Is photon happier? No mass of rest, travel at the speed of light, don’t experience time and space, existing in all places and all times simultaneously. And can provide us with so much information about our world. Massless means pure energy. From Einstein’s photon box and Schrödinger’s cat thought experiments to the field of experimental quantum optics that study exactly the intrinsic quantum properties of light.
Photons are fantastic particles and they have remarkable properties. Known also as light and wave: radio waves, microwaves, infrared and ultraviolet, X-rays, and gamma rays. Or bosons (gauge bosons, force-carrying particles that enable matter particles to interact via the fundamental forces). Or quanta. Or excitation. Depending on the perspective. The Higgs boson (how when you are massless to acquire a mass story, i.e. mass generation) decays into pairs of photons. A particle with the expected properties was discovered in 2012 by the ATLAS and CMS experiments at the Large Hadron Collider (LHC) at CERN.
Colliding two photons creates a positron-electron pair (the Breit–Wheeler process or Breit–Wheeler pair production), meaning matter and antimatter. Real or virtual? In particle physics, virtual particles appear only for brief instants and don’t carry their normal masses. The photons produced by the electromagnetic interaction are virtual. For a true Breit-Wheeler process, you need two real photons to collide.
A team of physicists is now claiming the first direct observation of the long-sought Breit-Wheeler process, in which two particles of light, or photons, crash into one another and produce an electron and its antimatter counterpart, a positron. But like a discussion from an introductory philosophy course, the detection’s significance hinges on the definition of the word “real.” Some physicists argue the photons don’t qualify as real, raising questions about the observation’s implications…
In the Relativistic Heavy Ion Collider, atomic nuclei travel at nearly the speed of light before ramming into one another. Those speedy nuclei are surrounded by electromagnetic fields, and those fields have photons associated with them. Normally, such photons from electromagnetic fields are virtual. But in the experiment, the photons act as if they are real due to the high speeds at which the two nuclei are zipping along.
Fig. 1 A view of one of the first full-energy collisions between gold ions at Brookhaven National Laboratory’s Relativistic Heavy Ion Collider, as captured by the Solenoidal Tracker At RHIC (STAR) detector. The tracks indicate the paths taken by thousands of subatomic particles produced in the collisions as they pass through the STAR Time Projection Chamber, a large, 3-D digital camera. (Image courtesy of Brookhaven National Laboratory.) https://www.anl.gov/article/nimbus-and-cloud-computing-meet-star-production-demands
Here is the STAR detector with a superimposed image as in Fig.1 showing particle tracks emerging from a nuclear collision as picked up by the detector, https://www.bnl.gov/newsroom/news.php?a=213067. The process involves accelerating gold ions. When gold ions are accelerated to very high speeds (0.99995c), they are surrounded by a cloud of photons. When two ions miss each other, their two clouds of photons can interact and collide. You detect the electron-positron pairs. When ions move at relativistic speeds, the virtual particles can behave like real photons. The way to distinguish which electron-positron pairs are generated by the Breit-Wheeler process is to look at the angles between the electron and the positron in the pair generated by the collision. Each type of collision – virtual-virtual, virtual-real, and real-real can be identified based on the angle between the two particles produced. The researchers detected and analyzed the angles of over 6000 electron-positron pairs generated during the experiment.
Daniel Brandenburg and colleagues take a different view, akin to a physics version of the classic duck test: If it walks like a duck and quacks like a duck, then it probably is a duck. If the reality of a photon is based only on how it behaves then these would be real photons.
Why not detect the Breit-Wheeler process with light as well, like lasers? [A laser-plasma platform for photon-photon physics: the two-photon Breit–Wheeler process, B Kettle et al 2021 New J. Phys.23 115006, https://iopscience.iop.org/article/10.1088/1367-2630/ac3048/meta. To transform light into matter, an additional energy source is required. Except for the SLAC E-144 experiment, in most cases, this has been provided by a nuclear field, with positrons formed as high-energy gamma raysinteract with matter. The different types of experiments that have been performed, and various others that have been proposed, are reviewed i.e. here [Particle Interactions in High-Temperature Plasmas, Oliver James Pike, PhD Thesis]. Different mechanisms for pair production could be similar to the various mechanisms for ionization. We may relate the Breit-Wheeler process (γγ ‘ → e + e − ) to the photoelectric effect, the multi-photon Breit-Wheeler process is analogous to multi-photon ionization.
Two-photon sources may be combined such that a gamma-ray beam, generated via the bremsstrahlung emission of a GeV electron beam in a solid high-Z target (taken to be gold in this analysis), is fired into a vacuum hohlraum. The gamma rays then interact with the X-rays produced inside the hohlraum. By deflecting away charged particles before the hohlraum using a magnetic field, it is ensured that the photon-photon scattering takes place in a vacuum.
Laser wakefield acceleration is a suitable mechanism for creating narrowly collimated GeV electron beams, containing around 109 particles.
Post-acceleration, the dynamics of the system can, to a first approximation, be described by three QED processes.
Particle Interactions in High-Temperature Plasmas, Oliver James Pike, PhD Thesis
The special theory of relativity is based on two postulates of Albert Einstein. All of the results of special relativity can be derived from them. Quantum electrodynamics (QED) mentioned above is founded upon the Dirac equation, the first theory to successfully unify special relativity and quantum mechanics in 1928. This is the first theory where full agreement between quantum mechanics and special relativity.
Postulate 1: Absolute uniform motion cannot be detected. Or, the laws of physics are the same in all inertial frames
Postulate 2: The speed of light is independent of the motion of the source. Or The speed of light in a vacuum is the same in all inertial frames
An important implication of these postulates is
Postulate 2 (alternate): Every observer measures the same value c for the speed of light.
The special theoryof relativity [https://galileoandeinstein.phys.virginia.edu/lectures/spec_rel.html] describes how different physical properties like mass, length, time intervals, momentum, etc. would appear if viewed by an observer in uniform motion (constant velocity) relative to the observed object. Postulate 1 (the principle of relativity) states that the laws of physics are the same for all observers in uniform motion relative to each other, and there is no absolute frame of reference to measure motion against. The same as Galileo proposed. The absolute frame to which you can compare just does not exist.
Postulate 2 (speed of light) comes from the idea of Maxwell that light behaves as a traveling wave that can propagate in a vacuum at a speed c. In 1868 Maxwell developed equations that predicted that the speed of light is a constant c. In the electromagnetism theory proposed by Maxwell, the velocity of electromagnetic waves is given by
The speed of light is a constant c = 3.00 x108 m/s in a vacuum. c was found not to depend on the velocity of the source or the observer. However, the speed of light does vary in a precise manner with the material it traverses. The speed of light is lower than c in the matter. The speed of light equals c only in a vacuum. Because of that fact, the index of refractionis always greater than or equal to one (n=c/υ).
Einstein’s postulates have important consequences for measuring time intervals, space intervals, and relative velocities. They also require modifications to such concepts as mass, momentum, and energy. In classical physics, time is an absolute quantity: the interval between two events that occurred in the same position would be the same, whoever measures it. However, according to the special theory of relativity, time is not an absolute quantity: it depends upon the motion of the frame of reference.
The frame in which an observer is viewing the event
The proper time interval between the two events is measured within the frame where these events occurred. If an object moves with relativistic speeds (relativistic speeds are speeds that are close to the speed of light), the observer in his frame will measure a time that is longer than the event itself in its own (proper) frame. The time has dilated when compared to the event.
Time dilation can be calculated using the following formula:
where t is the time in the stationary frame of the observer, t0 is the time in the moving frame or the frame where the event occurs (proper time), υ is the speed of the moving frame of reference, and c is the speed of light. Time t > t0 has dilated or stretched due to the relative motion of the observer and the frame of reference of events.
Example. You are on Earth communicating with astronauts in a spaceship traveling at υ =0.9c relative to Earth. The astronauts must give a technical report in two hours. How long will the team on Earth wait for their response? t = 4.5883 hours.
When length contraction occurs, an observer will measure a length shorter than the object itself in its own frame of reference:
where l is the length in the stationary frame in the direction of the observed motion, l0 is the length in the moving frame or the frame where the event is occurring (proper length), υ is the speed of the moving frame of reference, c is the speed of light. Lengthalong the direction of motion has decreased, l<l0.
Example. An observer on Earth is watching a spaceship fly past at υ =0.9c and records its length of l=100m. How long is the length measured by the spaceship’s crew? l0 = 229.42m.
Proper mass is the mass of an object measured by the observer at rest, m0. An object whose mass when measured at rest is m0 will have an increased mass m when observed moving at speed υ. The increased mass m (the relativistic mass) is given by the relation:
The mass of an object in motion increases. The relativistic mass of a particle, when it is at rest in some reference frame, is then called its rest massm. The speed of light c is thus an upper, unattainable limit for the speed of a particle with mass.
An infinite amount of energy is necessary to accelerate a particle with mass to the speed of light.Massless particles, such as photons, always move at the speed of lightbecause all their energy is kinetic.
Example: A particle is accelerated to a speed of υ=0.95c relative to an observer in a laboratory, the laboratory frame. If the particle was originally measured to have a mass of m0=10 grams, what is the mass observed in the laboratory? m=32.026 grams.
And of course, Einstein’s energy-mass relation, where the total energy E and mass m of an object are related by the expression E=mc2 (the rest mass energy). You need huge energy changes to provide measurable mass changes: Δm=ΔE/c2.
In classical mechanics, the momentum of a particle is defined as the product of its mass and its velocity, υ⃗, where υ⃗ is the velocity. In an isolated system of particles, with no net force acting on the system, the system’s total momentum remains constant. The total momentum of a system in classical mechanics is conserved when no external forces are acting on the system, as is the case with collisions. But it is conserved only in the approximation υ ≪ c.
In classical mechanics, the work done by the net force acting on a particle equals the change in the particle’s kinetic energy. In relativistic mechanics, we equate the net force to the rate of change of the relativistic momentum. The magnitude of the relativistic momentum:
where m is the particle’s mass, υ is the particle’s speed, and c is the speed of light. As you can see, p approaches mυ as υ/c approaches zero.
The work done by the net force can then be calculated and set equal to the change in kinetic energy.
The expression for kinetic energy consists of two terms. The first term depends on the speed of the particle υ. The second term, mc2, is independent of the speed. The quantity mc2 is called the rest energy E0 of the particle.
Consequently, thetotalrelativistic energy E is then defined to be the sum of the kinetic energy and the rest energy:
Thus, the work done by an unbalanced force increases the energy from the rest energy mc2 to the final energy mc²/√1−(υ²/c²).
Using the relation above relations for the relativistic momentum and the total relativistic energypc2=Eυ or υ/c=pc/E. Usually, the momentum or energy of a particle is often known rather than the speed. Rewriting the equation for total relativistic energy without speed will give this result:
If the energy of a particle is much greater than its rest energy mc2, the second term on the right side of the equation can be neglected, giving the useful approximation E≈pc for E≫mc2.
The connection our brains make between the size of an object and its weight must be one of those hardwired instincts – part of our automatic physics grokker. Consistently getting it wrong would probably indicate serious brain damage – unless the person just happened to be a quantum physicist.
One of the great rewiring jobs that followed Einstein‘s 1905 discoveries required undoing the big is heavy, small is light instinct and replacing it with exactly the opposite: big is light, small is heavy. As with so much else, it was Einstein who had the first inkling of this Alice-in-Wonderland inversion of logic. What was he smoking at the time? Most likely only his pipe. As always, Einstein’s most far-reaching conclusions flowed out of the simplest imaginary experiments that he did inside his head.
THE BLACK HOLE WAR, MY BATTLE WITH STEPHEN HAWKING TO MAKE THE WORLD SAFE FOR QUANTUM MECHANICS, Leonard Susskind
The mass of an object is measured by its resistance to a force, like the Earth’s gravity. Massless particles are purely energy and gravity affects anything with energy-even a particle that has no mass at all. According to the general theory of relativity, if the density of an object such as a star is great enough, its gravitational attraction will be so great that once inside a critical radius, nothing can escape, not even light or other electromagnetic radiation. The effect of a black hole on objects outside the critical radius is the same as that of any other mass.
Example Positron emission tomography (PET), Fig. 2. Positrons are emitted by radioactive nuclei that have been introduced into the body. An emitted positron with negligible kinetic energy (moving slowly) collides with an electron traveling at the same slow speed in the opposite direction. They undergo annihilation and two quanta of light (photons) are formed. These two photons come off in exactly opposite directions. The positron-electron pair had a momentum zero before their annihilation. Due to the conservation of momentum, the emission of the two photons must be in the opposite direction to receive the momentum zero. The rest energy of a positron plus the rest energy of an electron is 2*0.511 MeV. The are two photons, and each of them will have the rest mass half the available initial rest energy of 2mec2, 0.511 MeV.
Fig. 2 The basic principle of a positron emission tomography (PET) system: A PET detector ring detects a pair of gamma photons with an energy of 511 keV (red arrows) which results from the annihilation of an electron with a positron emitted by the radiotracer (FDG) [Sensors for Positron Emission Tomography Applications, by Wei Jiang et al., Sensors2019, 19(22), 5019; https://doi.org/10.3390/s19225019].
Einstein’s box of light
In the search for a grand unified theory that would wed the small-scale world of quantum mechanics with Einstein’s relativistic description of the universe at large, the most popular current ideas are bereft of observational support from actual experiments. Can thought alone sustain them? How far can we trust logical deduction? Where is the line between scientific intuition and fantasy? Einstein’s legacy offers no certain answers: On one hand, his reliance on the power of thought was a spectacular success. On the other, many of his best-known thought experiments were based on data from real experimentation, such as the classic Michelson-Morley experiment that first measured the constancy of the speed of light. Moreover, Einstein’s fixation on that which can be measured at times blinded him to deeper layers of reality—although even his mistakes in thought experiments contributed to later breakthroughs.
Using a simple thought experiment, Einstein showed that mass is associated with electromagnetic radiation. Consider a box of length L and mass M resting on a frictionless surface. Attached to the left wall of the box is a light source that emits a directed pulse of radiation of energy E, which is completely absorbed in the right wall of the box. According to classical electromagnetic theory, this radiation carries momentum of magnitude p = E/c. The box recoils when the pulse is emitted by the light source (Fig.3).
The box moves a distance Δx in a time Δt with a velocity υ in the opposite direction to the photons, which carry the equivalent of a mass m. Assuming conservation of momentum and energy (for the case υ≪c),
υ is the recoil velocity of the box. The distance Δx traveled by the box in a time Δt is:
Using the formula for υ from above
The center of mass of the box-photon system is
where x1 and x2 is the position of the box and photon, correspondingly. The center of mass at the start of the experiment must be the same as at the end of the experiment.
Photon position x2 initially is 0. Therefore, the relation above takes the form:
From here E=mc2, the sign shows the opposite direction of box movement.
The famous equation E = mc2 was suggested in the Compton Effect in 1923 and later confirmed by the neutron-induced fission reaction first reported by Otto Hahn and Fritz Srassmann in 1938. At about the same time, Hans Bethe presented a model for the thermonuclear reactions in the sun that showed that the age of the sun must be about 4-5 billion years [THOUGHT EXPERIMENTS, EINSTEIN, AND PHYSICS EDUCATION by Art Stinner and Don Metz].
2. This particular thought experiment begins with an adjustable box – empty except for some photons – that can be made bigger or smaller at will. The interior walls are perfectly reflecting mirrors so that the photons trapped in the box bounce back and forth between the mirrored surfaces and can’t leak out. Wave confined in an enclosed region of space cannot have a wavelength longer than the size of the region. Einstein imagined making the box smaller and smaller, while the photons remained trapped inside. As the box shrinks, the wavelength of the photons cannot remain unchanged. The only possibility is that the wavelength of each photon must shrink along with the box. Eventually, the box will become microscopically small and be filled with very high-energy photons – high energy because their wavelength is so short. Further shrinking the box will increase the energy even more.
If the object is massless, as is the case for a photon, then the equation for total relativistic energy (energy-momentum relation) reduces to
if the wavelength λ or wavenumber k is given. Photons have a momentum that is related to their energy and wavelength in a known way: the shorter the wavelength and the higher the energy, the higher the momentum. Let’s recall Einstein’s most famous equation, E = mc2. If the energy in the box increases, so does its mass. Thus, the smaller it becomes, the more its mass increases: small is heavy, and big is light.
Ordinary white light has a continuous spectrum because it contains all the wavelengths in the visible spectrum. If you take atoms and excite them, they emit light of specific wavelengths that are characteristic of the element or the compound. Because the energy of a photon is related to its wavelength by E = hc/λ, a discrete set of wavelengths implies a discrete set of energies. Conservation of energy then implies that if an atom absorbs a photon, its internal energy increases by a discrete amount, an amount equal to the energy of the photon. It also implies that if an atom emits a photon, its internal energy decreases by a discrete amount that is equal to the energy of the photon. That is, the internal energy of an atom is quantized.
3. Fig. 4 shows the famous photon box supposed to keep photons for some time and release them on demand, imagined by Einstein and Bohr to illustrate their debate [N. Bohr, Discussion with Einstein on epistemological problems in atomic physics, in Albert Einstein, Philosopher-Scientist (Ed.: P. A. Shilpp), Harper, San Francisco, (1949)], the consistency check of Heisenberg’s uncertainty principle.
The idea of the experiment is to start with a box filled with radiation hanging stationary in the gravitational field. The total energy of the box and its contents has a well-defined value. Inside the box, a clock opens a small shutter when its hands reach a fixed position. This shutter remains open for a very brief time interval, during which one photon escapes. After the photon’s escape, the box is weighed to determine its mass (energy). Comparison with the initial situation gives the escaped photon energy. Besides, we can read off the internal clock, which tells us how much time has elapsed since the shutter was opened. The weighing is performed by looking at how the center of mass of the box has moved under the influence of gravity since the photon’s escape. The mathematical workout you can see i.e. here or here.
The fact that Bohr had to invoke general relativity to show the coherence of quantum physics is odd if we remark that gravitation is not yet explained by quantum theory [Exploring the Quantum: Atoms, Cavities, and Photons, Serge Haroche & Jean-Michel Raimond, Oxford University Press, 11 ago 2006].
Fig. 4 The Einstein–Bohr photon box
As Bohr tells us, Einstein had devised an ingenious thought experiment (involving a “photon box“) with which he wanted to demonstrate that an individual photon can have both a sharply defined energy and a precisely predictable time of arrival at a detector. If successful, this would mean the demise of the time-uncertainty relation. Einstein himself later maintained that Bohr had misunderstood his intentions: that it was not the validity of the uncertainty relation, but rather the unpalatable implications of complementarity in the case of correlated distant systems that he was targeting. Considered either way, the thought experiment furnishes a remarkable illustration of quantum mechanical complementarity. Denis Diekes and Sandler Lam, Complementarity in the Einstein–Bohr photon box, Am. J. Phys. 76, 838–842 (2008), https://doi.org/10.1119/1.2919740
Relativity thought experiments have even become part of routine technology. Correcting time dilation and gravitational effects is essential to operating the Global Positioning System (GPS). Satellites also provide modern versions of free-falling elevators of the general relativity thought experiments
Quantum optics box of light
Also, quantum thought experiments have become real. Here you need to manipulate and detect single particles WITHOUT destroying them, which is different from particle physics. Repeating the measurements gives access to correlations of various kinds.
Single-atom manipulation experiments were first performed in ion traps [Exploring the Quantum: Atoms, Cavities, and Photons, Serge Haroche & Jean-Michel Raimond, Oxford University Press, 11 ago 2006]. You use Paul (static and oscillating electric field) or Penning traps (static and magnetic fields) to confine the ions in the region of space and you can observe them “live” even with the naked eye [https://medium.com/@anastasiya.khromova17/seeing-atoms-with-the-naked-eye-7ccf73e60666], or using a ICCD, depending on the emitted photons wavelengths. Laser beams are used to manipulate the ion, to cool down its motion in the trap, and to detect it.
Fig. 5 Individually addressing a particular 172Yb ion that is part of a linear Coulomb crystal composed of four 172Yb ions [Individual Addressing of Trapped Ions and Coupling of Motional and Spin States Using rf Radiation M. Johanning, A. Braun, N. Timoney, V. Elman, W. Neuhauser, and Chr. Wunderlich, Phys. Rev. Lett. 102, 073004 – Published 20 February 2009, https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.102.073004].
The sudden changes in fluorescence due to transitions between atomic levels are called quantum jumps. Fig 6. shows the good distinction between the bright and the dark levels. Something that Schrödinger believed could not be observed [Exploring the Quantum: Atoms, Cavities, and Photons, Serge Haroche & Jean-Michel Raimond, Oxford University Press, 11 ago 2006].
Fig. 6 left: Quantum jumps of a single Ca + ion in the temporal evolution of the fluorescence signal, the lower trace shows the switching of the exciting diode laser at 729 nm; right: Histogram of the fluorescence signal visualizing the distinction between the upper and the lower trace [Metastable level lifetimes from electron-shelving measurements with ion clouds and single ions, Martina Knoop, Caroline Champenois, Ga ̈etan Hagel, Marie Houssin, Caroline Lisowski, Michel Vedel, and Fernande Vedel, Eur. Phys. J. D29, 163–171 (2004). https://doi.org/10.1140/epjd/e2004-00022-6].
If photons are stored in a cavity with highly reflecting walls and atoms, sent one by one across the cavity, interacting with them, contrary to the trapped ions, the experiments belong to Cavity Quantum Electrodynamics (CQED). A cavity-QED experiment similar to the gedanken experiment envisioned by Schrödinger is realized by first preparing a Rydberg atom in a superposition of two internal energy eigenstates |e⟩and |g⟩ (Observing the Progressive Decoherence of the “Meter” in a Quantum Measurement, Brune M, Hagley E, Dreyer J, Matre X, Maali A, Wunderlich C, Raimond J M & Haroche S 1996 Phys. Rev. Lett. 77, 4887–4890, https://journals.aps.org/prl/pdf/10.1103/PhysRevLett.77.4887). Then, this quantum system is sent through a cavity containing an electromagnetic field in a Glauber state (a coherent state corresponding to the cat in the Gedanken experiment), |α⟩ whose phase is changed by dispersive interaction (no energy exchange takes place between atom and field) depending on the state of the atom [Quantum measurements and new concepts for experiments with trapped ions, Ch. Wunderlich and Ch. Balzer, https://www.sciencedirect.com/science/article/abs/pii/S1049250X0380006X, https://doi.org/10.1016/S1049-250X(03)80006-X,]. Or suppose you see the CQED as the modern Einstein–Bohr photon box. In that case, the photons are not directly weighed by a pointer attached to a scale, but rather by the atoms that interact with them and carry away, imprinted on their own quantum state, information about the field. This way, photons can be counted without being destroyed, as one could count marbles in a box Fig. 7.
Fig.7 (Color online) Proposed quantum feedback scheme adapted to a microwave cavity QED setup. C: high-Q microwave cavity, B: box producing Rydberg atoms, R1 and R2: low-Q Ramsey cavities, D: atomic field-ionization detector, S and S′: microwave sources coupled to C and R’s, respectively. In a quantum filtering process, a real-time control system analyzes the results of QND measurements of the cavity field and computes the amplitude of a control injection pulse [Quantum feedback by discrete quantum nondemolition measurements: Towards on-demand generation of photon-number states, I. Dotsenko, M. Mirrahimi, M. Brune, S. Haroche, J.-M. Raimond, and P. Rouchon, Phys. Rev. A 80, 013805 – Published 9 July 2009, https://journals.aps.org/pra/abstract/10.1103/PhysRevA.80.013805].
When Schrödinger came up with the idea that a particle could exist in two states at once, he never thought we would be able to directly observe this quantum strangeness. Yet this is exactly what Serge Haroche did when he succeeded in observing a single photon in a trap.
The pioneer scientist must have “a vivid intuitive imagination, for new ideas are not generated by deduction, but by artistically creative imagination.”Max Planck
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