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84-567: The company is a historic contributor to silver halide photography. The company still sells photographic enlargers ; one of the few remaining companies to market the device. The name Charles Beseler Company comes from Charles Beseler, a businessman in Germany in the 19th century who sold magic lanterns and stereopticons . Beseler died in 1909, but his company remained and then moved to New Jersey in 1919. The company manufactured photographic enlargers and other photographic equipment throughout

168-402: A Hermitian operator . In 1924, Satyendra Nath Bose derived Planck's law of black-body radiation without using any electromagnetism, but rather by using a modification of coarse-grained counting of phase space . Einstein showed that this modification is equivalent to assuming that photons are rigorously identical and that it implied a "mysterious non-local interaction", now understood as

252-663: A conduction band (de-localized electron orbital with higher energy than a valence band ) which can be attracted by a sensitivity speck , which is a shallow electron trap, which may be a crystalline defect or a cluster of silver sulfide , gold, other trace elements ( dopant ), or combination thereof, and then combined with an interstitial silver ion to form a silver metal speck. Silver halides are also used to make corrective lenses darken when exposed to ultraviolet light (see photochromism ). Silver halides, except for silver fluoride, are very insoluble in water. Silver nitrate can be used to precipitate halides ; this application

336-422: A film base , glass or paper substrate . The gelatin is a vital part of the emulsion as the protective colloid of appropriate physical and chemical properties. The gelatin may also contain trace elements (such as sulfur ) which increase the light sensitivity of the emulsion , although modern practice uses gelatin without such components. When a silver halide crystal is exposed to light, a sensitivity speck on

420-521: A point-like particle since it is absorbed or emitted as a whole by arbitrarily small systems, including systems much smaller than its wavelength, such as an atomic nucleus (≈10 m across) or even the point-like electron . While many introductory texts treat photons using the mathematical techniques of non-relativistic quantum mechanics, this is in some ways an awkward oversimplification, as photons are by nature intrinsically relativistic. Because photons have zero rest mass , no wave function defined for

504-744: A certain symmetry at every point in spacetime . The intrinsic properties of particles, such as charge , mass , and spin , are determined by gauge symmetry . The photon concept has led to momentous advances in experimental and theoretical physics, including lasers , Bose–Einstein condensation , quantum field theory , and the probabilistic interpretation of quantum mechanics. It has been applied to photochemistry , high-resolution microscopy , and measurements of molecular distances . Moreover, photons have been studied as elements of quantum computers , and for applications in optical imaging and optical communication such as quantum cryptography . The word quanta (singular quantum, Latin for how much )

588-594: 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 black-body radiation carried out over four decades (1860–1900) by various researchers culminated in Max Planck 's hypothesis that

672-513: 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, ranging from radio waves to gamma rays . Photons can also be emitted when a particle and its corresponding antiparticle are annihilated (for example, electron–positron annihilation ). In empty space, the photon moves at c (the speed of light ) and its energy and momentum are related by E = pc , where p

756-467: A choice of measuring either one of two "canonically conjugate" quantities, like the position and the momentum of a particle. According to the uncertainty principle, no matter how the particle is prepared, it is not possible to make a precise prediction for both of the two alternative measurements: if the outcome of the position measurement is made more certain, the outcome of the momentum measurement becomes less so, and vice versa. A coherent state minimizes

840-502: A gauge boson , below.) 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. However, before Compton's experiment showed that photons carried momentum proportional to their wave number (1922), most physicists were reluctant to believe that electromagnetic radiation itself might be particulate. (See, for example,

924-517: A geometric sum. However, Debye's approach failed to give the correct formula for the energy fluctuations of black-body radiation, which were derived by Einstein in 1909. In 1925, Born , Heisenberg and Jordan reinterpreted Debye's concept in a key way. 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

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1008-622: A group, they are often referred to as the silver halides, and are often given the pseudo-chemical notation AgX. Although most silver halides involve silver atoms with oxidation states of +1 (Ag ), silver halides in which the silver atoms have oxidation states of +2 (Ag ) are known, of which silver(II) fluoride is the only known stable one. Silver halides are light-sensitive chemicals, and are commonly used in photographic film and paper. Silver halides are used in photographic film and photographic paper , including graphic art film and paper, where silver halide crystals in gelatin are coated on to

1092-475: A higher energy E i {\displaystyle E_{i}} is proportional to the number N j {\displaystyle N_{j}} of atoms with energy E j {\displaystyle E_{j}} and to the energy density ρ ( ν ) {\displaystyle \rho (\nu )} of ambient photons of that frequency, where B j i {\displaystyle B_{ji}}

1176-504: A higher energy E i {\displaystyle E_{i}} to a lower energy E j {\displaystyle E_{j}} is where A i j {\displaystyle A_{ij}} is the rate constant for emitting a photon spontaneously , and B i j {\displaystyle B_{ij}} is the rate constant for emissions in response to ambient photons ( induced or stimulated emission ). In thermodynamic equilibrium,

1260-455: A light beam may have mixtures of these two values; a linearly polarized light beam will act as if it were composed of equal numbers of the two possible angular momenta. The spin angular momentum of light does not depend on its frequency, and was experimentally verified by C. V. Raman and S. Bhagavantam in 1931. The collision of a particle with its antiparticle can create photons. In free space at least two photons must be created since, in

1344-600: A paper in which he proposed that many light-related phenomena—including black-body radiation and the photoelectric effect —would be better explained by modelling electromagnetic waves as consisting of spatially localized, discrete energy quanta. He called these a light quantum (German: ein Lichtquant ). The name photon derives from the Greek word for light, φῶς (transliterated phôs ). Arthur Compton used photon in 1928, referring to Gilbert N. Lewis , who coined

1428-459: A photon can have all the properties familiar from wave functions in non-relativistic quantum mechanics. In order to avoid these difficulties, physicists employ the second-quantized theory of photons described below, quantum electrodynamics , in which photons are quantized excitations of electromagnetic modes. Another difficulty is finding the proper analogue for the uncertainty principle , an idea frequently attributed to Heisenberg, who introduced

1512-399: A photon is calculated by equations that describe waves. This combination of aspects is known as wave–particle duality . For example, the probability distribution for the location at which a photon might be detected displays clearly wave-like phenomena such as diffraction and interference . A single photon passing through a double slit has its energy received at a point on the screen with

1596-402: A probability distribution given by its interference pattern determined by Maxwell's wave equations . However, experiments confirm that the photon is not a short pulse of electromagnetic radiation; a photon's Maxwell waves will diffract, but photon energy does not spread out as it propagates, nor does this energy divide when it encounters a beam splitter . Rather, the received photon acts like

1680-410: A relatively simple assumption. He 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 ν {\displaystyle h\nu } , where ν {\displaystyle \nu } is the frequency of the electromagnetic mode. Planck's law of black-body radiation follows immediately as

1764-497: A semi-classical, statistical treatment of photons and atoms, which implies a link between the rates at which atoms emit and absorb photons. The condition follows from the assumption that functions of the emission and absorption of radiation by the atoms are independent of each other, and that thermal equilibrium is made by way of the radiation's interaction with the atoms. Consider a cavity in thermal equilibrium with all parts of itself and filled with electromagnetic radiation and that

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1848-450: A semiclassical approach, and, in 1927, succeeded in deriving all the rate constants from first principles within the framework of quantum theory. 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 ; earlier quantum mechanical treatments only treat material particles as quantum mechanical, not

1932-460: A set of uncoupled simple harmonic oscillators . Treated quantum mechanically, the energy levels of such oscillators are known to be E = n h ν {\displaystyle E=nh\nu } , where ν {\displaystyle \nu } is the oscillator frequency. The key new step was to identify an electromagnetic mode with energy E = n h ν {\displaystyle E=nh\nu } as

2016-399: A state with n {\displaystyle n} photons, each of energy h ν {\displaystyle h\nu } . This approach gives the correct energy fluctuation formula. 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

2100-427: A sufficiently large quantity, due to formation of highly soluble complex ions, but they also significantly depress solubility when present in a very small quantity, due to formation of sparingly soluble complex ions. Silver halide can be used to deposit fine details of metallic silver on surfaces, such as film. Because of the chemical stability of metallic silver, this film can be used for archival purposes. For example,

2184-414: A unit related to the illumination of the eye and the resulting sensation of light and was used later in a physiological context. Although Wolfers's and Lewis's theories were contradicted by many experiments and never accepted, the new name was adopted by most physicists very soon after Compton used it. In physics, a photon is usually denoted by the symbol γ (the Greek letter gamma ). This symbol for

2268-483: Is not quantized, but matter appears to obey the laws of quantum mechanics . Although the evidence from chemical and physical experiments for the existence of photons was overwhelming by the 1970s, this evidence could not be considered as absolutely definitive; since it relied on the interaction of light with matter, and a sufficiently complete theory of matter could in principle account for the evidence. Nevertheless, all semiclassical theories were refuted definitively in

2352-509: Is the gauge boson for electromagnetism , and therefore all other quantum numbers of the photon (such as lepton number , baryon number , and flavour quantum numbers ) are zero. Also, the photon obeys Bose–Einstein statistics , and not Fermi–Dirac statistics . That is, they do not obey the Pauli exclusion principle and more than one can occupy the same bound quantum state. Photons are emitted in many natural processes. For example, when

2436-414: Is the magnitude of the momentum vector p . This derives from the following relativistic relation, with m = 0 : The energy and momentum of a photon depend only on its frequency ( ν {\displaystyle \nu } ) or inversely, its wavelength ( λ ): where k is the wave vector , where Since p {\displaystyle {\boldsymbol {p}}} points in

2520-512: Is the rate constant for absorption. For the reverse process, there are two possibilities: spontaneous emission of a photon, or the emission of a photon initiated by the interaction of the atom with a passing photon and the return of the atom to the lower-energy state. Following Einstein's approach, the corresponding rate R i j {\displaystyle R_{ij}} for the emission of photons of frequency ν {\displaystyle \nu } and transition from

2604-427: Is the photon's frequency . The photon has no electric charge , is generally considered to have zero rest mass and is a stable particle . The experimental upper limit on the photon mass is very small, on the order of 10 kg; its lifetime would be more than 10 years. For comparison the age of the universe is about 1.38 × 10 years. In a vacuum, a photon has two possible polarization states. The photon

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2688-444: Is useful in quantitative analysis of halides. The three main silver halide compounds have distinctive colours that can be used to quickly identify halide ions in a solution. The silver chloride compound forms a white precipitate, silver bromide a creamy coloured precipitate and silver iodide a yellow coloured precipitate. Some compounds can considerably increase or decrease the solubility of AgX. Examples of compounds that increase

2772-616: The Arctic World Archive uses film developed with silver halides to store data of historical and cultural interest, such as a snapshot of the Open Source code in all active GitHub repositories as of 2020 . Photon A photon (from Ancient Greek φῶς , φωτός ( phôs, phōtós )  'light') is an elementary particle that is a quantum of the electromagnetic field , including electromagnetic radiation such as light and radio waves , and

2856-499: The center of momentum frame , the colliding antiparticles have no net momentum, whereas a single photon always has momentum (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. The energy of the two photons, or, equivalently, their frequency, may be determined from conservation of four-momentum . Seen another way,

2940-463: The degeneracy of the state i {\displaystyle i} and that of j {\displaystyle j} , respectively, E i {\displaystyle E_{i}} and E j {\displaystyle E_{j}} their energies, k {\displaystyle k} the Boltzmann constant and T {\displaystyle T}

3024-423: 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 Planck's law regarding black-body radiation is accepted, the energy quanta must also carry momentum p = ⁠ h  / λ  ⁠ , making them full-fledged particles. This photon momentum

3108-439: The force carrier for the electromagnetic force . Photons are massless particles that always move at the speed of light measured in vacuum. The photon belongs to the class of boson particles. As with other elementary particles, photons are best explained by quantum mechanics and exhibit wave–particle duality , their behavior featuring properties of both waves and particles . The modern photon concept originated during

3192-483: The photoelectric effect , Einstein introduced the idea that light itself is made of discrete units of energy. In 1926, Gilbert N. Lewis popularized the term photon for these energy units. Subsequently, many other experiments validated Einstein's approach. In the Standard Model of particle physics , photons and other elementary particles are described as a necessary consequence of physical laws having

3276-407: 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 c {\displaystyle E=pc} , and may have extra polarization states; depending on the gauge used, virtual photons may have three or four polarization states, instead of

3360-415: The 1970s and 1980s by photon-correlation experiments. Hence, Einstein's hypothesis that quantization is a property of light itself is considered to be proven. Photons obey the laws of quantum mechanics, and so their behavior has both wave-like and particle-like aspects. When a photon is detected by a measuring instrument, it is registered as a single, particulate unit. However, the probability of detecting

3444-795: The 2000s, the Charles Beseler Company was a supplier to high schools for photography classes in Minnesota and Ontario. This article about an industrial corporation or company is a stub . You can help Misplaced Pages by expanding it . Silver halide A silver halide (or silver salt) is one of the chemical compounds that can form between the element silver (Ag) and one of the halogens . In particular, bromine (Br), chlorine (Cl), iodine (I) and fluorine (F) may each combine with silver to produce silver bromide (AgBr), silver chloride (AgCl), silver iodide (AgI), and four forms of silver fluoride , respectively. As

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3528-515: The 20th century. It also imported the Topcon line of cameras into the US during the time that the company made cameras. Following a three-way merger in 1987, the company introduced other industrial lines to its business, and assumed new ownership. Around 2004, the president died and ownership passed to his wife, with the previous CEO taking on the role of president. From as early as the 1990s and as of

3612-548: 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

3696-470: The Nobel lectures of Wien , Planck and Millikan.) Instead, there was a widespread belief that energy quantization resulted from some unknown constraint on the matter that absorbed or emitted radiation. Attitudes changed over time. In part, the change can be traced to experiments such as those revealing Compton scattering , where it was much more difficult not to ascribe quantization to light itself to explain

3780-438: The atoms can emit and absorb that radiation. Thermal equilibrium requires that the energy density ρ ( ν ) {\displaystyle \rho (\nu )} of photons with frequency ν {\displaystyle \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

3864-530: The average across many interactions between matter and radiation. However, refined Compton experiments showed that the conservation laws hold for individual interactions. Accordingly, Bohr and his co-workers gave their model "as honorable a funeral as possible". Nevertheless, the failures of the BKS model inspired Werner Heisenberg in his development of matrix mechanics . A few physicists persisted in developing semiclassical models in which electromagnetic radiation

3948-486: The coefficients A i j {\displaystyle A_{ij}} , B j i {\displaystyle B_{ji}} and B i j {\displaystyle B_{ij}} once physicists had obtained "mechanics and electrodynamics modified to accommodate the quantum hypothesis". Not long thereafter, in 1926, Paul Dirac derived the B i j {\displaystyle B_{ij}} rate constants by using

4032-418: The concept in analyzing a thought experiment involving an electron and a high-energy photon . However, Heisenberg did not give precise mathematical definitions of what the "uncertainty" in these measurements meant. The precise mathematical statement of the position–momentum uncertainty principle is due to Kennard , Pauli , and Weyl . The uncertainty principle applies to situations where an experimenter has

4116-466: The direction of the photon's propagation, the magnitude of its momentum is The photon also carries spin angular momentum , which is related to photon polarization . (Beams of light also exhibit properties described as orbital angular momentum of light ). The angular momentum of the photon has two possible values, either +ħ or −ħ . These two possible values correspond to the two possible pure states of circular polarization . Collections of photons in

4200-484: The electric field of an atomic nucleus. 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. Current commonly accepted physical theories imply or assume

4284-450: 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 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

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4368-487: The electromagnetic wave, Δ N {\displaystyle \Delta N} , and the uncertainty in the phase of the wave, Δ ϕ {\displaystyle \Delta \phi } . However, this cannot be an uncertainty relation of the Kennard–Pauli–Weyl type, since unlike position and momentum, the phase ϕ {\displaystyle \phi } cannot be represented by

4452-441: 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 , 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

4536-501: 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

4620-411: The first two decades of the 20th century with the work of Albert Einstein , who built upon the research of Max Planck . While Planck was trying to explain how matter and electromagnetic radiation could be in thermal equilibrium with one another, he proposed that the energy stored within a material object should be regarded as composed of an integer number of discrete, equal-sized parts. To explain

4704-418: The galactic vector potential . Although the galactic vector potential is large because the galactic magnetic field exists on great length scales, only the magnetic field would be observable if the photon is massless. In the case that the photon has mass, the mass term ⁠ 1 / 2 ⁠ m A μ A would affect the galactic plasma. The fact that no such effects are seen implies an upper bound on

4788-661: The galactic vector potential have been shown to be model-dependent. If the photon mass is generated via the Higgs mechanism then the upper limit of m ≲ 10  eV/ c from the test of Coulomb's law is valid. In most theories up to the eighteenth century, light was pictured as being made 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), Robert Hooke (1665), and Christiaan Huygens (1678); however, particle models remained dominant, chiefly due to

4872-409: The greatest development and therefore results in the highest optical density. Silver bromide and silver chloride may be used separately or combined, depending on the sensitivity and tonal qualities desired in the product. Silver iodide is always combined with silver bromide or silver chloride, except in the case of some historical processes such as the collodion wet plate and daguerreotype , in which

4956-404: The influence of Isaac Newton . In the early 19th century, Thomas Young and August Fresnel clearly demonstrated the interference and diffraction of light, and by 1850 wave models were generally accepted. James Clerk Maxwell 's 1865 prediction that light was an electromagnetic wave – which was confirmed experimentally in 1888 by Heinrich Hertz 's detection of radio waves – seemed to be

5040-458: The iodide is sometimes used alone (generally regarded as necessary if a daguerreotype is to be developed by the Becquerel method, in which exposure to strong red light, which affects only the crystals bearing latent image specks, is substituted for exposure to mercury fumes). Silver fluoride is not used in photography. When absorbed by an AgX crystal, photons cause electrons to be promoted to

5124-455: The light particle determined which of the two paths a single photon would take. 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 was inspired by Einstein's later work searching for a more complete theory. In 1910, Peter Debye derived Planck's law of black-body radiation from

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5208-418: The number of atoms in state i {\displaystyle i} and those in state j {\displaystyle j} must, on average, be constant; hence, the rates R j i {\displaystyle R_{ji}} and R i j {\displaystyle R_{ij}} must be equal. Also, by arguments analogous to the derivation of Boltzmann statistics ,

5292-509: The numbers of photons in the modes, while conserving energy and momentum overall. Dirac was able to derive Einstein's A i j {\displaystyle A_{ij}} and B i j {\displaystyle 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

5376-476: The observed results. 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 so-called BKS theory . An important feature of the BKS theory is how it treated the conservation of energy and the conservation of momentum . In the BKS theory, energy and momentum are only conserved on

5460-472: The opposite direction; he derived Planck's law of black-body 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 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 ,

5544-405: The overall uncertainty as far as quantum mechanics allows. Quantum optics makes use of coherent states for modes of the electromagnetic field. There is a tradeoff, reminiscent of the position–momentum uncertainty relation, between measurements of an electromagnetic wave's amplitude and its phase. This is sometimes informally expressed in terms of the uncertainty in the number of photons present in

5628-400: The photon can be considered as its own antiparticle (thus an "antiphoton" is simply a normal photon with opposite momentum, equal polarization, and 180° out of phase). The reverse process, pair production , is the dominant mechanism by which high-energy photons such as gamma rays lose energy while passing through matter. That process is the reverse of "annihilation to one photon" allowed in

5712-472: The photon mass of m < 3 × 10  eV/ c . The galactic vector potential can also be probed directly by measuring the torque exerted on a magnetized ring. Such methods were used to obtain the sharper upper limit of 1.07 × 10  eV/ c (the equivalent of 10   daltons ) given by the Particle Data Group . These sharp limits from the non-observation of the effects caused by

5796-467: The photon probably derives from gamma rays , which were discovered in 1900 by Paul Villard , named by Ernest Rutherford in 1903, and shown to be a form of electromagnetic radiation in 1914 by Rutherford and Edward Andrade . In chemistry and optical engineering , photons are usually symbolized by hν , which is the photon energy , where h is the Planck constant and the Greek letter ν ( nu )

5880-473: The photon to be strictly massless. If photons were not purely massless, their speeds would vary with frequency, with lower-energy (redder) photons moving slightly slower than higher-energy photons. Relativity would be unaffected by this; the so-called speed of light, c , would then not be the actual speed at which light moves, but a constant of nature which is the upper bound on speed that any object could theoretically attain in spacetime. Thus, it would still be

5964-444: The rate at which they are absorbed . Einstein began by postulating simple proportionality relations for the different reaction rates involved. In his model, the rate R j i {\displaystyle R_{ji}} for a system to absorb a photon of frequency ν {\displaystyle \nu } and transition from a lower energy E j {\displaystyle E_{j}} to

6048-524: The ratio of N i {\displaystyle N_{i}} and N j {\displaystyle N_{j}} is g i / g j exp ⁡ ( E j − E i ) / ( k T ) , {\displaystyle g_{i}/g_{j}\exp {(E_{j}-E_{i})/(kT)},} where g i {\displaystyle g_{i}} and g j {\displaystyle g_{j}} are

6132-405: 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. It

6216-615: The solubility include: cyanide, thiocyanate, thiosulfate, thiourea , amines, ammonia, sulfite, thioether, crown ether. Examples of compounds that reduces the solubility include many organic thiols and nitrogen compounds that do not possess solubilizing group other than mercapto group or the nitrogen site, such as mercaptooxazoles, mercaptotetrazoles, especially 1-phenyl-5-mercaptotetrazole, benzimidazoles, especially 2-mercaptobenzimidazole, benzotriazole, and these compounds further substituted by hydrophobic groups. Compounds such as thiocyanate and thiosulfate enhance solubility when they are present in

6300-465: The speed of light. If Coulomb's law is not exactly valid, then that would allow the presence of an electric field to exist within a hollow conductor when it is subjected to an external electric field. This provides a means for precision tests of Coulomb's law . A null result of such an experiment has set a limit of m ≲ 10  eV/ c . Sharper upper limits on the mass of light have been obtained in experiments designed to detect effects caused by

6384-412: The speed of spacetime ripples ( gravitational waves and gravitons ), but it would not be the speed of photons. If a photon did have non-zero 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

6468-501: The summation as well; for example, two photons may interact indirectly through virtual electron – positron pairs . Such photon–photon scattering (see two-photon physics ), as well as electron–photon scattering, is meant to be one of the modes of operations of the planned particle accelerator, the International Linear Collider . In modern physics notation, the quantum state of the electromagnetic field

6552-431: The surface of the crystal is turned into a speck of metallic silver (these comprise the invisible or latent image ). If the speck of silver contains approximately four or more atoms, it is rendered developable - meaning that it can undergo development which turns the entire crystal into metallic silver. Areas of the emulsion receiving larger amounts of light (reflected from a subject being photographed, for example) undergo

6636-587: The system's temperature . From this, it is readily derived that g i B i j = g j B j i {\displaystyle g_{i}B_{ij}=g_{j}B_{ji}} and The A i j {\displaystyle A_{ij}} and B i j {\displaystyle B_{ij}} are collectively known as the Einstein coefficients . Einstein could not fully justify his rate equations, but claimed that it should be possible to calculate

6720-578: The term in a letter to Nature on 18 December 1926. The same name was used earlier but was never widely adopted before Lewis: in 1916 by the American physicist and psychologist Leonard T. Troland , in 1921 by the Irish physicist John Joly , in 1924 by the French physiologist René Wurmser (1890–1993), and in 1926 by the French physicist Frithiof Wolfers (1891–1971). The name was suggested initially as

6804-423: 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

6888-441: Was later used by Lene Hau to slow, and then completely stop, light in 1999 and 2001. The modern view on this is that photons are, by virtue of their integer spin, bosons (as opposed to fermions with half-integer spin). By the spin-statistics theorem , all bosons obey Bose–Einstein statistics (whereas all fermions obey Fermi–Dirac statistics ). In 1916, Albert Einstein showed that Planck's radiation law could be derived from

6972-499: Was observed experimentally by Arthur Compton , for which he received the Nobel Prize in 1927. The pivotal question then, was 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, and was solved in quantum electrodynamics and its successor, the Standard Model . (See § Quantum field theory and § As

7056-537: Was used before 1900 to mean particles or amounts of different quantities , including electricity . In 1900, the German physicist Max Planck was studying black-body radiation , and he suggested that the experimental observations, specifically at shorter wavelengths , would be explained if the energy stored within a molecule was a "discrete quantity composed of an integral number of finite equal parts", which he called "energy elements". In 1905, Albert Einstein published

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