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Particle Information   Name Photon   Caption Photons emitted in a Coherent beam from a Laser   Composition Elementary Particle   Family Boson   Group Gauge Boson   Interaction Electromagnetic   Theorized Albert Einstein (1905–17)   Symbol <math>\gamma\ </math> or <math>\ h   Mass 01   Mean Lifetime Stable Official particle table for gauge and Higgs bosons Retrieved October 24 , 2006   Electric Charge 0   Spin 1 In modern Physics the photon is the Elementary Particle responsible for Electromagnetic phenomena. It is the carrier of Electromagnetic Radiation of all Wavelength s, including Gamma Ray s, X-ray s, Ultraviolet Light , Visible Light , Infrared Light , Microwave s, and Radio Waves . The photon differs from many other elementary particles, such as the Electron and the Quark , in that it has zero rest Mass ; therefore, it travels (in vacuum) at the Speed Of Light , ''c''. Like all Quanta , the photon has both wave and particle properties (“ Wave–particle Duality ”). As a wave, a single photon is distributed over space and shows wave-like phenomena, such as Refraction by a lens and destructive interference when reflected waves cancel each other out; however, as a particle, it can only interact with matter by transferring the amount of energy : where ''h'' is Planck's Constant , ''c'' is the Speed Of Light , and $\backslash lambda$ is its wavelength. This is different from a classical wave, which may gain or lose arbitrary amounts of energy. For visible light the energy carried by a single photon is around a tiny $4\; imes10^\{-19\}$ Joule s; this energy is just sufficient to excite a single molecule in a Photoreceptor Cell of an Eye , thus contributing to Vision .Vimal, R. L. P., Pokorny, J., Smith, V. C., & Shevell, S. K. (1989). Foveal cone thresholds. Vision Res, 29(1), 61-78.http://www.geocities.com/vri98/Vimal-foveal-cone-ratio-VR-1989 Apart from energy a photon also carries Momentum and has a Polarization . It follows the laws of Quantum Mechanics , which means that often these properties do not have a well-defined value for a given photon. Rather, they are defined as a probability to measure a certain polarization, position, or momentum. For example, although a photon can excite a single molecule, it is often impossible to predict beforehand ''which'' molecule will be excited. The above description of a photon as a carrier of electromagnetic radiation is commonly used by physicists. However, in theoretical physics, a photon can be considered as a mediator for any type of electromagnetic interactions, including magnetic fields and electrostatic repulsion between like charges. The modern concept of the photon was developed gradually (1905–17) by is available from Wikisource . 4 5 Also ''Physikalische Zeitschrift'', 18, 121–128 (1917). 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 . Other physicists sought to explain these anomalous observations by ''semiclassical models'', in which light is still described by Maxwell's Equations , but the material objects that emit and absorb light are quantized. Although these semiclassical models contributed to the development of Quantum Mechanics , further experiments proved Einstein's hypothesis that ''light itself'' is Quantized ; the Quanta of light are photons. The photon concept has led to momentous advances in experimental and theoretical physics, such as Laser s, Bose–Einstein Condensation , Quantum Field Theory , and the Probabilistic Interpretation of quantum mechanics. According to the Standard Model of Particle Physics , photons are responsible for producing all Electric and Magnetic Field s, and are themselves the product of requiring that physical laws have a certain Symmetry at every point in Spacetime . The intrinsic properties of photons — such as Charge , Mass and Spin — are determined by the properties of this Gauge Symmetry . The concept of photons is applied to many areas such as Photochemistry , High-resolution Microscopy , and Measurements Of Molecular Distances . Recently, photons have been studied as elements of Quantum Computer s and for sophisticated applications in Optical Communication such as Quantum Cryptography . NOMENCLATURE The photon was originally called a “light quantum” (''das Lichtquant'') by Albert Einstein . The modern name “photon” derives from the Greek Word for light, '''', (transliterated ''phôs''), and was coined in 1926 by the physical chemist Gilbert N. Lewis , who published a speculative theory6 in which photons were “uncreatable and indestructible”. Although Lewis' theory was never accepted — being contradicted by many experiments — his new name, ''photon'', was adopted immediately by most physicists. Isaac Asimov credits Arthur Compton with defining quanta of light as photons in 1927.78 In physics, a photon is usually denoted by the symbol $\backslash gamma\backslash !$, the Greek Letter Gamma . This symbol for the photon probably derives from Gamma Ray s, which were discovered and named in 1900 by Villard 9 10 and shown to be a form of Electromagnetic Radiation in 1914 by Rutherford and Andrade .11 In Chemistry and Optical Engineering , photons are usually symbolized by $h$ u \!, the energy of a photon, where $h\; \backslash !$ is Planck's Constant and the Greek Letter $$ u \! ( Nu ) is the photon's Frequency . Much less commonly, the photon can be symbolized by ''hf'', where its frequency is denoted by ''f''. PHYSICAL PROPERTIES of the exchange of a virtual photon (symbolized by a wavy-line and a gamma, $\backslash gamma\; \backslash ,$) between a Positron and an Electron .]] See Also: Special relativity The photon is , which determine its wavelength $\backslash lambda\; \backslash !$ and its direction of propagation. The photon is the Gauge Boson for Electromagnetism , and therefore all other quantum numbers — such as Lepton Number , Baryon Number , or Strangeness — are exactly zero. Photons are emitted in many natural processes, e.g., when a charge is accelerated, during a molecular, atomic or nuclear transition to a lower energy level, or when or in molecular, atomic or nuclear transitions to a higher energy level. In empty space, the photon moves at $c\; \backslash !$ (the Speed Of Light ) and its Energy $E\; \backslash !$ and Momentum $\backslash mathbf\{p\}$ are related by $E\; =\; c\; \backslash ,\; p\; \backslash !$, where $p\; \backslash !$ is the magnitude of the momentum. For comparison, the corresponding equation for particles with a Mass $m\; \backslash !$ is $E^\{2\}\; =\; c^\{2\}\; p^\{2\}\; +\; m^\{2\}\; c^\{4\}\; \backslash !$, as shown in Special Relativity . The energy and momentum of a photon depend only on its Frequency $$ u \! or, equivalently, its Wavelength $\backslash lambda\; \backslash !$ :$$ E = \hbar\omega = h u = rac{h c}{\lambda} :$\backslash mathbf\{p\}\; =\; \backslash hbar\backslash mathbf\{k\}$ and consequently the magnitude of the momentum is :$$ p = \hbar k = rac{h}{\lambda} = rac{h u}{c} where $\backslash hbar\; =\; h/2\backslash pi\; \backslash !$ (known as Dirac's Constant Or Planck's Reduced Constant ); $\backslash mathbf\{k\}$ is the Wave Vector (with the wave number $k\; =\; 2\backslash pi/\backslash lambda\; \backslash !$ as its magnitude) and $\backslash omega\; =\; 2\backslash pi$ u \! is the Angular Frequency . Notice that $\backslash mathbf\{k\}$ points in the direction of the photon's propagation. The photon also carries Spin Angular Momentum that does not depend on its frequency. The magnitude of its spin is $\backslash sqrt\{2\}\; \backslash hbar$ and the component measured along its direction of motion, its Helicity , must be $\backslash pm\backslash hbar$. These two possible helicities correspond to the two possible Circular Polarization states of the photon (right-handed and left-handed). To illustrate the significance of these formulae, the Annihilation Of A Particle With Its Antiparticle must result in the creation of at least ''two'' photons for the following reason. In the Center Of Mass Frame , the colliding antiparticles have no net momentum, whereas a single photon always has momentum. Hence, Conservation Of Momentum requires that at least two photons are created, with zero net momentum. The energy of the two photons — or, equivalently, their frequency — may be determined from Conservation Of Four-momentum . Seen another way, the photon can be considered as its own antiparticle. The reverse process, Pair Production , is the dominant mechanism by which high-energy photons such as Gamma Ray s lose energy while passing through matter. The classical formulae for the energy and momentum of Electromagnetic Radiation can be re-expressed 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. HISTORICAL DEVELOPMENT See Also: Light 's Double-slit Experiment in 1805 showed that light can act as a Wave , helping to defeat early Particle theories of light.]] 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 however, particle models remained dominant, chiefly due to the influence of Isaac Newton .16 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.17 In 1865, James Clerk Maxwell 's Prediction 18 This article followed a presentation by Maxwell on 8 December 1864 to the Royal Society. that light was an electromagnetic wave — which was confirmed experimentally in 1888 by Heinrich Hertz 's detection of Radio Waves 19 — seemed to be the final blow to particle models of light. 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. At the same time, investigations of Blackbody Radiation carried out over four decades (1860–1900) by various researchers20 Delivered 11 December 1911 . culminated in Max Planck 's Hypothesis 21 22 Delivered 2 June 1920 . that the energy of ''any'' system that absorbs or emits electromagnetic radiation of frequency $$ u is an integer multiple of an energy quantum $E\; =\; h$ u . As shown by Albert Einstein , 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. 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. 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 point-like quanta that move independently of one another, even if the wave itself is spread continuously over space. In 1909 and 1916, Einstein showed that, if for the rest of his life,24 and was solved in Quantum Electrodynamics and its successor, the Standard Model . EARLY OBJECTIONS of the Hydrogen Atom (shown here). Although all semiclassical models have been disproved by experiment, these early atomic models led to Quantum Mechanics .]] Einstein's 1905 predictions were verified experimentally in several ways within the first two decades of the 20th century, as recounted in Robert Millikan 's Nobel lecture.25 Delivered 23 May 1924 . However, before Compton's Experiment showing that photons carried Momentum proportional to their Frequency (1922), most physicists were reluctant to believe that Electromagnetic Radiation itself might be particulate. (See, for example, the Nobel lectures of Wien , Planck and Millikan.) This reluctance is understandable, given the success and plausibility of Maxwell's electromagnetic wave model of light. Therefore, most physicists assumed rather that energy quantization resulted from some unknown constraint on the matter that absorbs or emits radiation. Niels Bohr , Arnold Sommerfeld and others developed atomic models with discrete energy levels that could account qualitatively for the sharp spectral lines and energy quantization observed in the Emission and Absorption of light by atoms; their models agreed excellently with the spectrum of hydrogen, but not with those of other atoms. It was only the Compton scattering of a photon by a ''free'' electron (which can have no energy levels, since it has no internal structure) that convinced most physicists that light itself was quantized. Even after Compton's experiment, Bohr, Hendrik Kramers and John Slater made one last attempt to preserve the Maxwellian continuous electromagnetic field model of light, the so-called BKS model.26 Also '' Zeitschrift Für Physik '', 24, 69 (1924). To account for the then-available data, 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 Emission s 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 1933 . of Quantum Mechanics . A few physicists persisted27 in developing semiclassical models in which Electromagnetic Radiation is not quantized, but matter obeys 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 elegant photon-correlation experiments.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 anti-bunching effect of photons interacting with a beam splitter; this approach was simplified and sources of error eliminated in the photon-anticorrelation 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.) 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 Photons, like all quantum objects, exhibit both wave-like and particle-like properties. Their dual wave–particle nature can be difficult to visualize. The photon displays clearly wave-like phenomena such as Diffraction and Interference on the length scale of its wavelength. For example, a single photon passing through a Double-slit Experiment lands on the screen with a Probability Distribution given by its interference pattern determined by Maxwell's Equations .28 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 . Rather, the photon seems like a Point-like 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 point-like Electron . Nevertheless, the photon is ''not'' a point-like particle whose trajectory is shaped probabilistically by the Electromagnetic Field , as conceived by Einstein and others; that hypothesis was also refuted by the photon-correlation 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). Thought Experiment for locating an Electron (shown in blue) with a high-resolution gamma-ray 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.29 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 rac{\lambda}{\sin heta} where $heta$ is the Aperture Angle of the microscope. Thus, the position uncertainty $\backslash Delta\; x$ can be made arbitrarily small by reducing the wavelength. The momentum of the electron is uncertain, since it received a “kick” $\backslash Delta\; p$ from the light scattering from it into the microscope. If light were ''not'' quantized into photons, the uncertainty $\backslash Delta\; p$ 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 :$$ \Delta p \sim p_{\mathrm{photon}} \sin heta = rac{h}{\lambda} \sin heta giving the product $\backslash Delta\; x\; \backslash Delta\; p\; \backslash ,\; \backslash sim\; \backslash ,\; h$, which is Heisenberg's uncertainty principle. Thus, the entire world is quantized; both matter and fields must obey a consistent set of quantum laws, if either one is to be quantized. The analogous uncertainty principle for photons forbids the simultaneous measurement of the number $n$ of photons (see Fock State and the Second Quantization section below) in an electromagnetic wave and the phase $\backslash phi$ of that wave :$$ \Delta n \Delta \phi > 1 See Coherent State and Squeezed Coherent State for more details.

Einstein did not attempt to justify his rate equations but noted that $A\_\{ij\}$ and $B\_\{ij\}$ should be derivable from a “mechanics and electrodynamics modified to accommodate the quantum hypothesis”. This prediction was borne out in Quantum Mechanics and Quantum Electrodynamics , respectively; both are required to derive Einstein's rate constants from first principles. Paul Dirac derived the $B\_\{ij\}$ rate constants in 1926 using a semiclassical approach,⁴¹ and, in 1927, succeeded in deriving ''all'' the rate constants from first principles.⁴²⁴³ 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 ;^{44 45 46} the earlier quantum mechanics (the quantization of material particles moving in a potential) represents the “first quantization”.

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 light-particle 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. Similarly, Einstein hoped for a more complete theory that would leave nothing to chance, beginning his separation from quantum mechanics. Ironically, Max Born 's Probabilistic Interpretation of the Wave Function ^{47 48} was inspired by Einstein's later work searching for a more complete theory.⁴⁹ Specifically, Born claimed to have been inspired by Einstein's never-published attempts to develop a “ghost-field” theory, in which point-like photons are guided probabilistically by ghost fields that follow Maxwell's equations.


SECOND QUANTIZATION

See Also: Quantum field theory


. A photon corresponds to a unit of energy E=hν in its electromagnetic mode.]]

In 1910, Peter Debye derived Planck's Law Of Black-body Radiation from a relatively simple assumption.⁵⁰ 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 $h$
u \!, where $$
u \! is the frequency of the electromagnetic mode. Planck's law of black-body 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.

In 1925, Born , Heisenberg and Jordan reinterpreted Debye's concept in a key way.⁵¹ As may be shown classically, the Fourier Modes of the Electromagnetic Field — a complete set of electromagnetic plane waves indexed by their wave vector $\backslash mathbf\{k\}$ 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 $E\; =\; nh$
u \!, where $$
u \! is the oscillator frequency. The key new step was to identify an electromagnetic mode with energy $E\; =\; nh$
u \! as a state with $n\; \backslash !$ photons, each of energy $h$
u \!. This approach gives the correct energy fluctuation formula.
are computed by summing over all possible ways in which they can happen, as in the Feynman Diagram shown here.]]

Dirac took this one step further. 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 $A\_\{ij\}\; \backslash !$ and $B\_\{ij\}\; \backslash !$ 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 Black Body Radiation by ''assuming'' BE statistics). In Dirac's time, it was not yet known that all bosons, including photons, must obey BE statistics.

Dirac's second-order 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 $E\; =\; p\; \backslash ,\; c\; \backslash !$, 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 second-order and higher-order 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 .

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