Photon

• 1. The Quantum Of Light

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  A photon has no electric charge, no rest mass, and can travel at only one speed: the speed of light in a vacuum. That is the whole of its physical biography, and yet this massless particle carries every flicker of light, every radio wave, and the entire electromagnetic force that binds matter together. The experimental upper limit on its mass sits near 10 to the minus 53 grams. If it had any mass at all, its lifetime would still exceed 10 to the 18 years. How does something so close to nothing come to carry so much? The answer took the first two decades of the 20th century to assemble. It pulled in Max Planck, Albert Einstein, and a long argument over whether light was a wave or a thing. It produced lasers, quantum field theory, and a strange double life in which a single particle behaves like both a smear of probability and a hard point. This is the story of the photon, the particle that refused to choose.

• 2. Two Faces Of Light

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  Before the eighteenth century, most theories pictured light as made of particles, an idea carried largely by the authority of Isaac Newton. Particle models struggled to explain refraction, diffraction, and birefringence, so wave theories were offered by Rene Descartes in 1637, Robert Hooke in 1665, and Christiaan Huygens in 1678. Yet the particle view held on.

  Thomas Young and August Fresnel changed that in the early 19th century by clearly demonstrating the interference and diffraction of light. By 1850 wave models were generally accepted. James Clerk Maxwell predicted in 1865 that light was an electromagnetic wave, and Heinrich Hertz confirmed it in 1888 by detecting radio waves. To most physicists this looked like the final defeat of particle models.

  Maxwell's theory, however, could not explain everything. It predicted that a light wave's energy depends only on its intensity, not its frequency. But several experiments showed the opposite. Some chemical reactions fire only above a certain frequency threshold, and weaker high-frequency light still works where intense low-frequency light fails. In the photoelectric effect, electrons knocked from a metal plate gain energy tied to the light's frequency, not its intensity. The wave that had just won was already cracking.

• 3. Einstein's Wager

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  Investigations of black-body radiation ran across four decades, from 1860 to 1900, before Max Planck offered a hypothesis. He proposed that the energy a system absorbs or emits at frequency nu must be an integer multiple of an energy quantum. Most physicists assumed this restriction lived in the matter doing the absorbing, not in the light itself.

  In 1905 Albert Einstein took the harder position. He argued that energy quantization was a property of electromagnetic radiation itself. Light, he suggested, could be modeled as spatially localized, discrete energy quanta moving independently, even while the wave spread continuously through space. In 1909 and 1916 he showed that if Planck's law holds, these quanta must also carry momentum, making them full particles. For this explanation of the photoelectric effect, Einstein received the 1921 Nobel Prize in physics.

  Most physicists were reluctant to accept that radiation itself might be particulate. The settling blow came in 1922, when Arthur Compton's experiment showed that photons carried momentum proportional to their wave number, in an effect now called Compton scattering. Compton received the Nobel Prize in 1927 for that work. As recounted in Robert Millikan's 1923 Nobel lecture, Einstein's 1905 energy relationship had been verified by 1916, yet the local quantum concept stayed unsettled until Compton.

• 4. The Last Holdouts

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  Niels Bohr, Hendrik Kramers, and John Slater made one final attempt to save Maxwell's continuous field, in what became known as the BKS theory. Its defining feature was its treatment of conservation: in the BKS theory, energy and momentum are conserved only on average across many interactions, not in each single event.

  Refined Compton experiments demolished that idea by showing the conservation laws hold for individual interactions. Bohr and his co-workers gave their model, in his words, as honorable a funeral as possible. The failure was not wasted. It helped inspire Werner Heisenberg in his development of matrix mechanics.

  A few physicists kept building semiclassical models, in which radiation is not quantized but matter obeys quantum mechanics. By the 1970s the chemical and physical evidence for photons was overwhelming, yet not absolutely definitive, since it all relied on light interacting with matter. The decisive proof came from photon-correlation experiments. In 1974 the first such experiment, by Clauser, reported a violation of a classical Cauchy-Schwarz inequality. In 1977 Kimble and colleagues demonstrated an anti-bunching effect at a beam splitter, an approach simplified by Grangier, Roger, and Aspect in 1986 and refined further by Thorn, Neel, and others in 2004.

• 5. Particle And Wave At Once

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  When a photon is detected by an instrument, it registers as a single particulate unit. Yet the probability of detecting it is calculated using equations that describe waves. This is wave-particle duality. A single photon passing through a double slit lands at a point on the screen, but the probability distribution of where it lands follows the interference pattern set by Maxwell's wave equations.

  A photon is not a short pulse of radiation. Its Maxwell waves diffract, but its energy does not spread out as it travels, nor does it split when it meets a beam splitter. Instead the photon is absorbed or emitted whole, even by systems far smaller than its wavelength, such as an atomic nucleus about 10 to the minus 15 meters across, or the point-like electron.

  Treating photons with non-relativistic quantum mechanics is an awkward oversimplification, because photons are intrinsically relativistic. Since they have zero rest mass, no photon wave function carries all the familiar properties of ordinary wave functions. The uncertainty principle adds its own trouble. Heisenberg introduced the idea analyzing a thought experiment with an electron and a high-energy photon, but the precise mathematical statement is due to Kennard, Pauli, and Weyl. For light there is a tradeoff between an electromagnetic wave's amplitude and its phase, yet phase cannot be represented by a Hermitian operator, so this is not an uncertainty relation of the Kennard-Pauli-Weyl type.

• 6. Statistics And The Laser

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  In a vacuum a photon has two possible polarization states, and it carries spin angular momentum tied to that polarization. Its angular momentum takes one of two values, plus h-bar or minus h-bar, corresponding to the two pure states of circular polarization. A linearly polarized beam behaves as an equal mixture of both. The spin angular momentum of light does not depend on frequency, a fact C. V. Raman and Suri Bhagavantam verified experimentally in 1931.

  Photons obey Bose-Einstein statistics rather than Fermi-Dirac. They do not obey the Pauli exclusion principle, so more than one photon can occupy the same bound quantum state. In 1924 Satyendra Nath Bose derived Planck's law without using electromagnetism, through a modified counting of phase space. Einstein showed this implied photons were rigorously identical and a mysterious non-local interaction, now understood as a symmetric quantum state. This work led to coherent states and the development of the laser.

  Einstein extended Bose's formalism to material particles in the same papers and predicted they would condense into their lowest quantum state at low enough temperatures. This Bose-Einstein condensation was observed experimentally in 1995. Lene Hau later used it to slow light, and then to stop it completely, in 1999 and 2001.

• 7. Building The Quantum Field

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  In 1916 Einstein derived Planck's radiation law from a semi-classical treatment of photons and atoms, linking the rates at which atoms emit and absorb light. His model used simple proportionality relations now known as the Einstein coefficients. He could not fully justify them, but predicted they could be calculated once mechanics and electrodynamics were modified for the quantum hypothesis.

  Peter Debye derived Planck's law in 1910 by decomposing the field in a cavity into its Fourier modes, though his approach failed on the energy fluctuations that Einstein had derived in 1909. In 1925 Born, Heisenberg, and Jordan reinterpreted Debye's modes as uncoupled simple harmonic oscillators, and identified a mode of a given energy with a state holding a certain number of photons. This recovered the correct fluctuation formula.

  Paul Dirac took the decisive step. In 1926 he derived the rate constants by a semiclassical approach, and in 1927 derived all of them from first principles within quantum theory. His work founded quantum electrodynamics, the quantization of the electromagnetic field itself, also called second quantization. Dirac's second-order perturbation theory introduced virtual photons, transient intermediate states that mediate static electric and magnetic interactions. These photons need not satisfy the usual constraints and may carry three or four polarization states rather than the two of real photons. They can never be observed, yet contribute measurably to observable events.

• 8. Photons In The World

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  The photon is one of four gauge bosons in the electroweak interaction, alongside the W-plus, W-minus, and Z-zero that carry the weak force. The electromagnetic field is a gauge field built on the Abelian U(1) symmetry, and the quanta of such a field must be massless, uncharged bosons of integer spin. Sheldon Glashow, Abdus Salam, and Steven Weinberg unified the photon with the W and Z bosons, work that earned them the 1979 Nobel Prize in physics.

  Light through transparent matter moves slower than c, by a factor called the refractive index. In a particle picture, the photon blends with quantum excitations of the matter to form quasi-particles called polaritons, which have nonzero effective mass and so cannot travel at c. Inside the Sun, photons scatter so often in the radiative zone that radiant energy takes about a million years to reach the convection zone. Photons leaving the Sun's photosphere reach Earth in only 8.3 minutes.

  A single photon can break chemical bonds or trigger vision. The molecular transition of retinal, formula C20H28O, was identified in 1958 by the biochemist George Wald and co-workers as responsible for sight. Photons now serve as detectors, random number generators, and candidate elements of fast quantum computers, and they anchor quantum cryptography. Two-photon physics studies the rare interactions between photons themselves. In 2018, researchers at the Massachusetts Institute of Technology announced the discovery of bound photon triplets, which may involve polaritons.