Bohm theory Photons in a Mach–Zehnder interferometer exhibit wavelike interference and particlelike detection at singlephoton detectors.
Photons, like all quantum objects, exhibit wavelike and particlelike properties. Their dual wave–particle nature can be difficult to visualize. The photon displays clearly wavelike phenomena such as diffraction and interference on the length scale of its wavelength. For example, a single photon passing through a doubleslit experiment lands on the screen exhibiting interference phenomena but only if no measure was made on the actual slit being run across. To account for the particle interpretation that phenomenon is called probability distribution but behaves according to Maxwell's equations.[52] However, experiments confirm that the photon is not a short pulse of electromagnetic radiation; it does not spread out as it propagates, nor does it divide when it encounters a beam splitter.[53] Rather, the photon seems to be a pointlike particle since it is absorbed or emitted as a whole by arbitrarily small systems, systems much smaller than its wavelength, such as an atomic nucleus (≈10−15 m across) or even the pointlike electron. Nevertheless, the photon is not a pointlike particle whose trajectory is shaped probabilistically by the electromagnetic field, as conceived by Einstein and others; that hypothesis was also refuted by the photoncorrelation experiments cited above. According to our present understanding, the electromagnetic field itself is produced by photons, which in turn result from a local gauge symmetry and the laws of quantum field theory (see the Second quantization and Gauge boson sections below). Heisenberg's thought experiment for locating an electron (shown in blue) with a highresolution gammaray microscope. The incoming gamma ray (shown in green) is scattered by the electron up into the microscope's aperture angle θ. The scattered gamma ray is shown in red. Classical optics shows that the electron position can be resolved only up to an uncertainty Δx that depends on θ and the wavelength λ of the incoming light.
A key element of quantum mechanics is Heisenberg's uncertainty principle, which forbids the simultaneous measurement of the position and momentum of a particle along the same direction. Remarkably, the uncertainty principle for charged, material particles requires the quantization of light into photons, and even the frequency dependence of the photon's energy and momentum. An elegant illustration is Heisenberg's thought experiment for locating an electron with an ideal microscope.[54] The position of the electron can be determined to within the resolving power of the microscope, which is given by a formula from classical optics
\Delta x \sim \frac{\lambda}{\sin \theta}
where \theta is the aperture angle of the microscope. Thus, the position uncertainty \Delta x can be made arbitrarily small by reducing the wavelength λ. The momentum of the electron is uncertain, since it received a "kick" \Delta p from the light scattering from it into the microscope. If light were not quantized into photons, the uncertainty \Delta p could be made arbitrarily small by reducing the light's intensity. In that case, since the wavelength and intensity of light can be varied independently, one could simultaneously determine the position and momentum to arbitrarily high accuracy, violating the uncertainty principle. By contrast, Einstein's formula for photon momentum preserves the uncertainty principle; since the photon is scattered anywhere within the aperture, the uncertainty of momentum transferred equals
\Delta p \sim p_{\text{photon}} \sin\theta=\frac{h}{\lambda} \sin\theta
giving the product \Delta x \Delta p \, \sim \, h, which is Heisenberg's uncertainty principle. Thus, the entire world is quantized; both matter and fields must obey a consistent set of quantum laws, if either one is to be quantized.[55]
The analogous uncertainty principle for photons forbids the simultaneous measurement of the number n of photons (see Fock state and the Second quantization section below) in an electromagnetic wave and the phase \phi of that wave
\Delta n \Delta \phi > 1
See coherent state and squeezed coherent state for more details.
Both (photons and material) particles such as electrons create analogous interference patterns when passing through a doubleslit experiment. For photons, this corresponds to the interference of a Maxwell light wave whereas, for material particles, this corresponds to the interference of the Schrödinger wave equation. Although this similarity might suggest that Maxwell's equations are simply Schrödinger's equation for photons, most physicists do not agree.[56][57] For one thing, they are mathematically different; most obviously, Schrödinger's one equation solves for a complex field, whereas Maxwell's four equations solve for real fields. More generally, the normal concept of a Schrödinger probability wave function cannot be applied to photons.[58] Being massless, they cannot be localized without being destroyed; technically, photons cannot have a position eigenstate \mathbf{r} \rangle, and, thus, the normal Heisenberg uncertainty principle \Delta x \Delta p > h/2 does not pertain to photons. A few substitute wave functions have been suggested for the photon,[59][60][61][62] but they have not come into general use. Instead, physicists generally accept the secondquantized theory of photons described below, quantum electrodynamics, in which photons are quantized excitations of electromagnetic modes.
Another interpretation, that avoids duality, is the De Broglie–Bohm theory: known also as the pilotwave model, the photon in this theory is both, wave and particle.[63] "This idea seems to me so natural and simple, to resolve the waveparticle dilemma in such a clear and ordinary way, that it is a great mystery to me that it was so generally ignored",[64] J.S.Bell. Bose–Einstein model of a photon gas Main articles: Bose gas, Bose–Einstein statistics, Spinstatistics theorem and Gas in a box
In 1924, Satyendra Nath Bose derived Planck's law of blackbody radiation without using any electromagnetism, but rather a modification of coarsegrained counting of phase space.[65] Einstein showed that this modification is equivalent to assuming that photons are rigorously identical and that it implied a "mysterious nonlocal interaction",[66][67] now understood as the requirement for a symmetric quantum mechanical state. This work led to the concept of coherent states and the development of the laser. In the same papers, Einstein extended Bose's formalism to material particles (bosons) and predicted that they would condense into their lowest quantum state at low enough temperatures; this Bose–Einstein condensation was observed experimentally in 1995.[68] It was later used by Lene Hau to slow, and then completely stop, light in 1999[69] and 2001.[70]
The modern view on this is that photons are, by virtue of their integer spin, bosons (as opposed to fermions with halfinteger spin). By the spinstatistics theorem, all bosons obey Bose–Einstein statistics (whereas all fermions obey Fermi–Dirac statistics).[71] Stimulated and spontaneous emission Main articles: Stimulated emission and Laser Stimulated emission (in which photons "clone" themselves) was predicted by Einstein in his kinetic analysis, and led to the development of the laser. Einstein's derivation inspired further developments in the quantum treatment of light, which led to the statistical interpretation of quantum mechanics.
In 1916, Einstein showed that Planck's radiation law could be derived from a semiclassical, statistical treatment of photons and atoms, which implies a relation between the rates at which atoms emit and absorb photons. The condition follows from the assumption that light is emitted and absorbed by atoms independently, and that the thermal equilibrium is preserved by interaction with atoms. Consider a cavity in thermal equilibrium and filled with electromagnetic radiation and atoms that can emit and absorb that radiation. Thermal equilibrium requires that the energy density \rho(\nu) of photons with frequency \nu (which is proportional to their number density) is, on average, constant in time; hence, the rate at which photons of any particular frequency are emitted must equal the rate of absorbing them.[72]
Einstein began by postulating simple proportionality relations for the different reaction rates involved. In his model, the rate R_{ji} for a system to absorb a photon of frequency \nu and transition from a lower energy E_{j} to a higher energy E_{i} is proportional to the number N_{j} of atoms with energy E_{j} and to the energy density \rho(\nu) of ambient photons with that frequency,
R_{ji}=N_{j} B_{ji} \rho(\nu) \!
where B_{ji} is the rate constant for absorption. For the reverse process, there are two possibilities: spontaneous emission of a photon, and a return to the lowerenergy state that is initiated by the interaction with a passing photon. Following Einstein's approach, the corresponding rate R_{ij} for the emission of photons of frequency \nu and transition from a higher energy E_{i} to a lower energy E_{j} is
R_{ij}=N_{i} A_{ij} + N_{i} B_{ij} \rho(\nu) \!
where A_{ij} is the rate constant for emitting a photon spontaneously, and B_{ij} is the rate constant for emitting it in response to ambient photons (induced or stimulated emission). In thermodynamic equilibrium, the number of atoms in state i and that of atoms in state j must, on average, be constant; hence, the rates R_{ji} and R_{ij} must be equal. Also, by arguments analogous to the derivation of Boltzmann statistics, the ratio of N_{i} and N_{j} is g_i/g_j\exp{(E_jE_i)/kT)}, where g_{i,j} are the degeneracy of the state i and that of j, respectively, E_{i,j} their energies, k the Boltzmann constant and T the system's temperature. From this, it is readily derived that g_iB_{ij}=g_jB_{ji} and
A_{ij}=\frac{8 \pi h \nu^{3}}{c^{3}} B_{ij}.
The A and Bs are collectively known as the Einstein coefficients.[73]
Einstein could not fully justify his rate equations, but claimed that it should be possible to calculate the coefficients A_{ij}, B_{ji} and B_{ij} once physicists had obtained "mechanics and electrodynamics modified to accommodate the quantum hypothesis".[74] In fact, in 1926, Paul Dirac derived the B_{ij} rate constants in using a semiclassical approach,[75] and, in 1927, succeeded in deriving all the rate constants from first principles within the framework of quantum theory.[76][77] Dirac's work was the foundation of quantum electrodynamics, i.e., the quantization of the electromagnetic field itself. Dirac's approach is also called second quantization or quantum field theory;[78][79][80] earlier quantum mechanical treatments only treat material particles as quantum mechanical, not the electromagnetic field.
Einstein was troubled by the fact that his theory seemed incomplete, since it did not determine the direction of a spontaneously emitted photon. A probabilistic nature of lightparticle motion was first considered by Newton in his treatment of birefringence and, more generally, of the splitting of light beams at interfaces into a transmitted beam and a reflected beam. Newton hypothesized that hidden variables in the light particle determined which path it would follow.[34] Similarly, Einstein hoped for a more complete theory that would leave nothing to chance, beginning his separation[45] from quantum mechanics. Ironically, Max Born's probabilistic interpretation of the wave function[81][82] was inspired by Einstein's later work searching for a more complete theory.[83] Second quantization and high energy photon interactions Main article: Quantum field theory Different electromagnetic modes (such as those depicted here) can be treated as independent simple harmonic oscillators. A photon corresponds to a unit of energy E=hν in its electromagnetic mode.
In 1910, Peter Debye derived Planck's law of blackbody radiation from a relatively simple assumption.[84] He correctly decomposed the electromagnetic field in a cavity into its Fourier modes, and assumed that the energy in any mode was an integer multiple of h\nu, where \nu is the frequency of the electromagnetic mode. Planck's law of blackbody radiation follows immediately as a geometric sum. However, Debye's approach failed to give the correct formula for the energy fluctuations of blackbody radiation, which were derived by Einstein in 1909.[41]
In 1925, Born, Heisenberg and Jordan reinterpreted Debye's concept in a key way.[85] As may be shown classically, the Fourier modes of the electromagnetic field—a complete set of electromagnetic plane waves indexed by their wave vector k and polarization state—are equivalent to a set of uncoupled simple harmonic oscillators. Treated quantum mechanically, the energy levels of such oscillators are known to be E=nh\nu, where \nu is the oscillator frequency. The key new step was to identify an electromagnetic mode with energy E=nh\nu as a state with n photons, each of energy h\nu. This approach gives the correct energy fluctuation formula. In quantum field theory, the probability of an event is computed by summing the probability amplitude (a complex number) for all possible ways in which the event can occur, as in the Feynman diagram shown here; the probability equals the square of the modulus of the total amplitude.
Dirac took this one step further.[76][77] He treated the interaction between a charge and an electromagnetic field as a small perturbation that induces transitions in the photon states, changing the numbers of photons in the modes, while conserving energy and momentum overall. Dirac was able to derive Einstein's A_{ij} and B_{ij} coefficients from first principles, and showed that the Bose–Einstein statistics of photons is a natural consequence of quantizing the electromagnetic field correctly (Bose's reasoning went in the opposite direction; he derived Planck's law of blackbody radiation by assuming B–E statistics). In Dirac's time, it was not yet known that all bosons, including photons, must obey Bose–Einstein statistics.
Dirac's secondorder perturbation theory can involve virtual photons, transient intermediate states of the electromagnetic field; the static electric and magnetic interactions are mediated by such virtual photons. In such quantum field theories, the probability amplitude of observable events is calculated by summing over all possible intermediate steps, even ones that are unphysical; hence, virtual photons are not constrained to satisfy E=pc, and may have extra polarization states; depending on the gauge used, virtual photons may have three or four polarization states, instead of the two states of real photons. Although these transient virtual photons can never be observed, they contribute measurably to the probabilities of observable events. Indeed, such secondorder and higherorder perturbation calculations can give apparently infinite contributions to the sum. Such unphysical results are corrected for using the technique of renormalization.
Other virtual particles may contribute to the summation as well; for example, two photons may interact indirectly through virtual electron–positron pairs.[86] In fact, such photonphoton scattering (see twophoton physics), as well as electronphoton scattering, is meant to be one of the modes of operations of the planned particle accelerator, the International Linear Collider.[87]
In modern physics notation, the quantum state of the electromagnetic field is written as a Fock state, a tensor product of the states for each electromagnetic mode
n_{k_0}\rangle\otimesn_{k_1}\rangle\otimes\dots\otimesn_{k_n}\rangle\dots
where n_{k_i}\rangle represents the state in which \, n_{k_i} photons are in the mode k_i. In this notation, the creation of a new photon in mode k_i (e.g., emitted from an atomic transition) is written as n_{k_i}\rangle \rightarrown_{k_i}+1\rangle. This notation merely expresses the concept of Born, Heisenberg and Jordan described above, and does not add any physics. The hadronic properties of the photon
Measurements of the interaction between energetic photons and hadrons show that the interaction is much more intense than expected by the interaction of merely photons with the hadron's electric charge. Furthermore, the interaction of energetic photons with protons is similar to the interaction of photons with neutrons[88] in spite of the fact that the electric charge structures of protons and neutrons are substantially different.
A theory called Vector Meson Dominance (VMD) was developed to explain this effect. According to VMD, the photon is a superposition of the pure electromagnetic photon (which interacts only with electric charges) and vector meson.[89]
However, if experimentally probed at very short distances, the intrinsic structure of the photon is recognized as a flux of quark and gluon components, quasifree according to asymptotic freedom in QCD and described by the photon structure function.[90][91] A comprehensive comparison of data with theoretical predictions is presented in a recent review.[92] The photon as a gauge boson Main article: Gauge theory
The electromagnetic field can be understood as a gauge field, i.e., as a field that results from requiring that a gauge symmetry holds independently at every position in spacetime.[93] For the electromagnetic field, this gauge symmetry is the Abelian U(1) symmetry of complex numbers of absolute value 1, which reflects the ability to vary the phase of a complex number without affecting observables or real valued functions made from it, such as the energy or the Lagrangian.
The quanta of an Abelian gauge field must be massless, uncharged bosons, as long as the symmetry is not broken; hence, the photon is predicted to be massless, and to have zero electric charge and integer spin. The particular form of the electromagnetic interaction specifies that the photon must have spin ±1; thus, its helicity must be \pm \hbar. These two spin components correspond to the classical concepts of righthanded and lefthanded circularly polarized light. However, the transient virtual photons of quantum electrodynamics may also adopt unphysical polarization states.[93]
In the prevailing Standard Model of physics, the photon is one of four gauge bosons in the electroweak interaction; the other three are denoted W+, W− and Z0 and are responsible for the weak interaction. Unlike the photon, these gauge bosons have mass, owing to a mechanism that breaks their SU(2) gauge symmetry. The unification of the photon with W and Z gauge bosons in the electroweak interaction was accomplished by Sheldon Glashow, Abdus Salam and Steven Weinberg, for which they were awarded the 1979 Nobel Prize in physics.[94][95][96] Physicists continue to hypothesize grand unified theories that connect these four gauge bosons with the eight gluon gauge bosons of quantum chromodynamics; however, key predictions of these theories, such as proton decay, have not been observed experimentally.[97] Contributions to the mass of a system See also: Mass in special relativity and General relativity
The energy of a system that emits a photon is decreased by the energy E of the photon as measured in the rest frame of the emitting system, which may result in a reduction in mass in the amount {E}/{c^2}. Similarly, the mass of a system that absorbs a photon is increased by a corresponding amount. As an application, the energy balance of nuclear reactions involving photons is commonly written in terms of the masses of the nuclei involved, and terms of the form {E}/{c^2} for the gamma photons (and for other relevant energies, such as the recoil energy of nuclei).[98]
This concept is applied in key predictions of quantum electrodynamics (QED, see above). In that theory, the mass of electrons (or, more generally, leptons) is modified by including the mass contributions of virtual photons, in a technique known as renormalization. Such "radiative corrections" contribute to a number of predictions of QED, such as the magnetic dipole moment of leptons, the Lamb shift, and the hyperfine structure of bound lepton pairs, such as muonium and positronium.[99]
Since photons contribute to the stress–energy tensor, they exert a gravitational attraction on other objects, according to the theory of general relativity. Conversely, photons are themselves affected by gravity; their normally straight trajectories may be bent by warped spacetime, as in gravitational lensing, and their frequencies may be lowered by moving to a higher gravitational potential, as in the Pound–Rebka experiment. However, these effects are not specific to photons; exactly the same effects would be predicted for classical electromagnetic waves.[100] Photons in matter See also: Group velocity and Photochemistry
Any 'explanation' of how photons travel through matter has to explain why different arrangements of matter are transparent or opaque at different wavelengths (light through carbon as diamond or not, as graphite) and why individual photons behave in the same way as large groups. Explanations that invoke 'absorption' and 'reemission' have to provide an explanation for the directionality of the photons (diffraction, reflection) and further explain how entangled photon pairs can travel through matter without their quantum state collapsing.
The simplest explanation is that light that travels through transparent matter does so at a lower speed than c, the speed of light in a vacuum. In addition, light can also undergo scattering and absorption. There are circumstances in which heat transfer through a material is mostly radiative, involving emission and absorption of photons within it. An example would be in the core of the Sun. Energy can take about a million years to reach the surface.[101] However, this phenomenon is distinct from scattered radiation passing diffusely through matter, as it involves local equilibrium between the radiation and the temperature. Thus, the time is how long it takes the energy to be transferred, not the photons themselves. Once in open space, a photon from the Sun takes only 8.3 minutes to reach Earth. The factor by which the speed of light is decreased in a material is called the refractive index of the material. In a classical wave picture, the slowing can be explained by the light inducing electric polarization in the matter, the polarized matter radiating new light, and the new light interfering with the original light wave to form a delayed wave. In a particle picture, the slowing can instead be described as a blending of the photon with quantum excitation of the matter (quasiparticles such as phonons and excitons) to form a polariton; this polariton has a nonzero effective mass, which means that it cannot travel at c.
Alternatively, photons may be viewed as always traveling at c, even in matter, but they have their phase shifted (delayed or advanced) upon interaction with atomic scatters: this modifies their wavelength and momentum, but not speed.[102] A light wave made up of these photons does travel slower than the speed of light. In this view the photons are "bare", and are scattered and phase shifted, while in the view of the preceding paragraph the photons are "dressed" by their interaction with matter, and move without scattering or phase shifting, but at a lower speed.
Light of different frequencies may travel through matter at different speeds; this is called dispersion. In some cases, it can result in extremely slow speeds of light in matter. The effects of photon interactions with other quasiparticles may be observed directly in Raman scattering and Brillouin scattering.[103]
Photons can also be absorbed by nuclei, atoms or molecules, provoking transitions between their energy levels. A classic example is the molecular transition of retinal C20H28O, which is responsible for vision, as discovered in 1958 by Nobel laureate biochemist George Wald and coworkers. The absorption provokes a cistrans isomerization that, in combination with other such transitions, is transduced into nerve impulses. The absorption of photons can even break chemical bonds, as in the photodissociation of chlorine; this is the subject of photochemistry.[104][105] Analogously, gamma rays can in some circumstances dissociate atomic nuclei in a process called photodisintegration. Technological applications
Photons have many applications in technology. These examples are chosen to illustrate applications of photons per se, rather than general optical devices such as lenses, etc. that could operate under a classical theory of light. The laser is an extremely important application and is discussed above under stimulated emission.
Individual photons can be detected by several methods. The classic photomultiplier tube exploits the photoelectric effect: a photon landing on a metal plate ejects an electron, initiating an everamplifying avalanche of electrons. Chargecoupled device chips use a similar effect in semiconductors: an incident photon generates a charge on a microscopic capacitor that can be detected. Other detectors such as Geiger counters use the ability of photons to ionize gas molecules, causing a detectable change in conductivity.[106]
Planck's energy formula E=h\nu is often used by engineers and chemists in design, both to compute the change in energy resulting from a photon absorption and to predict the frequency of the light emitted for a given energy transition. For example, the emission spectrum of a gasdischarge lamp can be altered by filling it with (mixtures of) gasses with different electronic energy level configurations.
Under some conditions, an energy transition can be excited by "two" photons that individually would be insufficient. This allows for higher resolution microscopy, because the sample absorbs energy only in the region where two beams of different colors overlap significantly, which can be made much smaller than the excitation volume of a single beam (see twophoton excitation microscopy). Moreover, these photons cause less damage to the sample, since they are of lower energy.[107]
In some cases, two energy transitions can be coupled so that, as one system absorbs a photon, another nearby system "steals" its energy and reemits a photon of a different frequency. This is the basis of fluorescence resonance energy transfer, a technique that is used in molecular biology to study the interaction of suitable proteins.[108]
Several different kinds of hardware random number generator involve the detection of single photons. In one example, for each bit in the random sequence that is to be produced, a photon is sent to a beamsplitter. In such a situation, there are two possible outcomes of equal probability. The actual outcome is used to determine whether the next bit in the sequence is "0" or "1".[109][110] Recent research See also: Quantum optics
Much research has been devoted to applications of photons in the field of quantum optics. Photons seem wellsuited to be elements of an extremely fast quantum computer, and the quantum entanglement of photons is a focus of research. Nonlinear optical processes are another active research area, with topics such as twophoton absorption, selfphase modulation, modulational instability and optical parametric oscillators. However, such processes generally do not require the assumption of photons per se; they may often be modeled by treating atoms as nonlinear oscillators. The nonlinear process of spontaneous parametric down conversion is often used to produce singlephoton states. Finally, photons are essential in some aspects of optical communication, especially for quantum cryptography.[Note 6] See also Portal icon Physics portal
Advanced Photon Source at Argonne National Laboratory Ballistic photon Doppler shift Electromagnetic radiation HEXITEC Laser Light Luminiferous aether Medipix Phonons Photon counting Photon energy Photon polarization Photonic molecule Photography Photonics Quantum optics Single photon sources Static forces and virtualparticle exchange Twophoton physics EPR paradox Dirac equation
Notes
Although the 1967 Elsevier translation of Planck's Nobel Lecture interprets Planck's Lichtquant as "photon", the more literal 1922 translation by Hans Thacher Clarke and Ludwik Silberstein The origin and development of the quantum theory, The Clarendon Press, 1922 (here [1]) uses "lightquantum". No evidence is known that Planck himself used the term "photon" by 1926 (see also this note). Isaac Asimov credits Arthur Compton with defining quanta of energy as photons in 1923. Asimov, I. (1966). The Neutrino, Ghost Particle of the Atom. Garden City (NY): Doubleday. ISBN 0380004836. LCCN 66017073. and Asimov, I. (1966). The Universe From Flat Earth To Quasar. New York (NY): Walker. ISBN 080270316X. LCCN 66022515. The mass of the photon is believed to be exactly zero, based on experiment and theoretical considerations described in the article. Some sources also refer to the relativistic mass concept, which is just the energy scaled to units of mass. For a photon with wavelength λ or energy E, this is h/λc or E/c2. This usage for the term "mass" is no longer common in scientific literature. Further info: What is the mass of a photon? http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/photon_mass.html The phrase "no matter how intense" refers to intensities below approximately 1013 W/cm2 at which point perturbation theory begins to break down. In contrast, in the intense regime, which for visible light is above approximately 1014 W/cm2, the classical wave description correctly predicts the energy acquired by electrons, called ponderomotive energy. (See also: Boreham et al. (1996). "Photon density and the correspondence principle of electromagnetic interaction".) By comparison, sunlight is only about 0.1 W/cm2. These experiments produce results that cannot be explained by any classical theory of light, since they involve anticorrelations that result from the quantum measurement process. In 1974, the first such experiment was carried out by Clauser, who reported a violation of a classical Cauchy–Schwarz inequality. In 1977, Kimble et al. demonstrated an analogous antibunching effect of photons interacting with a beam splitter; this approach was simplified and sources of error eliminated in the photonanticorrelation experiment of Grangier et al. (1986). This work is reviewed and simplified further in Thorn et al. (2004). (These references are listed below under #Additional references.)
Introductorylevel material on the various subfields of quantum optics can be found in Fox, M. (2006). Quantum Optics: An Introduction. Oxford University Press. ISBN 0198566735.
References
Amsler, C. (Particle Data Group); Amsler; Doser; Antonelli; Asner; Babu; Baer; Band; Barnett; Bergren; Beringer; Bernardi; Bertl; Bichsel; Biebel; Bloch; Blucher; Blusk; Cahn; Carena; Caso; Ceccucci; Chakraborty; Chen; Chivukula; Cowan; Dahl; d'Ambrosio; Damour; et al. (2008). "Review of Particle Physics: Gauge and Higgs bosons" (PDF). Physics Letters B 667: 1. Bibcode:2008PhLB..667....1P. doi:10.1016/j.physletb.2008.07.018. Joos, George (1951). Theoretical Physics. London and Glasgow: Blackie and Son Limited. p. 679. Kimble, H.J.; Dagenais, M.; Mandel, L.; Dagenais; Mandel (1977). "Photon Antibunching in Resonance Fluorescence". Physical Review Letters 39 (11): 691–695. Bibcode:1977PhRvL..39..691K. doi:10.1103/PhysRevLett.39.691. Grangier, P.; Roger, G.; Aspect, A.; Roger; Aspect (1986). "Experimental Evidence for a Photon Anticorrelation Effect on a Beam Splitter: A New Light on SinglePhoton Interferences". Europhysics Letters 1 (4): 173–179. Bibcode:1986EL......1..173G. doi:10.1209/02955075/1/4/004. Planck, M. (1901). "Über das Gesetz der Energieverteilung im Normalspectrum". Annalen der Physik (in German) 4 (3): 553–563. Bibcode:1901AnP...309..553P. doi:10.1002/andp.19013090310. English translation Einstein, A. (1905). "Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt" (PDF). Annalen der Physik (in German) 17 (6): 132–148. Bibcode:1905AnP...322..132E. doi:10.1002/andp.19053220607.. An English translation is available from Wikisource. "Discordances entre l'expérience et la théorie électromagnétique du rayonnement." In Électrons et Photons. Rapports et Discussions de Cinquième Conseil de Physique, edited by Institut International de Physique Solvay. Paris: GauthierVillars, pp. 5585. Helge Kragh: Photon: New light on an old name. Arxiv, 2014228 Villard, P. (1900). "Sur la réflexion et la réfraction des rayons cathodiques et des rayons déviables du radium". Comptes Rendus des Séances de l'Académie des Sciences (in French) 130: 1010–1012. Villard, P. (1900). "Sur le rayonnement du radium". Comptes Rendus des Séances de l'Académie des Sciences (in French) 130: 1178–1179. Rutherford, E.; Andrade, E.N.C. (1914). "The Wavelength of the Soft Gamma Rays from Radium B". Philosophical Magazine 27 (161): 854–868. doi:10.1080/14786440508635156. Kobychev, V.V.; Popov, S.B. (2005). "Constraints on the photon charge from observations of extragalactic sources". Astronomy Letters 31 (3): 147–151. arXiv:hepph/0411398. Bibcode:2005AstL...31..147K. doi:10.1134/1.1883345. Role as gauge boson and polarization section 5.1 inAitchison, I.J.R.; Hey, A.J.G. (1993). Gauge Theories in Particle Physics. IOP Publishing. ISBN 0852743289. See p.31 inAmsler, C.; et al. (2008). "Review of Particle Physics". Physics Letters B 667: 1–1340. Bibcode:2008PhLB..667....1P. doi:10.1016/j.physletb.2008.07.018. Halliday, David; Resnick, Robert; Walker, Jerl (2005), Fundamental of Physics (7th ed.), USA: John Wiley and Sons, Inc., ISBN 0471232319 See section 1.6 in Alonso, M.; Finn, E.J. (1968). Fundamental University Physics Volume III: Quantum and Statistical Physics. AddisonWesley. ISBN 0201002620. Davison E. Soper, Electromagnetic radiation is made of photons, Institute of Theoretical Science, University of Oregon This property was experimentally verified by Raman and Bhagavantam in 1931: Raman, C.V.; Bhagavantam, S. (1931). "Experimental proof of the spin of the photon" (PDF). Indian Journal of Physics 6: 353. Burgess, C.; Moore, G. (2007). "1.3.3.2". The Standard Model. A Primer. Cambridge University Press. ISBN 0521860369. Griffiths, David J. (2008), Introduction to Elementary Particles (2nd revised ed.), WILEYVCH, ISBN 9783527406012 E.g., section 9.3 in Alonso, M.; Finn, E.J. (1968). Fundamental University Physics Volume III: Quantum and Statistical Physics. AddisonWesley. E.g., Appendix XXXII in Born, M. (1962). Atomic Physics. Blackie & Son. ISBN 0486659844. Mermin, David (February 1984). "Relativity without light". American Journal of Physics 52 (2): 119–124. Bibcode:1984AmJPh..52..119M. doi:10.1119/1.13917. Plimpton, S.; Lawton, W. (1936). "A Very Accurate Test of Coulomb's Law of Force Between Charges". Physical Review 50 (11): 1066. Bibcode:1936PhRv...50.1066P. doi:10.1103/PhysRev.50.1066. Williams, E.; Faller, J.; Hill, H. (1971). "New Experimental Test of Coulomb's Law: A Laboratory Upper Limit on the Photon Rest Mass". Physical Review Letters 26 (12): 721. Bibcode:1971PhRvL..26..721W. doi:10.1103/PhysRevLett.26.721. Chibisov, G V (1976). "Astrophysical upper limits on the photon rest mass". Soviet Physics Uspekhi 19 (7): 624. Bibcode:1976SvPhU..19..624C. doi:10.1070/PU1976v019n07ABEH005277. Lakes, Roderic (1998). "Experimental Limits on the Photon Mass and Cosmic Magnetic Vector Potential". Physical Review Letters 80 (9): 1826. Bibcode:1998PhRvL..80.1826L. doi:10.1103/PhysRevLett.80.1826. Amsler, C; Doser, M; Antonelli, M; Asner, D; Babu, K; Baer, H; Band, H; Barnett, R; et al. (2008). "Review of Particle Physics⁎". Physics Letters B 667: 1. Bibcode:2008PhLB..667....1P. doi:10.1016/j.physletb.2008.07.018. Summary Table Adelberger, Eric; Dvali, Gia; Gruzinov, Andrei (2007). "PhotonMass Bound Destroyed by Vortices". Physical Review Letters 98 (1): 010402. arXiv:hepph/0306245. Bibcode:2007PhRvL..98a0402A. doi:10.1103/PhysRevLett.98.010402. PMID 17358459. preprint Wilczek, Frank (2010). The Lightness of Being: Mass, Ether, and the Unification of Forces. Basic Books. p. 212. ISBN 9780465018956. Descartes, R. (1637). Discours de la méthode (Discourse on Method) (in French). Imprimerie de Ian Maire. ISBN 0268008701. Hooke, R. (1667). Micrographia: or some physiological descriptions of minute bodies made by magnifying glasses with observations and inquiries thereupon ... London (UK): Royal Society of London. ISBN 0486495647. Huygens, C. (1678). Traité de la lumière (in French).. An English translation is available from Project Gutenberg Newton, I. (1952) [1730]. Opticks (4th ed.). Dover (NY): Dover Publications. Book II, Part III, Propositions XII–XX; Queries 25–29. ISBN 0486602052. Buchwald, J.Z. (1989). The Rise of the Wave Theory of Light: Optical Theory and Experiment in the Early Nineteenth Century. University of Chicago Press. ISBN 0226078868. OCLC 18069573. Maxwell, J.C. (1865). "A Dynamical Theory of the Electromagnetic Field". Philosophical Transactions of the Royal Society 155: 459–512. Bibcode:1865RSPT..155..459C. doi:10.1098/rstl.1865.0008. This article followed a presentation by Maxwell on 8 December 1864 to the Royal Society. Hertz, H. (1888). "Über Strahlen elektrischer Kraft". Sitzungsberichte der Preussischen Akademie der Wissenschaften (Berlin) (in German) 1888: 1297–1307. Frequencydependence of luminiscence p. 276f., photoelectric effect section 1.4 in Alonso, M.; Finn, E.J. (1968). Fundamental University Physics Volume III: Quantum and Statistical Physics. AddisonWesley. ISBN 0201002620. Wien, W. (1911). "Wilhelm Wien Nobel Lecture". Planck, M. (1920). "Max Planck's Nobel Lecture". Einstein, A. (1909). "Über die Entwicklung unserer Anschauungen über das Wesen und die Konstitution der Strahlung" (PDF). Physikalische Zeitschrift (in German) 10: 817–825.. An English translation is available from Wikisource. Presentation speech by Svante Arrhenius for the 1921 Nobel Prize in Physics, December 10, 1922. Online text from [nobelprize.org], The Nobel Foundation 2008. Access date 20081205. Einstein, A. (1916). "Zur Quantentheorie der Strahlung". Mitteilungen der Physikalischen Gesellschaft zu Zürich 16: 47. Also Physikalische Zeitschrift, 18, 121–128 (1917). (German) Compton, A. (1923). "A Quantum Theory of the Scattering of Xrays by Light Elements". Physical Review 21 (5): 483–502. Bibcode:1923PhRv...21..483C. doi:10.1103/PhysRev.21.483. Pais, A. (1982). Subtle is the Lord: The Science and the Life of Albert Einstein. Oxford University Press. ISBN 019853907X. Einstein and the Quantum: The Quest of the Valiant Swabian, A. Douglas Stone, Princeton University Press, 2013. Millikan, R.A (1924). "Robert A. Millikan's Nobel Lecture". Hendry, J. (1980). "The development of attitudes to the waveparticle duality of light and quantum theory, 1900–1920". Annals of Science 37 (1): 59–79. doi:10.1080/00033798000200121. Bohr, N.; Kramers, H.A.; Slater, J.C. (1924). "The Quantum Theory of Radiation". Philosophical Magazine 47: 785–802. doi:10.1080/14786442408565262. Also Zeitschrift für Physik, 24, 69 (1924). Heisenberg, W. (1933). "Heisenberg Nobel lecture". Mandel, L. (1976). E. Wolf, ed. "The case for and against semiclassical radiation theory". Progress in Optics. Progress in Optics (NorthHolland) 13: 27–69. doi:10.1016/S00796638(08)700180. ISBN 9780444108067. Taylor, G.I. (1909). Interference fringes with feeble light. Proceedings of the Cambridge Philosophical Society 15: 114–115. Saleh, B. E. A. and Teich, M. C. (2007). Fundamentals of Photonics. Wiley. ISBN 0471358320. Heisenberg, W. (1927). "Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik". Zeitschrift für Physik (in German) 43 (3–4): 172–198. Bibcode:1927ZPhy...43..172H. doi:10.1007/BF01397280. E.g., p. 10f. in Schiff, L.I. (1968). Quantum Mechanics (3rd ed.). McGrawHill. ASIN B001B3MINM. ISBN 0070552878. Kramers, H.A. (1958). Quantum Mechanics. Amsterdam: NorthHolland. ASIN B0006AUW5C. ISBN 0486495337. Bohm, D. (1989) [1954]. Quantum Theory. Dover Publications. ISBN 0486659690. Newton, T.D.; Wigner, E.P. (1949). "Localized states for elementary particles". Reviews of Modern Physics 21 (3): 400–406. Bibcode:1949RvMP...21..400N. doi:10.1103/RevModPhys.21.400. BialynickiBirula, I. (1994). "On the wave function of the photon" (PDF). Acta Physica Polonica A 86: 97–116. Sipe, J.E. (1995). "Photon wave functions". Physical Review A 52 (3): 1875–1883. Bibcode:1995PhRvA..52.1875S. doi:10.1103/PhysRevA.52.1875. BialynickiBirula, I. (1996). "Photon wave function". Progress in Optics. Progress in Optics 36: 245–294. doi:10.1016/S00796638(08)703160. ISBN 9780444825308. Scully, M.O.; Zubairy, M.S. (1997). Quantum Optics. Cambridge (UK): Cambridge University Press. ISBN 0521435951. The best illustration is the Couder experiment, demonstrating the behaviour of a mechanical analog, see https://www.youtube.com/watch?v=W9yWv5dqSKk Bell, J. S., "Speakable and Unspeakable in Quantum Mechanics", Cambridge: Cambridge University Press, 1987. Bose, S.N. (1924). "Plancks Gesetz und Lichtquantenhypothese". Zeitschrift für Physik (in German) 26: 178–181. Bibcode:1924ZPhy...26..178B. doi:10.1007/BF01327326. Einstein, A. (1924). "Quantentheorie des einatomigen idealen Gases". Sitzungsberichte der Preussischen Akademie der Wissenschaften (Berlin), Physikalischmathematische Klasse (in German) 1924: 261–267. Einstein, A. (1925). "Quantentheorie des einatomigen idealen Gases, Zweite Abhandlung". Sitzungsberichte der Preussischen Akademie der Wissenschaften (Berlin), Physikalischmathematische Klasse (in German) 1925: 3–14. doi:10.1002/3527608958.ch28. ISBN 9783527608959. Anderson, M.H.; Ensher, J.R.; Matthews, M.R.; Wieman, C.E.; Cornell, E.A. (1995). "Observation of Bose–Einstein Condensation in a Dilute Atomic Vapor". Science 269 (5221): 198–201. Bibcode:1995Sci...269..198A. doi:10.1126/science.269.5221.198. JSTOR 2888436. PMID 17789847. "Physicists Slow Speed of Light". News.harvard.edu (19990218). Retrieved on 20150511. "Light Changed to Matter, Then Stopped and Moved". photonics.com (February 2007). Retrieved on 20150511. Streater, R.F.; Wightman, A.S. (1989). PCT, Spin and Statistics, and All That. AddisonWesley. ISBN 020109410X. Einstein, A. (1916). "Strahlungsemission und absorption nach der Quantentheorie". Verhandlungen der Deutschen Physikalischen Gesellschaft (in German) 18: 318–323. Bibcode:1916DPhyG..18..318E. Section 1.4 in Wilson, J.; Hawkes, F.J.B. (1987). Lasers: Principles and Applications. New York: Prentice Hall. ISBN 013523705X. P. 322 in Einstein, A. (1916). "Strahlungsemission und absorption nach der Quantentheorie". Verhandlungen der Deutschen Physikalischen Gesellschaft (in German) 18: 318–323. Bibcode:1916DPhyG..18..318E.:
Die Konstanten A^n_m and B^n_m würden sich direkt berechnen lassen, wenn wir im Besitz einer im Sinne der Quantenhypothese modifizierten Elektrodynamik und Mechanik wären."
Dirac, P.A.M. (1926). "On the Theory of Quantum Mechanics". Proceedings of the Royal Society A 112 (762): 661–677. Bibcode:1926RSPSA.112..661D. doi:10.1098/rspa.1926.0133. Dirac, P.A.M. (1927). "The Quantum Theory of the Emission and Absorption of Radiation" (PDF). Proceedings of the Royal Society A 114 (767): 243–265. Bibcode:1927RSPSA.114..243D. doi:10.1098/rspa.1927.0039. Dirac, P.A.M. (1927b). The Quantum Theory of Dispersion. Proceedings of the Royal Society A 114: 710–728. doi:10.1098/rspa.1927.0071. Heisenberg, W.; Pauli, W. (1929). "Zur Quantentheorie der Wellenfelder". Zeitschrift für Physik (in German) 56: 1. Bibcode:1929ZPhy...56....1H. doi:10.1007/BF01340129. Heisenberg, W.; Pauli, W. (1930). "Zur Quantentheorie der Wellenfelder". Zeitschrift für Physik (in German) 59 (3–4): 139. Bibcode:1930ZPhy...59..168H. doi:10.1007/BF01341423. Fermi, E. (1932). "Quantum Theory of Radiation" (PDF). Reviews of Modern Physics 4: 87. Bibcode:1932RvMP....4...87F. doi:10.1103/RevModPhys.4.87. Born, M. (1926). "Zur Quantenmechanik der Stossvorgänge" (PDF). Zeitschrift für Physik (in German) 37 (12): 863–867. Bibcode:1926ZPhy...37..863B. doi:10.1007/BF01397477. Born, M. (1926). "Quantenmechanik der Stossvorgänge". Zeitschrift für Physik (in German) 38 (11–12): 803. Bibcode:1926ZPhy...38..803B. doi:10.1007/BF01397184. Pais, A. (1986). Inward Bound: Of Matter and Forces in the Physical World. Oxford University Press. p. 260. ISBN 0198519974. Specifically, Born claimed to have been inspired by Einstein's neverpublished attempts to develop a "ghostfield" theory, in which pointlike photons are guided probabilistically by ghost fields that follow Maxwell's equations. Debye, P. (1910). "Der Wahrscheinlichkeitsbegriff in der Theorie der Strahlung". Annalen der Physik (in German) 33 (16): 1427–1434. Bibcode:1910AnP...338.1427D. doi:10.1002/andp.19103381617. Born, M.; Heisenberg, W.; Jordan, P. (1925). "Quantenmechanik II". Zeitschrift für Physik (in German) 35 (8–9): 557–615. Bibcode:1926ZPhy...35..557B. doi:10.1007/BF01379806. Photonphotonscattering section 731, renormalization chapter 82 in Itzykson, C.; Zuber, J.B. (1980). Quantum Field Theory. McGrawHill. ISBN 0070320713. Weiglein, G. (2008). "Electroweak Physics at the ILC". Journal of Physics: Conference Series 110 (4): 042033. arXiv:0711.3003. Bibcode:2008JPhCS.110d2033W. doi:10.1088/17426596/110/4/042033. Bauer, T. H.; Spital, R. D.; Yennie, D. R.; Pipkin, F. M. (1978). "The hadronic properties of the photon in highenergy interactions". Reviews of Modern Physics 50 (2): 261. Bibcode:1978RvMP...50..261B. doi:10.1103/RevModPhys.50.261. Sakurai, J. J. (1960). "Theory of strong interactions". Annals of Physics 11: 1. Bibcode:1960AnPhy..11....1S. doi:10.1016/00034916(60)901263. Walsh, T. F.; Zerwas, P. (1973). "Twophoton processes in the parton model". Physics Letters B 44 (2): 195. Bibcode:1973PhLB...44..195W. doi:10.1016/03702693(73)905200. Witten, E. (1977). "Anomalous cross section for photonphoton scattering in gauge theories". Nuclear Physics B 120 (2): 189. Bibcode:1977NuPhB.120..189W. doi:10.1016/05503213(77)900384. Nisius, R. (2000). "The photon structure from deep inelastic electron–photon scattering". Physics Reports 332 (4–6): 165. Bibcode:2000PhR...332..165N. doi:10.1016/S03701573(99)001155. Ryder, L.H. (1996). Quantum field theory (2nd ed.). Cambridge University Press. ISBN 0521478146. Sheldon Glashow Nobel lecture, delivered 8 December 1979. Abdus Salam Nobel lecture, delivered 8 December 1979. Steven Weinberg Nobel lecture, delivered 8 December 1979. E.g., chapter 14 in Hughes, I. S. (1985). Elementary particles (2nd ed.). Cambridge University Press. ISBN 0521260922. E.g., section 10.1 in Dunlap, R.A. (2004). An Introduction to the Physics of Nuclei and Particles. Brooks/Cole. ISBN 0534392946. Radiative correction to electron mass section 712, anomalous magnetic moments section 721, Lamb shift section 732 and hyperfine splitting in positronium section 103 in Itzykson, C.; Zuber, J.B. (1980). Quantum Field Theory. McGrawHill. ISBN 0070320713. E. g. sections 9.1 (gravitational contribution of photons) and 10.5 (influence of gravity on light) in Stephani, H.; Stewart, J. (1990). General Relativity: An Introduction to the Theory of Gravitational Field. Cambridge University Press. pp. 86 ff, 108 ff. ISBN 0521379415. Naeye, R. (1998). Through the Eyes of Hubble: Birth, Life and Violent Death of Stars. CRC Press. ISBN 0750304847. OCLC 40180195. Ch 4 in Hecht, Eugene (2001). Optics. Addison Wesley. ISBN 9780805385663. Polaritons section 10.10.1, Raman and Brillouin scattering section 10.11.3 in Patterson, J.D.; Bailey, B.C. (2007). SolidState Physics: Introduction to the Theory. Springer. pp. 569 ff, 580 ff. ISBN 3540241159. E.g., section 115 C in Pine, S.H.; Hendrickson, J.B.; Cram, D.J.; Hammond, G.S. (1980). Organic Chemistry (4th ed.). McGrawHill. ISBN 0070501157. Nobel lecture given by G. Wald on December 12, 1967, online at nobelprize.org: The Molecular Basis of Visual Excitation. Photomultiplier section 1.1.10, CCDs section 1.1.8, Geiger counters section 1.3.2.1 in Kitchin, C.R. (2008). Astrophysical Techniques. Boca Raton (FL): CRC Press. ISBN 1420082434. Denk, W.; Svoboda, K. (1997). "Photon upmanship: Why multiphoton imaging is more than a gimmick". Neuron 18 (3): 351–357. doi:10.1016/S08966273(00)812374. PMID 9115730. Lakowicz, J.R. (2006). Principles of Fluorescence Spectroscopy. Springer. pp. 529 ff. ISBN 0387312781. Jennewein, T.; Achleitner, U.; Weihs, G.; Weinfurter, H.; Zeilinger, A. (2000). "A fast and compact quantum random number generator". Review of Scientific Instruments 71 (4): 1675–1680. arXiv:quantph/9912118. Bibcode:2000RScI...71.1675J. doi:10.1063/1.1150518.
Stefanov, A.; Gisin, N.; Guinnard, O.; Guinnard, L.; Zbiden, H. (2000). "Optical quantum random number generator". Journal of Modern Optics 47 (4): 595–598. doi:10.1080/095003400147908.
Additional references
By date of publication:
Clauser, J.F. (1974). "Experimental distinction between the quantum and classical fieldtheoretic predictions for the photoelectric effect". Physical Review D 9 (4): 853–860. Bibcode:1974PhRvD...9..853C. doi:10.1103/PhysRevD.9.853. Kimble, H.J.; Dagenais, M.; Mandel, L. (1977). "Photon Antibunching in Resonance Fluorescence". Physical Review Letters 39 (11): 691–695. Bibcode:1977PhRvL..39..691K. doi:10.1103/PhysRevLett.39.691. Pais, A. (1982). Subtle is the Lord: The Science and the Life of Albert Einstein. Oxford University Press. Feynman, Richard (1985). QED: The Strange Theory of Light and Matter. Princeton University Press. ISBN 9780691125756. Grangier, P.; Roger, G.; Aspect, A. (1986). "Experimental Evidence for a Photon Anticorrelation Effect on a Beam Splitter: A New Light on SinglePhoton Interferences". Europhysics Letters 1 (4): 173–179. Bibcode:1986EL......1..173G. doi:10.1209/02955075/1/4/004. Lamb, W.E. (1995). "Antiphoton". Applied Physics B 60 (2–3): 77–84. Bibcode:1995ApPhB..60...77L. doi:10.1007/BF01135846. Special supplemental issue of Optics and Photonics News (vol. 14, October 2003) article web link Roychoudhuri, C.; Rajarshi, R. (2003). "The nature of light: what is a photon?". Optics and Photonics News 14: S1 (Supplement). Zajonc, A. "Light reconsidered". Optics and Photonics News 14: S2–S5 (Supplement). Loudon, R. "What is a photon?". Optics and Photonics News 14: S6–S11 (Supplement). Finkelstein, D. "What is a photon?". Optics and Photonics News 14: S12–S17 (Supplement). Muthukrishnan, A.; Scully, M.O.; Zubairy, M.S. "The concept of the photon—revisited". Optics and Photonics News 14: S18–S27 (Supplement). Mack, H.; Schleich, W.P.. "A photon viewed from Wigner phase space". Optics and Photonics News 14: S28–S35 (Supplement). Glauber, R. (2005). "One Hundred Years of Light Quanta" (PDF). 2005 Physics Nobel Prize Lecture. Hentschel, K. (2007). "Light quanta: The maturing of a concept by the stepwise accretion of meaning". Physics and Philosophy 1 (2): 1–20.
Education with single photons:
Thorn, J.J.; Neel, M.S.; Donato, V.W.; Bergreen, G.S.; Davies, R.E.; Beck, M. (2004). "Observing the quantum behavior of light in an undergraduate laboratory" (PDF). American Journal of Physics 72 (9): 1210–1219. Bibcode:2004AmJPh..72.1210T. doi:10.1119/1.1737397. Bronner, P.; Strunz, Andreas; Silberhorn, Christine; Meyn, JanPeter (2009). "Interactive screen experiments with single photons". European Journal of Physics 30 (2): 345–353. Bibcode:2009EJPh...30..345B. doi:10.1088/01430807/30/2/014.
External links
The dictionary definition of photon at Wiktionary Media related to Photon at Wikimedia Commons
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Mean lifetime 
Stable^{[1]} 
Electric charge 
0 <1×10^{−35} e^{[1]} 
Spin 
1 
Parity 
−1^{[1]} 
C parity 
−1^{[1]} 
Condensed 
I(J^{PC})=0,1(1^{−−})^{[1]} 
112215 Copied from Wikipedia in the same area as above:
Photon
From Wikipedia, the free encyclopedia
This article is about the elementary particle of light. For other uses, see Photon (disambiguation).
Photon Composition Elementary particle
Statistics Bosonic
Interactions Electromagnetic
Symbol γ
Theorized Albert Einstein
Mass 0
<1×10−18 eV/c2[1]
Mean lifetime Stable[1]
Electric charge 0
<1×10−35 e[1]
Spin 1
Parity −1[1]
C parity −1[1]
Condensed I(JPC)=0,1(1−−)[1]
A photon is an elementary particle, the quantum of light and all other forms of electromagnetic radiation. It is the force carrier for the electromagnetic force, even when static via virtual photons. The effects of this force are easily observable at the microscopic and at the macroscopic level, because the photon has zero rest mass; this allows long distance interactions. Like all elementary particles, photons are currently best explained by quantum mechanics and exhibit wave–particle duality, exhibiting properties of waves and of particles. For example, a single photon may be refracted by a lens or exhibit wave interference with itself, but also act as a particle giving a definite result when its position is measured. Waves and quanta, being two observable aspects of a single phenomenon cannot have their true nature described in terms of any mechanical model. [2] A representation of this dual property of light, which assumes certain points on the wave front to be the seat of the energy is also impossible. Thus, the quanta in a light wave cannot be spatially localized. Some defined physical parameters of a photon are listed.
The modern photon concept was developed gradually by Albert Einstein in the first years of the 20th century to explain experimental observations that did not fit the classical wave model of light. In particular, the photon model accounted for the frequency dependence of light's energy, and explained the ability of matter and radiation to be in thermal equilibrium. It also accounted for anomalous observations, including the properties of blackbody radiation, that other physicists, most notably Max Planck, had sought to explain using semiclassical models, in which light is still described by Maxwell's equations, but the material objects that emit and absorb light do so in amounts of energy that are quantized (i.e., they change energy only by certain particular discrete amounts and cannot change energy in any arbitrary way). Although these semiclassical models contributed to the development of quantum mechanics, many further experiments[3][4] starting with Compton scattering of single photons by electrons, first observed in 1923, validated Einstein's hypothesis that light itself is quantized. In 1926 the optical physicist Frithiof Wolfers and the chemist Gilbert N. Lewis coined the name photon for these particles, and after 1927, when Arthur H. Compton won the Nobel Prize for his scattering studies, most scientists accepted the validity that quanta of light have an independent existence, and the term photon for light quanta was accepted.
In the Standard Model of particle physics, photons and other elementary particles are described as a necessary consequence of physical laws having a certain symmetry at every point in spacetime. The intrinsic properties of particles, such as charge, mass and spin, are determined by the properties of this gauge symmetry. The photon concept has led to momentous advances in experimental and theoretical physics, such as lasers, Bose–Einstein condensation, quantum field theory, and the probabilistic interpretation of quantum mechanics. It has been applied to photochemistry, highresolution microscopy, and measurements of molecular distances. Recently, photons have been studied as elements of quantum computers and for applications in optical imaging and optical communication such as quantum cryptography.
Contents
1 Nomenclature
2 Physical properties
2.1 Experimental checks on photon mass
3 Historical development
4 Einstein's light quantum
5 Early objections
6 Wave–particle duality and uncertainty principles
7 Bose–Einstein model of a photon gas
8 Stimulated and spontaneous emission
9 Second quantization and high energy photon interactions
10 The hadronic properties of the photon
11 The photon as a gauge boson
12 Contributions to the mass of a system
13 Photons in matter
14 Technological applications
15 Recent research
16 See also
17 Notes
18 References
19 Additional references
20 External links
Nomenclature
Standard Model of particle physics
CERN LHC Tunnel1.jpg
Large Hadron Collider tunnel at CERN
Background
[show]
Constituents
[show]
Limitations
[show]
Scientists
[show]
v t e
In 1900, the German physicist Max Planck was working on blackbody radiation and suggested that the energy in electromagnetic waves could only be released in "packets" of energy. In his 1901 article [5] in Annalen der Physik he called these packets "energy elements". The word quanta (singular quantum) was used even before 1900 to mean particles or amounts of different quantities, including electricity. Later, in 1905, Albert Einstein went further by suggesting that electromagnetic waves could only exist in these discrete wavepackets.[6] He called such a wavepacket the light quantum (German: das Lichtquant).[Note 1] The name photon derives from the Greek word for light, φῶς (transliterated phôs). Arthur Compton used photon in 1928, referring to Gilbert N. Lewis.[7] The same name was used earlier, by the American physicist and psychologist Leonard T. Troland, who coined the word in 1916, in 1921 by the Irish physicist John Joly, in 1924 by the French physiologist René Wurmser (18901993) and in 1926 by the French physicist Frithiof Wolfers (18911971).[8] The name was suggested initially as a unit related to the illumination of the eye and the resulting sensation of light and was used later on in a physiological context. Although Wolfers's and Lewis's theories were never accepted, as they were contradicted by many experiments, the new name was adopted very soon by most physicists after Compton used it.[8][Note 2]
In physics, a photon is usually denoted by the symbol γ (the Greek letter gamma). This symbol for the photon probably derives from gamma rays, which were discovered in 1900 by Paul Villard,[9][10] named by Ernest Rutherford in 1903, and shown to be a form of electromagnetic radiation in 1914 by Rutherford and Edward Andrade.[11] In chemistry and optical engineering, photons are usually symbolized by hν, the energy of a photon, where h is Planck's constant and the Greek letter ν (nu) is the photon's frequency. Much less commonly, the photon can be symbolized by hf, where its frequency is denoted by f.
Physical properties
See also: Special relativity and Photonic molecule
The cone shows possible values of wave 4vector of a photon. The "time" axis gives the angular frequency (rad⋅s−1) and the "space" axes represent the angular wavenumber (rad⋅m−1). Green and indigo represent left and right polarization
A photon is massless,[Note 3] has no electric charge,[12] and is stable. A photon has two possible polarization states. In the momentum representation, which is preferred in quantum field theory, a photon is described by its wave vector, which determines its wavelength λ and its direction of propagation. A photon's wave vector may not be zero and can be represented either as a spatial 3vector or as a (relativistic) fourvector; in the latter case it belongs to the light cone (pictured). Different signs of the fourvector denote different circular polarizations, but in the 3vector representation one should account for the polarization state separately; it actually is a spin quantum number. In both cases the space of possible wave vectors is threedimensional.
The photon is the gauge boson for electromagnetism,[13]:2930 and therefore all other quantum numbers of the photon (such as lepton number, baryon number, and flavour quantum numbers) are zero.[14] Also, the photon does not obey the Pauli exclusion principle.[15]:1221
Photons are emitted in many natural processes. For example, when a charge is accelerated it emits synchrotron radiation. During a molecular, atomic or nuclear transition to a lower energy level, photons of various energy will be emitted, from radio waves to gamma rays. A photon can also be emitted when a particle and its corresponding antiparticle are annihilated (for example, electron–positron annihilation).[15]:572, 1114, 1172
In empty space, the photon moves at c (the speed of light) and its energy and momentum are related by E = pc, where p is the magnitude of the momentum vector p. This derives from the following relativistic relation, with m = 0:[16]
E^{2}=p^{2} c^{2} + m^{2} c^{4}.
The energy and momentum of a photon depend only on its frequency (ν) or inversely, its wavelength (λ):
E=\hbar\omega=h\nu=\frac{hc}{\lambda}
\boldsymbol{p}=\hbar\boldsymbol{k},
where k is the wave vector (where the wave number k = k = 2π/λ), ω = 2πν is the angular frequency, and ħ = h/2π is the reduced Planck constant.[17]
Since p points in the direction of the photon's propagation, the magnitude of the momentum is
p=\hbar k=\frac{h\nu}{c}=\frac{h}{\lambda}.
The photon also carries spin angular momentum that does not depend on its frequency.[18] The magnitude of its spin is \scriptstyle{\sqrt{2} \hbar} and the component measured along its direction of motion, its helicity, must be ±ħ. These two possible helicities, called righthanded and lefthanded, correspond to the two possible circular polarization states of the photon.[19]
To illustrate the significance of these formulae, the annihilation of a particle with its antiparticle in free space must result in the creation of at least two photons for the following reason. In the center of momentum frame, the colliding antiparticles have no net momentum, whereas a single photon always has momentum (since, as we have seen, it is determined by the photon's frequency or wavelength, which cannot be zero). Hence, conservation of momentum (or equivalently, translational invariance) requires that at least two photons are created, with zero net momentum. (However, it is possible if the system interacts with another particle or field for annihilation to produce one photon, as when a positron annihilates with a bound atomic electron, it is possible for only one photon to be emitted, as the nuclear Coulomb field breaks translational symmetry.)[20]:6465 The energy of the two photons, or, equivalently, their frequency, may be determined from conservation of fourmomentum. Seen another way, the photon can be considered as its own antiparticle. The reverse process, pair production, is the dominant mechanism by which highenergy photons such as gamma rays lose energy while passing through matter.[21] That process is the reverse of "annihilation to one photon" allowed in the electric field of an atomic nucleus.
The classical formulae for the energy and momentum of electromagnetic radiation can be reexpressed in terms of photon events. For example, the pressure of electromagnetic radiation on an object derives from the transfer of photon momentum per unit time and unit area to that object, since pressure is force per unit area and force is the change in momentum per unit time.[22]
Experimental checks on photon mass
Current commonly accepted physical theories imply or assume the photon to be strictly massless. If the photon is not a strictly massless particle, it would not move at the exact speed of light in vacuum, c. Its speed would be lower and depend on its frequency. Relativity would be unaffected by this; the socalled speed of light, c, would then not be the actual speed at which light moves, but a constant of nature which is the maximum speed that any object could theoretically attain in spacetime.[23] Thus, it would still be the speed of spacetime ripples (gravitational waves and gravitons), but it would not be the speed of photons.
If a photon did have nonzero mass, there would be other effects as well. Coulomb's law would be modified and the electromagnetic field would have an extra physical degree of freedom. These effects yield more sensitive experimental probes of the photon mass than the frequency dependence of the speed of light. If Coulomb's law is not exactly valid, then that would cause the presence of an electric field inside a hollow conductor when it is subjected to an external electric field. This thus allows one to test Coulomb's law to very high precision.[24] A null result of such an experiment has set a limit of m ≲ 10−14 eV/c2.[25]
Sharper upper limits have been obtained in experiments designed to detect effects caused by the galactic vector potential. Although the galactic vector potential is very large because the galactic magnetic field exists on very long length scales, only the magnetic field is observable if the photon is massless. In case of a massive photon, the mass term \scriptstyle\frac{1}{2} m^2 A_{\mu}A^{\mu} would affect the galactic plasma. The fact that no such effects are seen implies an upper bound on the photon mass of m < 3×10−27 eV/c2.[26] The galactic vector potential can also be probed directly by measuring the torque exerted on a magnetized ring.[27] Such methods were used to obtain the sharper upper limit of 10−18eV/c2 (the equivalent of 1.07×10−27 atomic mass units) given by the Particle Data Group.[28]
These sharp limits from the nonobservation of the effects caused by the galactic vector potential have been shown to be model dependent.[29] If the photon mass is generated via the Higgs mechanism then the upper limit of m≲10−14 eV/c2 from the test of Coulomb's law is valid.
Photons inside superconductors do develop a nonzero effective rest mass; as a result, electromagnetic forces become shortrange inside superconductors.[30]
See also: Supernova/Acceleration Probe
Historical development
Main article: Light
Thomas Young's doubleslit experiment in 1801 showed that light can act as a wave, helping to invalidate early particle theories of light.[15]:964
In most theories up to the eighteenth century, light was pictured as being made up of particles. Since particle models cannot easily account for the refraction, diffraction and birefringence of light, wave theories of light were proposed by René Descartes (1637),[31] Robert Hooke (1665),[32] and Christiaan Huygens (1678);[33] however, particle models remained dominant, chiefly due to the influence of Isaac Newton.[34] In the early nineteenth century, Thomas Young and August Fresnel clearly demonstrated the interference and diffraction of light and by 1850 wave models were generally accepted.[35] In 1865, James Clerk Maxwell's prediction[36] that light was an electromagnetic wave—which was confirmed experimentally in 1888 by Heinrich Hertz's detection of radio waves[37]—seemed to be the final blow to particle models of light.
In 1900, Maxwell's theoretical model of light as oscillating electric and magnetic fields seemed complete. However, several observations could not be explained by any wave model of electromagnetic radiation, leading to the idea that lightenergy was packaged into quanta described by E=hν. Later experiments showed that these lightquanta also carry momentum and, thus, can be considered particles: the photon concept was born, leading to a deeper understanding of the electric and magnetic fields themselves.
The Maxwell wave theory, however, does not account for all properties of light. The Maxwell theory predicts that the energy of a light wave depends only on its intensity, not on its frequency; nevertheless, several independent types of experiments show that the energy imparted by light to atoms depends only on the light's frequency, not on its intensity. For example, some chemical reactions are provoked only by light of frequency higher than a certain threshold; light of frequency lower than the threshold, no matter how intense, does not initiate the reaction. Similarly, electrons can be ejected from a metal plate by shining light of sufficiently high frequency on it (the photoelectric effect); the energy of the ejected electron is related only to the light's frequency, not to its intensity.[38][Note 4]
At the same time, investigations of blackbody radiation carried out over four decades (1860–1900) by various researchers[39] culminated in Max Planck's hypothesis[5][40] that the energy of any system that absorbs or emits electromagnetic radiation of frequency ν is an integer multiple of an energy quantum E = hν. As shown by Albert Einstein,[6][41] some form of energy quantization must be assumed to account for the thermal equilibrium observed between matter and electromagnetic radiation; for this explanation of the photoelectric effect, Einstein received the 1921 Nobel Prize in physics.[42]
Since the Maxwell theory of light allows for all possible energies of electromagnetic radiation, most physicists assumed initially that the energy quantization resulted from some unknown constraint on the matter that absorbs or emits the radiation. In 1905, Einstein was the first to propose that energy quantization was a property of electromagnetic radiation itself.[6] Although he accepted the validity of Maxwell's theory, Einstein pointed out that many anomalous experiments could be explained if the energy of a Maxwellian light wave were localized into pointlike quanta that move independently of one another, even if the wave itself is spread continuously over space.[6] In 1909[41] and 1916,[43] Einstein showed that, if Planck's law of blackbody radiation is accepted, the energy quanta must also carry momentum p = h/λ, making them fullfledged particles. This photon momentum was observed experimentally[44] by Arthur Compton, for which he received the Nobel Prize in 1927. The pivotal question was then: how to unify Maxwell's wave theory of light with its experimentally observed particle nature? The answer to this question occupied Albert Einstein for the rest of his life,[45] and was solved in quantum electrodynamics and its successor, the Standard Model (see Second quantization and The photon as a gauge boson, below).
Einstein's light quantum
Unlike Planck, Einstein entertained the possibility that there might be actual physical quanta of light—what we now call photons. He noticed that a light quantum with energy proportional to its frequency would explain a number of troubling puzzles and paradoxes, including an unpublished law by Stokes, the ultraviolet catastrophe, and of course the photoelectric effect. Stokes's law said simply that the frequency of fluorescent light cannot be greater than the frequency of the light (usually ultraviolet) inducing it. Einstein eliminated the ultraviolet catastrophe by imagining a gas of photons behaving like a gas of electrons that he had previously considered. He was advised by a colleague to be careful how he wrote up this paper, in order to not challenge Planck too directly, as he was a powerful figure, and indeed the warning was justified, as Planck never forgave him for writing it.[46]
Early objections
Up to 1923, most physicists were reluctant to accept that light itself was quantized. Instead, they tried to explain photon behavior by quantizing only matter, as in the Bohr model of the hydrogen atom (shown here). Even though these semiclassical models were only a first approximation, they were accurate for simple systems and they led to quantum mechanics.
Einstein's 1905 predictions were verified experimentally in several ways in the first two decades of the 20th century, as recounted in Robert Millikan's Nobel lecture.[47] However, before Compton's experiment[44] showing that photons carried momentum proportional to their wave number (or frequency) (1922), most physicists were reluctant to believe that electromagnetic radiation itself might be particulate. (See, for example, the Nobel lectures of Wien,[39] Planck[40] and Millikan.[47]) Instead, there was a widespread belief that energy quantization resulted from some unknown constraint on the matter that absorbs or emits radiation. Attitudes changed over time. In part, the change can be traced to experiments such as Compton scattering, where it was much more difficult not to ascribe quantization to light itself to explain the observed results.[48]
Even after Compton's experiment, Niels Bohr, Hendrik Kramers and John Slater made one last attempt to preserve the Maxwellian continuous electromagnetic field model of light, the socalled BKS model.[49] To account for the data then available, two drastic hypotheses had to be made:
Energy and momentum are conserved only on the average in interactions between matter and radiation, not in elementary processes such as absorption and emission. This allows one to reconcile the discontinuously changing energy of the atom (jump between energy states) with the continuous release of energy into radiation.
Causality is abandoned. For example, spontaneous emissions are merely emissions induced by a "virtual" electromagnetic field.
However, refined Compton experiments showed that energy–momentum is conserved extraordinarily well in elementary processes; and also that the jolting of the electron and the generation of a new photon in Compton scattering obey causality to within 10 ps. Accordingly, Bohr and his coworkers gave their model "as honorable a funeral as possible".[45] Nevertheless, the failures of the BKS model inspired Werner Heisenberg in his development of matrix mechanics.[50]
A few physicists persisted[51] in developing semiclassical models in which electromagnetic radiation is not quantized, but matter appears to obey the laws of quantum mechanics. Although the evidence for photons from chemical and physical experiments was overwhelming by the 1970s, this evidence could not be considered as absolutely definitive; since it relied on the interaction of light with matter, a sufficiently complicated theory of matter could in principle account for the evidence. Nevertheless, all semiclassical theories were refuted definitively in the 1970s and 1980s by photoncorrelation experiments.[Note 5] Hence, Einstein's hypothesis that quantization is a property of light itself is considered to be proven.
Wave–particle duality and uncertainty principles
See also: Wave–particle duality, Squeezed coherent state, Uncertainty principle and De Broglie–Bohm theory
Photons in a Mach–Zehnder interferometer exhibit wavelike interference and particlelike detection at singlephoton detectors.
Photons, like all quantum objects, exhibit wavelike and particlelike properties. Their dual wave–particle nature can be difficult to visualize. The photon displays clearly wavelike phenomena such as diffraction and interference on the length scale of its wavelength. For example, a single photon passing through a doubleslit experiment lands on the screen exhibiting interference phenomena but only if no measure was made on the actual slit being run across. To account for the particle interpretation that phenomenon is called probability distribution but behaves according to Maxwell's equations.[52] However, experiments confirm that the photon is not a short pulse of electromagnetic radiation; it does not spread out as it propagates, nor does it divide when it encounters a beam splitter.[53] Rather, the photon seems to be a pointlike particle since it is absorbed or emitted as a whole by arbitrarily small systems, systems much smaller than its wavelength, such as an atomic nucleus (≈10−15 m across) or even the pointlike electron. Nevertheless, the photon is not a pointlike particle whose trajectory is shaped probabilistically by the electromagnetic field, as conceived by Einstein and others; that hypothesis was also refuted by the photoncorrelation experiments cited above. According to our present understanding, the electromagnetic field itself is produced by photons, which in turn result from a local gauge symmetry and the laws of quantum field theory (see the Second quantization and Gauge boson sections below).
Heisenberg's thought experiment for locating an electron (shown in blue) with a highresolution gammaray microscope. The incoming gamma ray (shown in green) is scattered by the electron up into the microscope's aperture angle θ. The scattered gamma ray is shown in red. Classical optics shows that the electron position can be resolved only up to an uncertainty Δx that depends on θ and the wavelength λ of the incoming light.
A key element of quantum mechanics is Heisenberg's uncertainty principle, which forbids the simultaneous measurement of the position and momentum of a particle along the same direction. Remarkably, the uncertainty principle for charged, material particles requires the quantization of light into photons, and even the frequency dependence of the photon's energy and momentum. An elegant illustration is Heisenberg's thought experiment for locating an electron with an ideal microscope.[54] The position of the electron can be determined to within the resolving power of the microscope, which is given by a formula from classical optics
\Delta x \sim \frac{\lambda}{\sin \theta}
where \theta is the aperture angle of the microscope. Thus, the position uncertainty \Delta x can be made arbitrarily small by reducing the wavelength λ. The momentum of the electron is uncertain, since it received a "kick" \Delta p from the light scattering from it into the microscope. If light were not quantized into photons, the uncertainty \Delta p could be made arbitrarily small by reducing the light's intensity. In that case, since the wavelength and intensity of light can be varied independently, one could simultaneously determine the position and momentum to arbitrarily high accuracy, violating the uncertainty principle. By contrast, Einstein's formula for photon momentum preserves the uncertainty principle; since the photon is scattered anywhere within the aperture, the uncertainty of momentum transferred equals
\Delta p \sim p_{\text{photon}} \sin\theta=\frac{h}{\lambda} \sin\theta
giving the product \Delta x \Delta p \, \sim \, h, which is Heisenberg's uncertainty principle. Thus, the entire world is quantized; both matter and fields must obey a consistent set of quantum laws, if either one is to be quantized.[55]
The analogous uncertainty principle for photons forbids the simultaneous measurement of the number n of photons (see Fock state and the Second quantization section below) in an electromagnetic wave and the phase \phi of that wave
\Delta n \Delta \phi > 1
See coherent state and squeezed coherent state for more details.
Both (photons and material) particles such as electrons create analogous interference patterns when passing through a doubleslit experiment. For photons, this corresponds to the interference of a Maxwell light wave whereas, for material particles, this corresponds to the interference of the Schrödinger wave equation. Although this similarity might suggest that Maxwell's equations are simply Schrödinger's equation for photons, most physicists do not agree.[56][57] For one thing, they are mathematically different; most obviously, Schrödinger's one equation solves for a complex field, whereas Maxwell's four equations solve for real fields. More generally, the normal concept of a Schrödinger probability wave function cannot be applied to photons.[58] Being massless, they cannot be localized without being destroyed; technically, photons cannot have a position eigenstate \mathbf{r} \rangle, and, thus, the normal Heisenberg uncertainty principle \Delta x \Delta p > h/2 does not pertain to photons. A few substitute wave functions have been suggested for the photon,[59][60][61][62] but they have not come into general use. Instead, physicists generally accept the secondquantized theory of photons described below, quantum electrodynamics, in which photons are quantized excitations of electromagnetic modes.
Another interpretation, that avoids duality, is the De Broglie–Bohm theory: known also as the pilotwave model, the photon in this theory is both, wave and particle.[63] "This idea seems to me so natural and simple, to resolve the waveparticle dilemma in such a clear and ordinary way, that it is a great mystery to me that it was so generally ignored",[64] J.S.Bell.
Bose–Einstein model of a photon gas
Main articles: Bose gas, Bose–Einstein statistics, Spinstatistics theorem and Gas in a box
In 1924, Satyendra Nath Bose derived Planck's law of blackbody radiation without using any electromagnetism, but rather a modification of coarsegrained counting of phase space.[65] Einstein showed that this modification is equivalent to assuming that photons are rigorously identical and that it implied a "mysterious nonlocal interaction",[66][67] now understood as the requirement for a symmetric quantum mechanical state. This work led to the concept of coherent states and the development of the laser. In the same papers, Einstein extended Bose's formalism to material particles (bosons) and predicted that they would condense into their lowest quantum state at low enough temperatures; this Bose–Einstein condensation was observed experimentally in 1995.[68] It was later used by Lene Hau to slow, and then completely stop, light in 1999[69] and 2001.[70]
The modern view on this is that photons are, by virtue of their integer spin, bosons (as opposed to fermions with halfinteger spin). By the spinstatistics theorem, all bosons obey Bose–Einstein statistics (whereas all fermions obey Fermi–Dirac statistics).[71]
Stimulated and spontaneous emission
Main articles: Stimulated emission and Laser
Stimulated emission (in which photons "clone" themselves) was predicted by Einstein in his kinetic analysis, and led to the development of the laser. Einstein's derivation inspired further developments in the quantum treatment of light, which led to the statistical interpretation of quantum mechanics.
In 1916, Einstein showed that Planck's radiation law could be derived from a semiclassical, statistical treatment of photons and atoms, which implies a relation between the rates at which atoms emit and absorb photons. The condition follows from the assumption that light is emitted and absorbed by atoms independently, and that the thermal equilibrium is preserved by interaction with atoms. Consider a cavity in thermal equilibrium and filled with electromagnetic radiation and atoms that can emit and absorb that radiation. Thermal equilibrium requires that the energy density \rho(\nu) of photons with frequency \nu (which is proportional to their number density) is, on average, constant in time; hence, the rate at which photons of any particular frequency are emitted must equal the rate of absorbing them.[72]
Einstein began by postulating simple proportionality relations for the different reaction rates involved. In his model, the rate R_{ji} for a system to absorb a photon of frequency \nu and transition from a lower energy E_{j} to a higher energy E_{i} is proportional to the number N_{j} of atoms with energy E_{j} and to the energy density \rho(\nu) of ambient photons with that frequency,
R_{ji}=N_{j} B_{ji} \rho(\nu) \!
where B_{ji} is the rate constant for absorption. For the reverse process, there are two possibilities: spontaneous emission of a photon, and a return to the lowerenergy state that is initiated by the interaction with a passing photon. Following Einstein's approach, the corresponding rate R_{ij} for the emission of photons of frequency \nu and transition from a higher energy E_{i} to a lower energy E_{j} is
R_{ij}=N_{i} A_{ij} + N_{i} B_{ij} \rho(\nu) \!
where A_{ij} is the rate constant for emitting a photon spontaneously, and B_{ij} is the rate constant for emitting it in response to ambient photons (induced or stimulated emission). In thermodynamic equilibrium, the number of atoms in state i and that of atoms in state j must, on average, be constant; hence, the rates R_{ji} and R_{ij} must be equal. Also, by arguments analogous to the derivation of Boltzmann statistics, the ratio of N_{i} and N_{j} is g_i/g_j\exp{(E_jE_i)/kT)}, where g_{i,j} are the degeneracy of the state i and that of j, respectively, E_{i,j} their energies, k the Boltzmann constant and T the system's temperature. From this, it is readily derived that g_iB_{ij}=g_jB_{ji} and
A_{ij}=\frac{8 \pi h \nu^{3}}{c^{3}} B_{ij}.
The A and Bs are collectively known as the Einstein coefficients.[73]
Einstein could not fully justify his rate equations, but claimed that it should be possible to calculate the coefficients A_{ij}, B_{ji} and B_{ij} once physicists had obtained "mechanics and electrodynamics modified to accommodate the quantum hypothesis".[74] In fact, in 1926, Paul Dirac derived the B_{ij} rate constants in using a semiclassical approach,[75] and, in 1927, succeeded in deriving all the rate constants from first principles within the framework of quantum theory.[76][77] Dirac's work was the foundation of quantum electrodynamics, i.e., the quantization of the electromagnetic field itself. Dirac's approach is also called second quantization or quantum field theory;[78][79][80] earlier quantum mechanical treatments only treat material particles as quantum mechanical, not the electromagnetic field.
Einstein was troubled by the fact that his theory seemed incomplete, since it did not determine the direction of a spontaneously emitted photon. A probabilistic nature of lightparticle motion was first considered by Newton in his treatment of birefringence and, more generally, of the splitting of light beams at interfaces into a transmitted beam and a reflected beam. Newton hypothesized that hidden variables in the light particle determined which path it would follow.[34] Similarly, Einstein hoped for a more complete theory that would leave nothing to chance, beginning his separation[45] from quantum mechanics. Ironically, Max Born's probabilistic interpretation of the wave function[81][82] was inspired by Einstein's later work searching for a more complete theory.[83]
Second quantization and high energy photon interactions
Main article: Quantum field theory
Different electromagnetic modes (such as those depicted here) can be treated as independent simple harmonic oscillators. A photon corresponds to a unit of energy E=hν in its electromagnetic mode.
In 1910, Peter Debye derived Planck's law of blackbody radiation from a relatively simple assumption.[84] He correctly decomposed the electromagnetic field in a cavity into its Fourier modes, and assumed that the energy in any mode was an integer multiple of h\nu, where \nu is the frequency of the electromagnetic mode. Planck's law of blackbody radiation follows immediately as a geometric sum. However, Debye's approach failed to give the correct formula for the energy fluctuations of blackbody radiation, which were derived by Einstein in 1909.[41]
In 1925, Born, Heisenberg and Jordan reinterpreted Debye's concept in a key way.[85] As may be shown classically, the Fourier modes of the electromagnetic field—a complete set of electromagnetic plane waves indexed by their wave vector k and polarization state—are equivalent to a set of uncoupled simple harmonic oscillators. Treated quantum mechanically, the energy levels of such oscillators are known to be E=nh\nu, where \nu is the oscillator frequency. The key new step was to identify an electromagnetic mode with energy E=nh\nu as a state with n photons, each of energy h\nu. This approach gives the correct energy fluctuation formula.
In quantum field theory, the probability of an event is computed by summing the probability amplitude (a complex number) for all possible ways in which the event can occur, as in the Feynman diagram shown here; the probability equals the square of the modulus of the total amplitude.
Dirac took this one step further.[76][77] He treated the interaction between a charge and an electromagnetic field as a small perturbation that induces transitions in the photon states, changing the numbers of photons in the modes, while conserving energy and momentum overall. Dirac was able to derive Einstein's A_{ij} and B_{ij} coefficients from first principles, and showed that the Bose–Einstein statistics of photons is a natural consequence of quantizing the electromagnetic field correctly (Bose's reasoning went in the opposite direction; he derived Planck's law of blackbody radiation by assuming B–E statistics). In Dirac's time, it was not yet known that all bosons, including photons, must obey Bose–Einstein statistics.
Dirac's secondorder perturbation theory can involve virtual photons, transient intermediate states of the electromagnetic field; the static electric and magnetic interactions are mediated by such virtual photons. In such quantum field theories, the probability amplitude of observable events is calculated by summing over all possible intermediate steps, even ones that are unphysical; hence, virtual photons are not constrained to satisfy E=pc, and may have extra polarization states; depending on the gauge used, virtual photons may have three or four polarization states, instead of the two states of real photons. Although these transient virtual photons can never be observed, they contribute measurably to the probabilities of observable events. Indeed, such secondorder and higherorder perturbation calculations can give apparently infinite contributions to the sum. Such unphysical results are corrected for using the technique of renormalization.
Other virtual particles may contribute to the summation as well; for example, two photons may interact indirectly through virtual electron–positron pairs.[86] In fact, such photonphoton scattering (see twophoton physics), as well as electronphoton scattering, is meant to be one of the modes of operations of the planned particle accelerator, the International Linear Collider.[87]
In modern physics notation, the quantum state of the electromagnetic field is written as a Fock state, a tensor product of the states for each electromagnetic mode
n_{k_0}\rangle\otimesn_{k_1}\rangle\otimes\dots\otimesn_{k_n}\rangle\dots
where n_{k_i}\rangle represents the state in which \, n_{k_i} photons are in the mode k_i. In this notation, the creation of a new photon in mode k_i (e.g., emitted from an atomic transition) is written as n_{k_i}\rangle \rightarrown_{k_i}+1\rangle. This notation merely expresses the concept of Born, Heisenberg and Jordan described above, and does not add any physics.
The hadronic properties of the photon
Measurements of the interaction between energetic photons and hadrons show that the interaction is much more intense than expected by the interaction of merely photons with the hadron's electric charge. Furthermore, the interaction of energetic photons with protons is similar to the interaction of photons with neutrons[88] in spite of the fact that the electric charge structures of protons and neutrons are substantially different.
A theory called Vector Meson Dominance (VMD) was developed to explain this effect. According to VMD, the photon is a superposition of the pure electromagnetic photon (which interacts only with electric charges) and vector meson.[89]
However, if experimentally probed at very short distances, the intrinsic structure of the photon is recognized as a flux of quark and gluon components, quasifree according to asymptotic freedom in QCD and described by the photon structure function.[90][91] A comprehensive comparison of data with theoretical predictions is presented in a recent review.[92]
The photon as a gauge boson
Main article: Gauge theory
The electromagnetic field can be understood as a gauge field, i.e., as a field that results from requiring that a gauge symmetry holds independently at every position in spacetime.[93] For the electromagnetic field, this gauge symmetry is the Abelian U(1) symmetry of complex numbers of absolute value 1, which reflects the ability to vary the phase of a complex number without affecting observables or real valued functions made from it, such as the energy or the Lagrangian.
The quanta of an Abelian gauge field must be massless, uncharged bosons, as long as the symmetry is not broken; hence, the photon is predicted to be massless, and to have zero electric charge and integer spin. The particular form of the electromagnetic interaction specifies that the photon must have spin ±1; thus, its helicity must be \pm \hbar. These two spin components correspond to the classical concepts of righthanded and lefthanded circularly polarized light. However, the transient virtual photons of quantum electrodynamics may also adopt unphysical polarization states.[93]
In the prevailing Standard Model of physics, the photon is one of four gauge bosons in the electroweak interaction; the other three are denoted W+, W− and Z0 and are responsible for the weak interaction. Unlike the photon, these gauge bosons have mass, owing to a mechanism that breaks their SU(2) gauge symmetry. The unification of the photon with W and Z gauge bosons in the electroweak interaction was accomplished by Sheldon Glashow, Abdus Salam and Steven Weinberg, for which they were awarded the 1979 Nobel Prize in physics.[94][95][96] Physicists continue to hypothesize grand unified theories that connect these four gauge bosons with the eight gluon gauge bosons of quantum chromodynamics; however, key predictions of these theories, such as proton decay, have not been observed experimentally.[97]
Contributions to the mass of a system
See also: Mass in special relativity and General relativity
The energy of a system that emits a photon is decreased by the energy E of the photon as measured in the rest frame of the emitting system, which may result in a reduction in mass in the amount {E}/{c^2}. Similarly, the mass of a system that absorbs a photon is increased by a corresponding amount. As an application, the energy balance of nuclear reactions involving photons is commonly written in terms of the masses of the nuclei involved, and terms of the form {E}/{c^2} for the gamma photons (and for other relevant energies, such as the recoil energy of nuclei).[98]
This concept is applied in key predictions of quantum electrodynamics (QED, see above). In that theory, the mass of electrons (or, more generally, leptons) is modified by including the mass contributions of virtual photons, in a technique known as renormalization. Such "radiative corrections" contribute to a number of predictions of QED, such as the magnetic dipole moment of leptons, the Lamb shift, and the hyperfine structure of bound lepton pairs, such as muonium and positronium.[99]
Since photons contribute to the stress–energy tensor, they exert a gravitational attraction on other objects, according to the theory of general relativity. Conversely, photons are themselves affected by gravity; their normally straight trajectories may be bent by warped spacetime, as in gravitational lensing, and their frequencies may be lowered by moving to a higher gravitational potential, as in the Pound–Rebka experiment. However, these effects are not specific to photons; exactly the same effects would be predicted for classical electromagnetic waves.[100]
Photons in matter
See also: Group velocity and Photochemistry
Any 'explanation' of how photons travel through matter has to explain why different arrangements of matter are transparent or opaque at different wavelengths (light through carbon as diamond or not, as graphite) and why individual photons behave in the same way as large groups. Explanations that invoke 'absorption' and 'reemission' have to provide an explanation for the directionality of the photons (diffraction, reflection) and further explain how entangled photon pairs can travel through matter without their quantum state collapsing.
The simplest explanation is that light that travels through transparent matter does so at a lower speed than c, the speed of light in a vacuum. In addition, light can also undergo scattering and absorption. There are circumstances in which heat transfer through a material is mostly radiative, involving emission and absorption of photons within it. An example would be in the core of the Sun. Energy can take about a million years to reach the surface.[101] However, this phenomenon is distinct from scattered radiation passing diffusely through matter, as it involves local equilibrium between the radiation and the temperature. Thus, the time is how long it takes the energy to be transferred, not the photons themselves. Once in open space, a photon from the Sun takes only 8.3 minutes to reach Earth. The factor by which the speed of light is decreased in a material is called the refractive index of the material. In a classical wave picture, the slowing can be explained by the light inducing electric polarization in the matter, the polarized matter radiating new light, and the new light interfering with the original light wave to form a delayed wave. In a particle picture, the slowing can instead be described as a blending of the photon with quantum excitation of the matter (quasiparticles such as phonons and excitons) to form a polariton; this polariton has a nonzero effective mass, which means that it cannot travel at c.
Alternatively, photons may be viewed as always traveling at c, even in matter, but they have their phase shifted (delayed or advanced) upon interaction with atomic scatters: this modifies their wavelength and momentum, but not speed.[102] A light wave made up of these photons does travel slower than the speed of light. In this view the photons are "bare", and are scattered and phase shifted, while in the view of the preceding paragraph the photons are "dressed" by their interaction with matter, and move without scattering or phase shifting, but at a lower speed.
Light of different frequencies may travel through matter at different speeds; this is called dispersion. In some cases, it can result in extremely slow speeds of light in matter. The effects of photon interactions with other quasiparticles may be observed directly in Raman scattering and Brillouin scattering.[103]
Photons can also be absorbed by nuclei, atoms or molecules, provoking transitions between their energy levels. A classic example is the molecular transition of retinal C20H28O, which is responsible for vision, as discovered in 1958 by Nobel laureate biochemist George Wald and coworkers. The absorption provokes a cistrans isomerization that, in combination with other such transitions, is transduced into nerve impulses. The absorption of photons can even break chemical bonds, as in the photodissociation of chlorine; this is the subject of photochemistry.[104][105] Analogously, gamma rays can in some circumstances dissociate atomic nuclei in a process called photodisintegration.
Technological applications
Photons have many applications in technology. These examples are chosen to illustrate applications of photons per se, rather than general optical devices such as lenses, etc. that could operate under a classical theory of light. The laser is an extremely important application and is discussed above under stimulated emission.
Individual photons can be detected by several methods. The classic photomultiplier tube exploits the photoelectric effect: a photon landing on a metal plate ejects an electron, initiating an everamplifying avalanche of electrons. Chargecoupled device chips use a similar effect in semiconductors: an incident photon generates a charge on a microscopic capacitor that can be detected. Other detectors such as Geiger counters use the ability of photons to ionize gas molecules, causing a detectable change in conductivity.[106]
Planck's energy formula E=h\nu is often used by engineers and chemists in design, both to compute the change in energy resulting from a photon absorption and to predict the frequency of the light emitted for a given energy transition. For example, the emission spectrum of a gasdischarge lamp can be altered by filling it with (mixtures of) gasses with different electronic energy level configurations.
Under some conditions, an energy transition can be excited by "two" photons that individually would be insufficient. This allows for higher resolution microscopy, because the sample absorbs energy only in the region where two beams of different colors overlap significantly, which can be made much smaller than the excitation volume of a single beam (see twophoton excitation microscopy). Moreover, these photons cause less damage to the sample, since they are of lower energy.[107]
In some cases, two energy transitions can be coupled so that, as one system absorbs a photon, another nearby system "steals" its energy and reemits a photon of a different frequency. This is the basis of fluorescence resonance energy transfer, a technique that is used in molecular biology to study the interaction of suitable proteins.[108]
Several different kinds of hardware random number generator involve the detection of single photons. In one example, for each bit in the random sequence that is to be produced, a photon is sent to a beamsplitter. In such a situation, there are two possible outcomes of equal probability. The actual outcome is used to determine whether the next bit in the sequence is "0" or "1".[109][110]
Recent research
See also: Quantum optics
Much research has been devoted to applications of photons in the field of quantum optics. Photons seem wellsuited to be elements of an extremely fast quantum computer, and the quantum entanglement of photons is a focus of research. Nonlinear optical processes are another active research area, with topics such as twophoton absorption, selfphase modulation, modulational instability and optical parametric oscillators. However, such processes generally do not require the assumption of photons per se; they may often be modeled by treating atoms as nonlinear oscillators. The nonlinear process of spontaneous parametric down conversion is often used to produce singlephoton states. Finally, photons are essential in some aspects of optical communication, especially for quantum cryptography.[Note 6]
See also
Portal icon Physics portal
Advanced Photon Source at Argonne National Laboratory
Ballistic photon
Doppler shift
Electromagnetic radiation
HEXITEC
Laser
Light
Luminiferous aether
Medipix
Phonons
Photon counting
Photon energy
Photon polarization
Photonic molecule
Photography
Photonics
Quantum optics
Single photon sources
Static forces and virtualparticle exchange
Twophoton physics
EPR paradox
Dirac equation
Notes
Although the 1967 Elsevier translation of Planck's Nobel Lecture interprets Planck's Lichtquant as "photon", the more literal 1922 translation by Hans Thacher Clarke and Ludwik Silberstein The origin and development of the quantum theory, The Clarendon Press, 1922 (here [1]) uses "lightquantum". No evidence is known that Planck himself used the term "photon" by 1926 (see also this note).
Isaac Asimov credits Arthur Compton with defining quanta of energy as photons in 1923. Asimov, I. (1966). The Neutrino, Ghost Particle of the Atom. Garden City (NY): Doubleday. ISBN 0380004836. LCCN 66017073. and Asimov, I. (1966). The Universe From Flat Earth To Quasar. New York (NY): Walker. ISBN 080270316X. LCCN 66022515.
The mass of the photon is believed to be exactly zero, based on experiment and theoretical considerations described in the article. Some sources also refer to the relativistic mass concept, which is just the energy scaled to units of mass. For a photon with wavelength λ or energy E, this is h/λc or E/c2. This usage for the term "mass" is no longer common in scientific literature. Further info: What is the mass of a photon? http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/photon_mass.html
The phrase "no matter how intense" refers to intensities below approximately 1013 W/cm2 at which point perturbation theory begins to break down. In contrast, in the intense regime, which for visible light is above approximately 1014 W/cm2, the classical wave description correctly predicts the energy acquired by electrons, called ponderomotive energy. (See also: Boreham et al. (1996). "Photon density and the correspondence principle of electromagnetic interaction".) By comparison, sunlight is only about 0.1 W/cm2.
These experiments produce results that cannot be explained by any classical theory of light, since they involve anticorrelations that result from the quantum measurement process. In 1974, the first such experiment was carried out by Clauser, who reported a violation of a classical Cauchy–Schwarz inequality. In 1977, Kimble et al. demonstrated an analogous antibunching effect of photons interacting with a beam splitter; this approach was simplified and sources of error eliminated in the photonanticorrelation experiment of Grangier et al. (1986). This work is reviewed and simplified further in Thorn et al. (2004). (These references are listed below under #Additional references.)
Introductorylevel material on the various subfields of quantum optics can be found in Fox, M. (2006). Quantum Optics: An Introduction. Oxford University Press. ISBN 0198566735.
References
Amsler, C. (Particle Data Group); Amsler; Doser; Antonelli; Asner; Babu; Baer; Band; Barnett; Bergren; Beringer; Bernardi; Bertl; Bichsel; Biebel; Bloch; Blucher; Blusk; Cahn; Carena; Caso; Ceccucci; Chakraborty; Chen; Chivukula; Cowan; Dahl; d'Ambrosio; Damour; et al. (2008). "Review of Particle Physics: Gauge and Higgs bosons" (PDF). Physics Letters B 667: 1. Bibcode:2008PhLB..667....1P. doi:10.1016/j.physletb.2008.07.018.
Joos, George (1951). Theoretical Physics. London and Glasgow: Blackie and Son Limited. p. 679.
Kimble, H.J.; Dagenais, M.; Mandel, L.; Dagenais; Mandel (1977). "Photon Antibunching in Resonance Fluorescence". Physical Review Letters 39 (11): 691–695. Bibcode:1977PhRvL..39..691K. doi:10.1103/PhysRevLett.39.691.
Grangier, P.; Roger, G.; Aspect, A.; Roger; Aspect (1986). "Experimental Evidence for a Photon Anticorrelation Effect on a Beam Splitter: A New Light on SinglePhoton Interferences". Europhysics Letters 1 (4): 173–179. Bibcode:1986EL......1..173G. doi:10.1209/02955075/1/4/004.
Planck, M. (1901). "Über das Gesetz der Energieverteilung im Normalspectrum". Annalen der Physik (in German) 4 (3): 553–563. Bibcode:1901AnP...309..553P. doi:10.1002/andp.19013090310. English translation
Einstein, A. (1905). "Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt" (PDF). Annalen der Physik (in German) 17 (6): 132–148. Bibcode:1905AnP...322..132E. doi:10.1002/andp.19053220607.. An English translation is available from Wikisource.
"Discordances entre l'expérience et la théorie électromagnétique du rayonnement." In Électrons et Photons. Rapports et Discussions de Cinquième Conseil de Physique, edited by Institut International de Physique Solvay. Paris: GauthierVillars, pp. 5585.
Helge Kragh: Photon: New light on an old name. Arxiv, 2014228
Villard, P. (1900). "Sur la réflexion et la réfraction des rayons cathodiques et des rayons déviables du radium". Comptes Rendus des Séances de l'Académie des Sciences (in French) 130: 1010–1012.
Villard, P. (1900). "Sur le rayonnement du radium". Comptes Rendus des Séances de l'Académie des Sciences (in French) 130: 1178–1179.
Rutherford, E.; Andrade, E.N.C. (1914). "The Wavelength of the Soft Gamma Rays from Radium B". Philosophical Magazine 27 (161): 854–868. doi:10.1080/14786440508635156.
Kobychev, V.V.; Popov, S.B. (2005). "Constraints on the photon charge from observations of extragalactic sources". Astronomy Letters 31 (3): 147–151. arXiv:hepph/0411398. Bibcode:2005AstL...31..147K. doi:10.1134/1.1883345.
Role as gauge boson and polarization section 5.1 inAitchison, I.J.R.; Hey, A.J.G. (1993). Gauge Theories in Particle Physics. IOP Publishing. ISBN 0852743289.
See p.31 inAmsler, C.; et al. (2008). "Review of Particle Physics". Physics Letters B 667: 1–1340. Bibcode:2008PhLB..667....1P. doi:10.1016/j.physletb.2008.07.018.
Halliday, David; Resnick, Robert; Walker, Jerl (2005), Fundamental of Physics (7th ed.), USA: John Wiley and Sons, Inc., ISBN 0471232319
See section 1.6 in Alonso, M.; Finn, E.J. (1968). Fundamental University Physics Volume III: Quantum and Statistical Physics. AddisonWesley. ISBN 0201002620.
Davison E. Soper, Electromagnetic radiation is made of photons, Institute of Theoretical Science, University of Oregon
This property was experimentally verified by Raman and Bhagavantam in 1931: Raman, C.V.; Bhagavantam, S. (1931). "Experimental proof of the spin of the photon" (PDF). Indian Journal of Physics 6: 353.
Burgess, C.; Moore, G. (2007). "1.3.3.2". The Standard Model. A Primer. Cambridge University Press. ISBN 0521860369.
Griffiths, David J. (2008), Introduction to Elementary Particles (2nd revised ed.), WILEYVCH, ISBN 9783527406012
E.g., section 9.3 in Alonso, M.; Finn, E.J. (1968). Fundamental University Physics Volume III: Quantum and Statistical Physics. AddisonWesley.
E.g., Appendix XXXII in Born, M. (1962). Atomic Physics. Blackie & Son. ISBN 0486659844.
Mermin, David (February 1984). "Relativity without light". American Journal of Physics 52 (2): 119–124. Bibcode:1984AmJPh..52..119M. doi:10.1119/1.13917.
Plimpton, S.; Lawton, W. (1936). "A Very Accurate Test of Coulomb's Law of Force Between Charges". Physical Review 50 (11): 1066. Bibcode:1936PhRv...50.1066P. doi:10.1103/PhysRev.50.1066.
Williams, E.; Faller, J.; Hill, H. (1971). "New Experimental Test of Coulomb's Law: A Laboratory Upper Limit on the Photon Rest Mass". Physical Review Letters 26 (12): 721. Bibcode:1971PhRvL..26..721W. doi:10.1103/PhysRevLett.26.721.
Chibisov, G V (1976). "Astrophysical upper limits on the photon rest mass". Soviet Physics Uspekhi 19 (7): 624. Bibcode:1976SvPhU..19..624C. doi:10.1070/PU1976v019n07ABEH005277.
Lakes, Roderic (1998). "Experimental Limits on the Photon Mass and Cosmic Magnetic Vector Potential". Physical Review Letters 80 (9): 1826. Bibcode:1998PhRvL..80.1826L. doi:10.1103/PhysRevLett.80.1826.
Amsler, C; Doser, M; Antonelli, M; Asner, D; Babu, K; Baer, H; Band, H; Barnett, R; et al. (2008). "Review of Particle Physics⁎". Physics Letters B 667: 1. Bibcode:2008PhLB..667....1P. doi:10.1016/j.physletb.2008.07.018. Summary Table
Adelberger, Eric; Dvali, Gia; Gruzinov, Andrei (2007). "PhotonMass Bound Destroyed by Vortices". Physical Review Letters 98 (1): 010402. arXiv:hepph/0306245. Bibcode:2007PhRvL..98a0402A. doi:10.1103/PhysRevLett.98.010402. PMID 17358459. preprint
Wilczek, Frank (2010). The Lightness of Being: Mass, Ether, and the Unification of Forces. Basic Books. p. 212. ISBN 9780465018956.
Descartes, R. (1637). Discours de la méthode (Discourse on Method) (in French). Imprimerie de Ian Maire. ISBN 0268008701.
Hooke, R. (1667). Micrographia: or some physiological descriptions of minute bodies made by magnifying glasses with observations and inquiries thereupon ... London (UK): Royal Society of London. ISBN 0486495647.
Huygens, C. (1678). Traité de la lumière (in French).. An English translation is available from Project Gutenberg
Newton, I. (1952) [1730]. Opticks (4th ed.). Dover (NY): Dover Publications. Book II, Part III, Propositions XII–XX; Queries 25–29. ISBN 0486602052.
Buchwald, J.Z. (1989). The Rise of the Wave Theory of Light: Optical Theory and Experiment in the Early Nineteenth Century. University of Chicago Press. ISBN 0226078868. OCLC 18069573.
Maxwell, J.C. (1865). "A Dynamical Theory of the Electromagnetic Field". Philosophical Transactions of the Royal Society 155: 459–512. Bibcode:1865RSPT..155..459C. doi:10.1098/rstl.1865.0008. This article followed a presentation by Maxwell on 8 December 1864 to the Royal Society.
Hertz, H. (1888). "Über Strahlen elektrischer Kraft". Sitzungsberichte der Preussischen Akademie der Wissenschaften (Berlin) (in German) 1888: 1297–1307.
Frequencydependence of luminiscence p. 276f., photoelectric effect section 1.4 in Alonso, M.; Finn, E.J. (1968). Fundamental University Physics Volume III: Quantum and Statistical Physics. AddisonWesley. ISBN 0201002620.
Wien, W. (1911). "Wilhelm Wien Nobel Lecture".
Planck, M. (1920). "Max Planck's Nobel Lecture".
Einstein, A. (1909). "Über die Entwicklung unserer Anschauungen über das Wesen und die Konstitution der Strahlung" (PDF). Physikalische Zeitschrift (in German) 10: 817–825.. An English translation is available from Wikisource.
Presentation speech by Svante Arrhenius for the 1921 Nobel Prize in Physics, December 10, 1922. Online text from [nobelprize.org], The Nobel Foundation 2008. Access date 20081205.
Einstein, A. (1916). "Zur Quantentheorie der Strahlung". Mitteilungen der Physikalischen Gesellschaft zu Zürich 16: 47. Also Physikalische Zeitschrift, 18, 121–128 (1917). (German)
Compton, A. (1923). "A Quantum Theory of the Scattering of Xrays by Light Elements". Physical Review 21 (5): 483–502. Bibcode:1923PhRv...21..483C. doi:10.1103/PhysRev.21.483.
Pais, A. (1982). Subtle is the Lord: The Science and the Life of Albert Einstein. Oxford University Press. ISBN 019853907X.
Einstein and the Quantum: The Quest of the Valiant Swabian, A. Douglas Stone, Princeton University Press, 2013.
Millikan, R.A (1924). "Robert A. Millikan's Nobel Lecture".
Hendry, J. (1980). "The development of attitudes to the waveparticle duality of light and quantum theory, 1900–1920". Annals of Science 37 (1): 59–79. doi:10.1080/00033798000200121.
Bohr, N.; Kramers, H.A.; Slater, J.C. (1924). "The Quantum Theory of Radiation". Philosophical Magazine 47: 785–802. doi:10.1080/14786442408565262. Also Zeitschrift für Physik, 24, 69 (1924).
Heisenberg, W. (1933). "Heisenberg Nobel lecture".
Mandel, L. (1976). E. Wolf, ed. "The case for and against semiclassical radiation theory". Progress in Optics. Progress in Optics (NorthHolland) 13: 27–69. doi:10.1016/S00796638(08)700180. ISBN 9780444108067.
Taylor, G.I. (1909). Interference fringes with feeble light. Proceedings of the Cambridge Philosophical Society 15: 114–115.
Saleh, B. E. A. and Teich, M. C. (2007). Fundamentals of Photonics. Wiley. ISBN 0471358320.
Heisenberg, W. (1927). "Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik". Zeitschrift für Physik (in German) 43 (3–4): 172–198. Bibcode:1927ZPhy...43..172H. doi:10.1007/BF01397280.
E.g., p. 10f. in Schiff, L.I. (1968). Quantum Mechanics (3rd ed.). McGrawHill. ASIN B001B3MINM. ISBN 0070552878.
Kramers, H.A. (1958). Quantum Mechanics. Amsterdam: NorthHolland. ASIN B0006AUW5C. ISBN 0486495337.
Bohm, D. (1989) [1954]. Quantum Theory. Dover Publications. ISBN 0486659690.
Newton, T.D.; Wigner, E.P. (1949). "Localized states for elementary particles". Reviews of Modern Physics 21 (3): 400–406. Bibcode:1949RvMP...21..400N. doi:10.1103/RevModPhys.21.400.
BialynickiBirula, I. (1994). "On the wave function of the photon" (PDF). Acta Physica Polonica A 86: 97–116.
Sipe, J.E. (1995). "Photon wave functions". Physical Review A 52 (3): 1875–1883. Bibcode:1995PhRvA..52.1875S. doi:10.1103/PhysRevA.52.1875.
BialynickiBirula, I. (1996). "Photon wave function". Progress in Optics. Progress in Optics 36: 245–294. doi:10.1016/S00796638(08)703160. ISBN 9780444825308.
Scully, M.O.; Zubairy, M.S. (1997). Quantum Optics. Cambridge (UK): Cambridge University Press. ISBN 0521435951.
The best illustration is the Couder experiment, demonstrating the behaviour of a mechanical analog, see https://www.youtube.com/watch?v=W9yWv5dqSKk
Bell, J. S., "Speakable and Unspeakable in Quantum Mechanics", Cambridge: Cambridge University Press, 1987.
Bose, S.N. (1924). "Plancks Gesetz und Lichtquantenhypothese". Zeitschrift für Physik (in German) 26: 178–181. Bibcode:1924ZPhy...26..178B. doi:10.1007/BF01327326.
Einstein, A. (1924). "Quantentheorie des einatomigen idealen Gases". Sitzungsberichte der Preussischen Akademie der Wissenschaften (Berlin), Physikalischmathematische Klasse (in German) 1924: 261–267.
Einstein, A. (1925). "Quantentheorie des einatomigen idealen Gases, Zweite Abhandlung". Sitzungsberichte der Preussischen Akademie der Wissenschaften (Berlin), Physikalischmathematische Klasse (in German) 1925: 3–14. doi:10.1002/3527608958.ch28. ISBN 9783527608959.
Anderson, M.H.; Ensher, J.R.; Matthews, M.R.; Wieman, C.E.; Cornell, E.A. (1995). "Observation of Bose–Einstein Condensation in a Dilute Atomic Vapor". Science 269 (5221): 198–201. Bibcode:1995Sci...269..198A. doi:10.1126/science.269.5221.198. JSTOR 2888436. PMID 17789847.
"Physicists Slow Speed of Light". News.harvard.edu (19990218). Retrieved on 20150511.
"Light Changed to Matter, Then Stopped and Moved". photonics.com (February 2007). Retrieved on 20150511.
Streater, R.F.; Wightman, A.S. (1989). PCT, Spin and Statistics, and All That. AddisonWesley. ISBN 020109410X.
Einstein, A. (1916). "Strahlungsemission und absorption nach der Quantentheorie". Verhandlungen der Deutschen Physikalischen Gesellschaft (in German) 18: 318–323. Bibcode:1916DPhyG..18..318E.
Section 1.4 in Wilson, J.; Hawkes, F.J.B. (1987). Lasers: Principles and Applications. New York: Prentice Hall. ISBN 013523705X.
P. 322 in Einstein, A. (1916). "Strahlungsemission und absorption nach der Quantentheorie". Verhandlungen der Deutschen Physikalischen Gesellschaft (in German) 18: 318–323. Bibcode:1916DPhyG..18..318E.:
Die Konstanten A^n_m and B^n_m würden sich direkt berechnen lassen, wenn wir im Besitz einer im Sinne der Quantenhypothese modifizierten Elektrodynamik und Mechanik wären."
Dirac, P.A.M. (1926). "On the Theory of Quantum Mechanics". Proceedings of the Royal Society A 112 (762): 661–677. Bibcode:1926RSPSA.112..661D. doi:10.1098/rspa.1926.0133.
Dirac, P.A.M. (1927). "The Quantum Theory of the Emission and Absorption of Radiation" (PDF). Proceedings of the Royal Society A 114 (767): 243–265. Bibcode:1927RSPSA.114..243D. doi:10.1098/rspa.1927.0039.
Dirac, P.A.M. (1927b). The Quantum Theory of Dispersion. Proceedings of the Royal Society A 114: 710–728. doi:10.1098/rspa.1927.0071.
Heisenberg, W.; Pauli, W. (1929). "Zur Quantentheorie der Wellenfelder". Zeitschrift für Physik (in German) 56: 1. Bibcode:1929ZPhy...56....1H. doi:10.1007/BF01340129.
Heisenberg, W.; Pauli, W. (1930). "Zur Quantentheorie der Wellenfelder". Zeitschrift für Physik (in German) 59 (3–4): 139. Bibcode:1930ZPhy...59..168H. doi:10.1007/BF01341423.
Fermi, E. (1932). "Quantum Theory of Radiation" (PDF). Reviews of Modern Physics 4: 87. Bibcode:1932RvMP....4...87F. doi:10.1103/RevModPhys.4.87.
Born, M. (1926). "Zur Quantenmechanik der Stossvorgänge" (PDF). Zeitschrift für Physik (in German) 37 (12): 863–867. Bibcode:1926ZPhy...37..863B. doi:10.1007/BF01397477.
Born, M. (1926). "Quantenmechanik der Stossvorgänge". Zeitschrift für Physik (in German) 38 (11–12): 803. Bibcode:1926ZPhy...38..803B. doi:10.1007/BF01397184.
Pais, A. (1986). Inward Bound: Of Matter and Forces in the Physical World. Oxford University Press. p. 260. ISBN 0198519974. Specifically, Born claimed to have been inspired by Einstein's neverpublished attempts to develop a "ghostfield" theory, in which pointlike photons are guided probabilistically by ghost fields that follow Maxwell's equations.
Debye, P. (1910). "Der Wahrscheinlichkeitsbegriff in der Theorie der Strahlung". Annalen der Physik (in German) 33 (16): 1427–1434. Bibcode:1910AnP...338.1427D. doi:10.1002/andp.19103381617.
Born, M.; Heisenberg, W.; Jordan, P. (1925). "Quantenmechanik II". Zeitschrift für Physik (in German) 35 (8–9): 557–615. Bibcode:1926ZPhy...35..557B. doi:10.1007/BF01379806.
Photonphotonscattering section 731, renormalization chapter 82 in Itzykson, C.; Zuber, J.B. (1980). Quantum Field Theory. McGrawHill. ISBN 0070320713.
Weiglein, G. (2008). "Electroweak Physics at the ILC". Journal of Physics: Conference Series 110 (4): 042033. arXiv:0711.3003. Bibcode:2008JPhCS.110d2033W. doi:10.1088/17426596/110/4/042033.
Bauer, T. H.; Spital, R. D.; Yennie, D. R.; Pipkin, F. M. (1978). "The hadronic properties of the photon in highenergy interactions". Reviews of Modern Physics 50 (2): 261. Bibcode:1978RvMP...50..261B. doi:10.1103/RevModPhys.50.261.
Sakurai, J. J. (1960). "Theory of strong interactions". Annals of Physics 11: 1. Bibcode:1960AnPhy..11....1S. doi:10.1016/00034916(60)901263.
Walsh, T. F.; Zerwas, P. (1973). "Twophoton processes in the parton model". Physics Letters B 44 (2): 195. Bibcode:1973PhLB...44..195W. doi:10.1016/03702693(73)905200.
Witten, E. (1977). "Anomalous cross section for photonphoton scattering in gauge theories". Nuclear Physics B 120 (2): 189. Bibcode:1977NuPhB.120..189W. doi:10.1016/05503213(77)900384.
Nisius, R. (2000). "The photon structure from deep inelastic electron–photon scattering". Physics Reports 332 (4–6): 165. Bibcode:2000PhR...332..165N. doi:10.1016/S03701573(99)001155.
Ryder, L.H. (1996). Quantum field theory (2nd ed.). Cambridge University Press. ISBN 0521478146.
Sheldon Glashow Nobel lecture, delivered 8 December 1979.
Abdus Salam Nobel lecture, delivered 8 December 1979.
Steven Weinberg Nobel lecture, delivered 8 December 1979.
E.g., chapter 14 in Hughes, I. S. (1985). Elementary particles (2nd ed.). Cambridge University Press. ISBN 0521260922.
E.g., section 10.1 in Dunlap, R.A. (2004). An Introduction to the Physics of Nuclei and Particles. Brooks/Cole. ISBN 0534392946.
Radiative correction to electron mass section 712, anomalous magnetic moments section 721, Lamb shift section 732 and hyperfine splitting in positronium section 103 in Itzykson, C.; Zuber, J.B. (1980). Quantum Field Theory. McGrawHill. ISBN 0070320713.
E. g. sections 9.1 (gravitational contribution of photons) and 10.5 (influence of gravity on light) in Stephani, H.; Stewart, J. (1990). General Relativity: An Introduction to the Theory of Gravitational Field. Cambridge University Press. pp. 86 ff, 108 ff. ISBN 0521379415.
Naeye, R. (1998). Through the Eyes of Hubble: Birth, Life and Violent Death of Stars. CRC Press. ISBN 0750304847. OCLC 40180195.
Ch 4 in Hecht, Eugene (2001). Optics. Addison Wesley. ISBN 9780805385663.
Polaritons section 10.10.1, Raman and Brillouin scattering section 10.11.3 in Patterson, J.D.; Bailey, B.C. (2007). SolidState Physics: Introduction to the Theory. Springer. pp. 569 ff, 580 ff. ISBN 3540241159.
E.g., section 115 C in Pine, S.H.; Hendrickson, J.B.; Cram, D.J.; Hammond, G.S. (1980). Organic Chemistry (4th ed.). McGrawHill. ISBN 0070501157.
Nobel lecture given by G. Wald on December 12, 1967, online at nobelprize.org: The Molecular Basis of Visual Excitation.
Photomultiplier section 1.1.10, CCDs section 1.1.8, Geiger counters section 1.3.2.1 in Kitchin, C.R. (2008). Astrophysical Techniques. Boca Raton (FL): CRC Press. ISBN 1420082434.
Denk, W.; Svoboda, K. (1997). "Photon upmanship: Why multiphoton imaging is more than a gimmick". Neuron 18 (3): 351–357. doi:10.1016/S08966273(00)812374. PMID 9115730.
Lakowicz, J.R. (2006). Principles of Fluorescence Spectroscopy. Springer. pp. 529 ff. ISBN 0387312781.
Jennewein, T.; Achleitner, U.; Weihs, G.; Weinfurter, H.; Zeilinger, A. (2000). "A fast and compact quantum random number generator". Review of Scientific Instruments 71 (4): 1675–1680. arXiv:quantph/9912118. Bibcode:2000RScI...71.1675J. doi:10.1063/1.1150518.
Stefanov, A.; Gisin, N.; Guinnard, O.; Guinnard, L.; Zbiden, H. (2000). "Optical quantum random number generator". Journal of Modern Optics 47 (4): 595–598. doi:10.1080/095003400147908.
Additional references
By date of publication:
Clauser, J.F. (1974). "Experimental distinction between the quantum and classical fieldtheoretic predictions for the photoelectric effect". Physical Review D 9 (4): 853–860. Bibcode:1974PhRvD...9..853C. doi:10.1103/PhysRevD.9.853.
Kimble, H.J.; Dagenais, M.; Mandel, L. (1977). "Photon Antibunching in Resonance Fluorescence". Physical Review Letters 39 (11): 691–695. Bibcode:1977PhRvL..39..691K. doi:10.1103/PhysRevLett.39.691.
Pais, A. (1982). Subtle is the Lord: The Science and the Life of Albert Einstein. Oxford University Press.
Feynman, Richard (1985). QED: The Strange Theory of Light and Matter. Princeton University Press. ISBN 9780691125756.
Grangier, P.; Roger, G.; Aspect, A. (1986). "Experimental Evidence for a Photon Anticorrelation Effect on a Beam Splitter: A New Light on SinglePhoton Interferences". Europhysics Letters 1 (4): 173–179. Bibcode:1986EL......1..173G. doi:10.1209/02955075/1/4/004.
Lamb, W.E. (1995). "Antiphoton". Applied Physics B 60 (2–3): 77–84. Bibcode:1995ApPhB..60...77L. doi:10.1007/BF01135846.
Special supplemental issue of Optics and Photonics News (vol. 14, October 2003) article web link
Roychoudhuri, C.; Rajarshi, R. (2003). "The nature of light: what is a photon?". Optics and Photonics News 14: S1 (Supplement).
Zajonc, A. "Light reconsidered". Optics and Photonics News 14: S2–S5 (Supplement).
Loudon, R. "What is a photon?". Optics and Photonics News 14: S6–S11 (Supplement).
Finkelstein, D. "What is a photon?". Optics and Photonics News 14: S12–S17 (Supplement).
Muthukrishnan, A.; Scully, M.O.; Zubairy, M.S. "The concept of the photon—revisited". Optics and Photonics News 14: S18–S27 (Supplement).
Mack, H.; Schleich, W.P.. "A photon viewed from Wigner phase space". Optics and Photonics News 14: S28–S35 (Supplement).
Glauber, R. (2005). "One Hundred Years of Light Quanta" (PDF). 2005 Physics Nobel Prize Lecture.
Hentschel, K. (2007). "Light quanta: The maturing of a concept by the stepwise accretion of meaning". Physics and Philosophy 1 (2): 1–20.
Education with single photons:
Thorn, J.J.; Neel, M.S.; Donato, V.W.; Bergreen, G.S.; Davies, R.E.; Beck, M. (2004). "Observing the quantum behavior of light in an undergraduate laboratory" (PDF). American Journal of Physics 72 (9): 1210–1219. Bibcode:2004AmJPh..72.1210T. doi:10.1119/1.1737397.
Bronner, P.; Strunz, Andreas; Silberhorn, Christine; Meyn, JanPeter (2009). "Interactive screen experiments with single photons". European Journal of Physics 30 (2): 345–353. Bibcode:2009EJPh...30..345B. doi:10.1088/01430807/30/2/014.
External links
The dictionary definition of photon at Wiktionary
Media related to Photon at Wikimedia Commons
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The prior art above this date, Photon Mass <1×10−18 eV/c2 other than 0 is all I get so far.
112315 Copied from Wikipedia:
Measurement  Unit  SI value of unit 
Energy 
eV 
1.602176565(35)×10^{−19} J 
Mass 
eV/c^{2} 
1.782662×10^{−36} kg 
Momentum 
eV/c 
5.344286×10^{−28} kg⋅m/s 
Temperature 
eV/k_{B} 
11604.505(20) K 
Time 
ħ/eV 
6.582119×10^{−16} s 
Distance 
ħc/eV 
1.97327×10^{−7} m 
By mass–energy equivalence, the electronvolt is also a unit of mass. It is common in particle physics, where units of mass and energy are often interchanged, to express mass in units of eV/c^{2}, where c is the speed of light in vacuum (from E = mc^{2}). It is common to simply express mass in terms of "eV" as a unit of mass, effectively using a system of natural units with c set to 1.^{[9]} The mass equivalent of 1 eV/c^{2} is
For example, an electron and a positron, each with a mass of 0.511 MeV/c^{2}, can annihilate to yield 1.022 MeV of energy. The proton has a mass of0.938 GeV/c^{2}. In general, the masses of all hadrons are of the order of 1 GeV/c^{2}, which makes the GeV (gigaelectronvolt) a convenient unit of mass for particle physics:
 1 GeV/c^{2} = 1.783×10^{−27} kg.
The atomic mass unit, 1 gram divided by Avogadro's number, is almost the mass of a hydrogen atom, which is mostly the mass of the proton. To convert to megaelectronvolts, use the formula:
 1 amu = 931.4941 MeV/c^{2} = 0.9314941 GeV/c^{2}.
Momentum[edit]
In highenergy physics, the electron volt is often used as a unit of momentum. A potential difference of 1 volt causes an electron to gain an amount of energy (i.e., 1 eV). This gives rise to usage of eV (and keV, MeV, GeV or TeV) as units of momentum, for the energy supplied results in acceleration of the particle.
The dimensions of momentum units are LMT^{−1}. The dimensions of energy units are L^{2}MT^{−2}. Then, dividing the units of energy (such as eV) by a fundamental constant that has units of velocity (LT^{−1}), facilitates the required conversion of using energy units to describe momentum. In the field of highenergy particle physics, the fundamental velocity unit is the speed of light in vacuum c. Thus, dividing energy in eV by the speed of light, one can describe the momentum of an electron in units of eV/c.^{[10]} ^{[11]}
The fundamental velocity constant c is often dropped from the units of momentum by way of defining units of length such that the value of c is unity. For example, if the momentum p of an electron is said to be 1 GeV, then the conversion to MKS can be achieved by:
112315 Copied from Wikipedia to Excel spread sheet:
112815 Got Samsung Tablet Windows 7 PC with on screen Keyboard and the header doesn't file download like above? The Photon generic
Mass 
eV/c^{2} 
1.782662×10^{−36} kg * 137 may = 2.44E44

113015 copied from the END of Page EQUATIONS JWave JMass was 6.6491846058394 E33 kg?
12115 Copied all Mass values for J_Photon, Electron, J_Wave into Wikipedia's Propositional logic:
Material implication (rule of inference)
Connected to:
Propositional logic Negation If and only if
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12315 At the present time J_Paradigm includes 5 dimensions. J_5thdimemnsionis at the Black Holes events horizons to Bigbangs future creation. The State of art from Quora is copied here as follows
12415 Start collection sub atomic electronvolt to mass:
Edit

This page uses content from the English Wikipedia. The original article was at Electronvolt. The list of authors can be seen in the page history. As with the Units of Measurement Wiki, the text of Wikipedia is available under Creative Commons License see Wikia:Licensing. 
In physics, the electron volt (symbol eV; also written electronvolt^{[1]}^{[2]}) is a unit of energy equal to approximately 1.602×10^{−19} joule (symbol J). By definition, it is the amount of energy gained by the charge of a single electron moved across an electric potential difference of one volt. Thus it is 1 volt (1 joule per coulomb, 1 J/C) multiplied by the electron charge (1 e, or 1.602176565(35)×10^{−19} C). Therefore, one electron volt is equal to 1.602176565(35)×10^{−19} J.^{[3]} Historically, the electron volt was devised as a standard unit of measure through its usefulness in electrostatic particle accelerator sciences because a particle with charge q has an energy E=qV after passing through the potential V; if q is quoted in integer units of the elementary charge and the terminal bias in volts, one gets an energy in eV.
The electron volt is not an SI unit and its value must be obtained experimentally.^{[4]} Like the elementary charge on which it is based, it is not an independent quantity but is equal to (1 J/C)(2 h α / μ_{0} c_{0})^{0.5} It is a common unit of energy within physics, widely used in solid state, atomic, nuclear, and particle physics. It is commonly used with the SI prefixes milli, kilo, mega, giga, tera, or peta (meV, keV, MeV, GeV, TeV and PeV respectively). Thus meV stands for millielectron volt.
Atomic properties like the ionization energy are often quoted in electron volts.
In chemistry, it is often useful to have the molar equivalent, that is the energy that would be produced by one mole of charge (6.02214129(27)×10^{23}) passing through a potential difference of one volt. This is equal to 96.4853365(21) kJ/mol.^{[3]}
Conversion factors:
 1 eV = 1.602176487(40)×10^{−19} J (the conversion factor is numerically equal to the elementary charge expressed in coulombs).
 1 eV (per atom) is 96.4853365(21) kJ/mol.^{[3]}
For comparison:
 5.25×10^{32} eV: Total energy released from a 20 kt Nuclear Fission Device.
 ~624 EeV (6.24×10^{20} eV): energy needed to power a single 100 watt light bulb for one second. (100 W = 100 J/s = ~6.24×10^{20} eV/s).
 300 EeV (3×10^{20} eV) = (50 J) :^{[5]} the socalled OhMyGod particle (the most energetic cosmic ray particle ever observed).
 14 TeV: the designed proton collision energy at the Large Hadron Collider (which has operated at half of this energy Template:As of).
 1 TeV: A trillion electronvolts, or 1.602×10^{−7} J, about the kinetic energy of a flying mosquito.^{[6]}
 210 MeV: The average energy released in fission of one Pu239 atom.
 200 MeV: The average energy released in nuclear fission of one U235 atom .
 17.6 MeV: The average energy released in the fusion of deuterium and tritium to form He4; this is 0.41 PJ per kilogram of product produced.
 1 MeV: Or, 1.602×10^{−13} J, about twice the rest massenergy of an electron.
 13.6 eV: The energy required to ionize atomic hydrogen. Molecular bond energies are on the order of one eV per molecule.
 1.6 to 3.4 eV: the photon energy of visible light.
 1/40 eV: The thermal energy at room temperature. A single molecule in the air has an average kinetic energy 3/80 eV.
In some older documents, and in the name Bevatron, the symbol BeV is used, which stands for billion electron volts; it is equivalent to the GeV.
In highenergy physics, electronvolt is often used as a unit of momentum. A potential difference of 1 volt causes an electron to gain a discrete amount of energy (i.e., 1 eV). This gives rise to usage of eV (and keV, MeV, GeV or TeV) as units of momentum, for the energy supplied results in acceleration of the particle.
The dimensions of momentum units are M^{ 1 } L ^{ 1 } T ^{ 1 }. The dimensions of energy units are M ^{ 1 } L ^{ 2 } T ^{ 2 }. Then, dividing the units of energy (such as eV) by a fundamental constant that has units of velocity (M ^{ 0 } L ^{ 1 } T ^{ 1 }), facilitates the required conversion of using energy units to describe momentum. In the field of highenergy particle physics, the fundamental velocity unit is the speed of light c. Thus, dividing energy in eV by the speed of light in vacuum, one can describe the momentum of an electron in units of eV/c.^{[7]} ^{[8]}
The fundamental velocity constant c is often dropped from the units of momentum by way of defining units of length such that the value of c is unity. For example, if the momentum p of an electron is said to be 1 GeV, then the conversion to MKS can be achieved by:
By massenergy equivalence, the electron volt is also a unit of mass. It is common in particle physics, where mass and energy are often interchanged, to express mass in units of eV/c^{2}, where c is the speed of light in a vacuum (from E = mc^{2}). It is often common to simply express mass in terms of "eV" as a unit of mass, effectively using a system of natural units with c set to 1 (hence, E = m).
For example, an electron and a positron, each with a mass of 0.511 MeV/c^{2}, can annihilate to yield 1.022 MeV of energy. The proton has a mass of 0.938 GeV/c^{2}. In general, the masses of all hadrons are of the order of 1 GeV/c^{2}, which makes the GeV (gigaelectronvolt) a very convenient unit of mass for particle physics:
 1 GeV/c^{2} = 1.783×10^{−27} kg
The atomic mass unit, 1 gram divided by Avogadro's number, is almost the mass of a hydrogen atom, which is mostly the mass of the proton. To convert to megaelectronvolts, use the formula:
 1 amu = 931.46 MeV/c^{2} = 0.93146 GeV/c^{2}
 1 MeV/c^{2} = 1.074×10^{−3} amu
In particle physics, a system of units in which the speed of light in a vacuum c and the reduced Planck constant ħ are dimensionless and equal to unity is widely used: c = ħ = 1. In these units, both distances and times are expressed in inverse energy units (while energy and mass are expressed in the same units, see Mass–energy equivalence). In particular, particle scattering lengths are often presented in units of inverse particle masses.
Outside this system of units, the conversion factors between electronvolt, second, and nanometer are the following:^{[3]}
The above relations also allow expressing the mean lifetime τ of an unstable particle (in seconds) in terms of its decay width Γ (in eV) via Γ = ħ/τ. For example, the B^{0} meson has a lifetime of 1.530(9) picoseconds, mean decay length is cτ = 459.7 µm, or a decay width of 4.302±25×10^{−4} eV.
Conversely, the tiny meson mass mass differences responsible for meson oscillations are often expressed in the more convenient inverse picoseconds.
TemperatureEdit
In certain fields, such as plasma physics, it is convenient to use the electronvolt as a unit of temperature. The conversion to kelvins (symbol: uppercase K) is defined by using k_{B}, the Boltzmann constant:
For example, a typical magnetic confinement fusion plasma is 15 keV, or 170 megakelvins.
PropertiesEdit
File:Colors in eV.svg File:EV to nm vis.png
The energy E, frequency v, and wavelength λ of a photon are related by
where h is the Planck constant, c is the speed of light. For quick calculations, this reduces to
A photon with a wavelength of 532 nm (green light) would have an energy of approximately 2.33 eV. Similarly, 1 eV would correspond to an infrared photon of wavelength 1240 nm, and so on.
Scattering experimentsEdit
In a lowenergy nuclear scattering experiment, it is conventional to refer to the nuclear recoil energy in units of eVr, keVr, etc. This distinguishes the nuclear recoil energy from the "electron equivalent" recoil energy (eVee, keVee, etc.) measure8d by scintillation light. For example, the yield of a phototube is measured in phe/keVee (photoelectrons per keV electronequivalent energy). The relationship between eV, eVr, and eVee depends on the medium the scattering takes place in, and must be established empirically for each material.
12515 Copied from Quora Digest in yesterday Email:
In "natural" units, the equation would be E=m : it would be saying that energy and mass are really the same thing! So in natural units there really are no arbitrary constants at all in the formula, not even a c2. The only reason there is a c2 is because we are using totally unnatural units like meters and seconds which leads to using different units for measuring mass and energy. In natural units the speed of light is 1 exactly, with NO units. Natural units would mean that the distance and time units were related such that light travels 1 distance unit in 1 time unit. In those natural units the proper time equation in 4 dimensional spacetime would be
dτ2=dt2−dx2−dy2−dz2
The meaning of dτ is that it would be the time measured on the object itself (when dx=dy=dz=0). All observers will agree on this value if they measure the dt,dx,dy and dz in their frame that may be moving relative to the object. Two different observers moving at some speed relative to each other and the object will measure different values for dt,dx,dy and dz but they will all agree on dτ. This is the metric for the 4 dimensional spacetime and (t,x,y,z) is the 4vector specifying a position in that space time. The reason why "light" travels 1 unit of distance in 1 unit of time is because the proper time for light is always dτ=0.
Similarly in these natural units, the energy E and momentum p⃗ of a particle or object also form a 4vector. In these units the equivalent invariant equation would be:
m2=E2− p⃗ 2=E2−p2x−p2y−p2z
where m is the invariant rest mass of the particle or object. In particular, in the rest frame of the particle or object (where p⃗ =0 ) we would have m=E.
In the crazy unit system that we use, we have to put in a conversion factor "c" which converts between space units and time units. So in these crazy units these equations would become:
dτ2=dt2−(dx2+dy2+dz2)/c2
c2m2=E2/c2− p⃗ 2=E2/c2−(p2x+p2y+p2z)
and for a particle at rest:
c2m2=E2/c2
or:
E=mc2
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If by weight you mean mass, then Sun's light definitely has the equivalent of mass. In particular, the sunlight emitted in a day would be equivalent to 3.7×1014kg. This is about 5 times the biomass on Earth or about 370 cubic kilometers of water. (See (solar luminosity)*(1 day)/c^2  WolframAlpha).
If you collected all that light in a box with perfect mirrors, the mass of the box would increase by tha... (My input here.) The last of several at the end of my feed from Quora got cut off. I will review the Mass of sunlight and increase of 1/2 days sunshine, in mirror lined perfectly, in a box at sealevel would weight?
12615 J_Paradigm J_Photon's J_Mass is new and unique is Disclosed here being different than priorart above with J_String being smaller component of the priorart. The J_CosmicJ_String that fits in the J_ElectronShell circumference J_WaveLength integer number 137 sine like wavelengths. The J_Spiral out from J_Proton of which one of them in J_Probability ends; as a J_Electron others become J_StringJ_AetherJ_Fabric of J_Universe. J_ElectronsJ_Spin around in a J_ElectronShell. J_Spin of J_Electron in J_ElectronShell forms J_MagneticField with its polarity 90 degrees to plane of J_ElectronJ_Spin.
12715 Continue from 126 J_ElectronsJ_Spin and J_MagneticField with its polarity 90degrees to plane of J_ElectronJ_Spin What is the J_MagneticField? I Disclose here the J_StringJ_AetherJ_Fabric of J_Universe besides Creating J_Gravity also Creates J_MagneticField and Luminous Medium: This is done by having J_Mass in J_Strings that J_ Creates J_Fabric of J_Universe. See also first Page Home Spacetime&speed
30712 I agree with PBS How the Universe was made except J Waves instead of particles at the beginning after The Big Bang.
12815 My Concept is now J_Waves are components that are smaller than Elementary Particles. Copied from :
31815 The first J_String 1 J_Wave Length long nearly 1 Planck Length. The other = J_Mass with = volume is a rod nearly 1 Planck Length. The first moving at nearly the speed of light along J_Spiral in the direction from higher density of mass to lower density of mass the other = J_Mass is moving in the oposite direction along the same segment of J_Spiral. For every action in J_Aether there is an = and opposite reaction.
J_Quarks are the reorganization of derbus from neuculer particle's of J_Waves that particle physicists have smashed together at near the speed of light. J_Quarks are the different organized derbus parts J_Strings observed by particle physicists. J_Up Quark, J_Down Quark, J_Top Quark, J_Bottom Quark & J_Strange Quark are the reorganizations of neuculer particles parts. Latter I will calculate the number of J_waves in each comepared the 137 J_Waves perJ_Electron or J_Photon. From the outside Crest of
J_wave the J_Photon the same number of J_waves 137 that J_Electron J_Radiates when an J_Electron leaves an outer higher energy level for the next orbit in for this number of J_Waves 137. This was copied here to illustrate how small J_Waves are.
12915 As well as above 31815 Copy:"12615 J_Paradigm J_Photon's J_Mass is new and unique is Disclosed here being different than priorart above with J_String being smaller component of the priorart. The J_CosmicJ_String that fits in the J_ElectronShell circumference J_WaveLength integer number 137 sine like wavelengths. The J_Spiral out from J_Proton of which one of them in J_Probability ends; as a J_Electron others become J_StringJ_AetherJ_Fabric of J_Universe. J_ElectronsJ_Spin around in a J_ElectronShell. J_Spin of J_Electron in J_ElectronShell forms J_MagneticField with its polarity 90 degrees to plane of J_ElectronJ_Spin." I Will Edit these last 2 earlier post to see if they can be combined in a rewrite.Reviewing The first has the Quark which come from the elementary electron particle which is 137 sine wave lengths so compare mass of quark with the mass of electron.
121215 Collection of subatomic masses:
J_WaveJ_PhotonJ_Mass 6.6491846058394 E 33 kg @ !111015 END Equations Photon Mass <1×10−18 eV/c2 other than 0 is all I get so far.
112315 Copied from Wikipedia:
Measurement  Unit  SI value of unit 
Energy 
eV 
1.602176565(35)×10^{−19} J 
Mass 
eV/c^{2} 
1.782662×10^{−36} kg 
Momentum 
eV/c 
5.344286×10^{−28} kg⋅m/s 
Collect Quark average masses except Top Quark:
– 5–
approaches the percent level, more attention will now have to be
given to sources of systematic uncertainty which have only been
s t udied in a limited way up to now. In particular most current
simulations are performed with degenerate
u
and
d
quarks and
without including electromagnetic effects. Vacuum polarisa
tion
effects are included with
N
f
= 2 + 1 or
N
f
= 2 flavors of sea
quarks, although simulations with charm sea quarks are now
beginning. In earlier
reviews
, results were presented from sim
ulations in which vacuum polarization effects were completel
y
neglected (this is the socalled
quenched
approximation), lead
ing to systematic uncertainties which could not be estimate
d
reliably. It is no longer necessary to include quenched resu
lts in
compilations of quark masses.
D. Light quarks
In this section we review the determination of the masses
of the light quarks
u
,
d
and
s
from lattice simulations and then
discuss the consequences of the approximate chiral symmetr
y.
Lattice Gauge Theory:
The most reliable determinations
of the strange quark mass
m
s
and of the average of the up
and down quark masses
m
ud
= (
m
u
+
m
d
)
/
2 are obtained
from lattice simulations. As explained in section C above, t
he
simulations are performed with degenerate up and down quark
s
(
m
u
=
m
d
) and so it is the average which is obtained directly
from the computations. Below we discuss attempts to derive
m
u
and
m
d
separately using lattice results in combination with
other techniques, but here we briefly present our estimate of
the current status of the latest lattice results. Based larg
ely
on references [19–26], which have among the most reliable
estimates of the systematic errors, our summary is
m
s
= (93
.
5
±
2
.
5) MeV
,
m
ud
= (3
.
40
±
0
.
25) MeV (3)
and
m
s
m
ud
= 27
.
5
±
0
.
3
.
(4)
TThe masses are given in the
MS scheme at a renormalization
sscale of 2 GeV. Because the errors are dominated by systematics, these results are not simply the combinations of all the
121415 Copied from Quora Digest Emailed Me :
Book2.pdf
From Your Quora Digest •
Richard Muller, Professor of Physics, U. Calif. Berkeley, coFounder of Berkeley Earth
112315 Copied from Wikipedia:
According to the present theory, we have no way of finding out. When we extrapolate back to the initial moment of the Big Bang, we run into a mathematical problem known as a "singularity". When that has happened in past theories, it has always meant a failure in the theory, and that may be the case here. But it means we have no means to know.
Physicists speculate on aspects of this. My own feeling is that the singularity is real, and represents both the creation of space and time; that there was no "before". Others speculate that there was a prior universe that collapsed. The key thing is to recognize that speculation by scientists does not constitute science. If you look at the history of science, I don't believe that such speculation was ever accurate. The universe has always turned out to be more interesting than we have been able to anticipate.
Perhaps when we look at the first few seconds of the Big Bang (and we might be able to do this by seeing patterns of gravity waves in the cosmic microwave background polarization) maybe we will discover something that will open a new path to knowledge.
When you integrate a derivative, you get the total change in quantity.
If x is something that changes with time, we denote this as x(t).
(x can be distance traveled, air pressure near your ear, the volume of water in a cell, whatever).
The difference x(b)−x(a) is how much that thing changed between time a and time b. If a is 7am and b is 11am and x denotes how many miles you've biked, x(b)−x(a) is how many miles you've biked between 7am and 11am.
The distance you've covered  or generally, the total change in that quantity  can also be calculated by adding up the little changes that occurred over short periods of time. How much have you traveled between 9:06:03 and 9:06:04? Well, this is one second of travel, so the distance covered in that second is (whatever your speed was at that moment) times (one second). If your speed was 3 meters/sec, you'd have covered 3 meters in that second. If it had been 12 meters/sec, you'd have covered 12 meters.
The kicker is that speed is none other than the rate of change of distance. When you're going slow, the distance grows slowly with every passing second. When you're going fast, the distance grows quickly. This is what a derivative is  it's instantaneous rate of change:
speed = the derivative of distance
rate of change = the derivative of the quantity that is changing.
So,
total distance = sum over little intervals of (speed) x (length of interval).
or
total change in quantity = sum over little intervals of (derivative) x (length of interval)
but mathematicians call "sum over little intervals" an integral, and they write this fairly simple observation like this:
x(b)−x(a)=∫bax′(t)dt
but you can see that other than the scary notation, this is just what we wrote above: the total change in the quantity x from time a to time b is the sum total of the little changes it underwent over short periods of time, which is its rate of change times the length of the interval.
(The reason we need to take those limiting processes is that "speed" or "rate of change" are instantaneous notions. When you ride a bike, your speed varies within a second, but less so within half a second, and even less so within one tenth of a second.)
This is obviously a very crude overview of what (one form of) the FTC is all about. The thing is, other than subtleties around continuity and differentiability, the theorem really says nothing more than this: when you integrate a derivative, you get the total change in quantity. This makes perfect sense and can therefore serve as an intuitive explanation.
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121515 With the processes of singularity by Richard Muller, Professor of Physics at U. Berkley and Alon Amit PHD in calculus and calculus simplified which may help me my Math language.
The J_Paradigm of J_Singularity is in bottom of J_BlackHole where J_ FifthDimensionBegins.
and ends at J_BigBang of the start of another J_FourthDimension.
121615 I had trouble trying to save 3 times using Windows 10:
2917 Copied from My Quora Digest:Albert
What was Einstein's motivation to develop a new theory of Gravity?
I’d love to know what motivated Einstein to reimagine gravity and develop his General Theory of Relativity, in a time where Newton’s equations for gravity could explain almost anything observed at the time. Thank you! :)
Can you answer this question?
He was not the only one.
Since the development of Maxwells equations in the 1860s, people had tried (& mostly failed) to create a field theory of gravity. Lorentz and Mie tried to cast gravity as a residual electromagnetic force for example.
Other researchers had used srguments from special relativity to show that gravity should not be caused just by mass, but also by energy and momentum.
Then there's the fact that special relativity was incompatible with Newtonian gravity, both because of its infinite propagation speed & its lack of Lorentz invariance (which are connected, it was this lack which doomed attempts to use the retarded potentials approach).
Even given all of that, Einstein did not really concern himself with gravity, until he realised that the equivalence principle allowed him to extend his relativity arguments to gravity.
Even then he was not the only researcher as Mie, Minkowski, Abraham's, Nordstrom and others were busily working on their own approaches.
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OK, first of all… light has no rest mass. That is to say, you cannot bring a photon to a halt and measure its mass. It does not exist, just as photons standing still (in the vacuum) do not exist.
But an actual photon has massenergy. If you were to create a box lined with perfect mirrors and let a ray of light in, bouncing backandforth forever, you could measure, in principle, a small increase in the box’s weight. (And while such a box may not be realizable, something similar does exist: for stars, especially supergiant stars, a significant portion of their mass is in the form of trapped radiation, i.e., a “photon gas”.)
And “something” is not a synonym for “mass”. A photon has other properties, such as its angular momentum. When it comes to gravity, it’s all those properties together that determine how an object produces, or reacts to, a gravitational field. Rest mass is just one of several parameters (albeit at low speeds, in weak fields, as in our everyday experience, it is the most significant of them.)
Finally, as to why the photon is like this: They don’t usually teach this in undergraduate courses, but Maxwell’s equations are mathematical identities. The only thing that is needed to realize them is a (mathematical) definition of the electric charge. It is possible to define the charge differently, and end up with a modified set of equations: the socalled Proca equations, which describe a hypothetical form of electromagnetism in which the photon does have a nonzero rest mass. Why Nature chose Maxwell over Proca… it is not a question physicists may ever be able to answer. Although I note that in actuality, Nature chose both: The Z boson of the weak interaction is, for all practical intents and purposes, just like a very heavy, massive version of the photon.
August 21,