Tag / photon

Discoveries in physics in the first quarter of the 21st Century.
by David D. Nolte

The Best Physics of the Century (So Far)

Our century is now a quarter complete, from Y2K to today (2000 – 2025).  What have been the greatest discoveries in Physics so far? And what do they portend for the rest of the century?

Every century of physics tends to have its own character:

• The 1600’s were the time of Galileo, Descartes, Huygens, Leibniz and Newton who created the science of dynamics out of nothing. 

• The 1700’s were the time of du Chatelet, Maupertuis, Euler, Lagrange, and D’Alembert who constructed mathematical physics on the foundation of the calculus. 

• The 1800’s were the time of Young, Fresnel, Hamilton, Maxwell, Boltzmann, and Lord Kelvin who completed the program of classical physics. 

• The 1900’s were the time of Einstein and Bohr who invented relativistic and quantum physics and launched the grand program of unified forces.

Now we come to the 2000’s. What will this century be known for?

Two topics physicists have at the top of their mind today is Quantum and AI (and there is even quantum AI).  But AI is merely a tool (though an important one that is radically changing how physics is done), and quantum is a catch-all (almost everything is quantum at its core).

So, what are the greatest breakthroughs of the 21st Century so far?  And what do they portend for the eventual “character” of 21st-Century physics when seen in the rear-view mirror of history by the year 2100?

Single-photon Quantum Information (2001)

The century started on July 24, 2000, when a landmark paper was received by Nature magazine submitted by Emanuel Knill and Raymond Laflamme at Los Alamos National Lab in the United States with Gerald Milburn from the University of Queensland, Australia (collectively known as KLM). This little-heralded paper proposed a radical new idea in quantum information, an idea that would have profound effects on the development of quantum science for the coming quarter-century.

The idea was simply that quantum logic could be performed with single photons and linear optics [1]. Up to that point, most research on quantum optical computing was trying to get photons to interact with each other (which they really don’t like to do) in nonlinear media like crystals or trapped atoms. What KLM showed was that quantum information could be manipulated in general ways without interactions. The paper proposed a technique that could perform quantum logic in a universal way using only linear optical elements like single-photon sources, beam splitters, phase shifters, and single-photon detectors, introducing the novel idea of “measurement-based” quantum computing.

Recovery from Z Linear Optical Quantum Computing
Fig. 0. LOQC circuitry from the KLM paper.

In the quarter-century since the publication of the KLM paper, LOQC has steadily progressed via the development of single-photon sources and detectors. Today, numerous start-ups are pursuing LOQC, notably Xanadu in Toronto, Canada, and PsiQuantum in Palo Alto, USA and Brisbane, Australia. By 2100, this century will likely be viewed as the time when applications of quantum information reached their maturity.  Where the 20th century was a century of discovery of quantum phenomena, the 21st will be the century when it was reduced to practice.

Solar Neutrino Oscillation (2001)

The sun is fueled by the fusion of hydrogen that generates electron neutrinos. The reaction looks like

where p is a proton (hydrogen), 2H is deuterium (a hydrogen nucleus with an extra neutron), e+ is a positron (the anti-matter form of an electron) and ν e is an electron neutrino. This reaction accounts for 99% of the neutrinos generated by the Sun, calculated by the theoretical astrophysicist John Bahcall of the Institute for Advanced Study at Princeton University. Already by the late 1960’s it was suspected that too few of the neutrinos were being detected compared to predictions, so he teamed with Raymond Davis of Brookhaven National Lab to build an experiment to detect the flux of solar neutrinos. To shield the detector from cosmic rays, the experiment was placed at the 4850 level of the Homestake Gold Mine in Lead, South Dakota and operated from 1970 to 1994. The deficit of solar neutrinos was confirmed, and it was huge: Fully two-thirds of expected solar neutrinos were missing!

The simplest solution to the missing solar neutrinos was that they just weren’t there because, on their way to Earth from the Sun, they had converted to something else that was not detectedable. This conversion from one particle to another is possible if neutrinos have a non-zero (but extremely small) mass. If so, then an electron neutrino can convert to a muon neutrino, and if the distance is far enough, they can convert back. In other words, the nature of the neutrino particle is that its identity oscillates. This is called the solar neutrino oscillation, and by the time the neutrinos have arrived at Earth, two-thirds of them have converted to muon neutrinos.

There was a general reluctance to accept neutrino oscillations because it represented a departure from the Standard Model of particle physics and introduced uncomfortably small masses for neutrinos that otherwise behave like massless particles. Two experiments put these qualms to rest: the Super-Kamiokanda expeeriment in Japan and the Sudbury Neutrino Oscillation experiment in Canada. By the early years of the century, neutrino oscillations had been confirmed.

Neutrino oscillations
Fig. 1. Electron neutrinos (black) convert to muon (blue) and tau (red) neutrinos as a function of distance relative to their energy. The value of L/E for solar neutrinos and the Earth is much larger than plotted here, so the effects average out to a net deficit of electron neutrinos. From Ref.

By 2100, the mystery of the ultra-small neutrino masses will likely have been solved.  If the answer falls within the Standard Model, then this may be the crowning achievement that “completes” the standard model.  If the answer falls outside the Standard Model, then this may be the beginning of a new chapter in high-energy physics.

WMAP and Planck (2003)

The Big Bang may have occurred 13.7 billion years ago, but that Bang echoes to this day across the Universe. At its inception, the reverberations were incredibly hot, but they have cooled now to a mere 3 degrees Kelvin. In 1987, Paul Richards and Andrew Lange at the University of California at Berkeley, recorded the peak of the Planck black body spectrum during a sounding rocket flight that carried a far-infrared spectrometer to the edge of space. (The dichroic bandpass filters in their spectrometer were the first far-infrared metamaterials. I designed and built them as a young grad student at Berkeley! [2]) This experiment was followed by the COBE satellite that measured the presence of minuscule fluctuations in the temperature, representing the original heterogeneity of the universe just after the Big Bang.

COBE flew for a year, followed in 1998 by the BOOMerAng experiment, led by Andrew Lange, that was suspended from a high-altitude balloon circling the South Pole for ten days. This experiment discovered the literal echoes of the Big Bang, acoustic oscillations, in other words, the “sound” of the Bang. It also established that the universe is gravitationally “flat”, which is a direct consequence of cosmic inflation. Once again, these findings were followed by a satellite experiment, the WMAP mission in 2003, that mapped these oscillations over the entire sky. Even finer resolution was obtained by the Planck mission in 2013, measuring higher harmonics of the sound oscillations. These oscillations in the early universe helped seed regions of slightly higher density that condensed into galaxies, leading to the large-scale structure of the universe that we see today.

Anisotropy of the cosmic background radiation
Fig. 2. Successively higher resolution views of the echos of the Big Bang from COBE (1992) to WMAP (2003) to Planck (2013). From Ref.

The 21st Century will likely be known as the time when the physics of the early universe was finally pinned down, and maybe even of what can before. The answers may tell us if there are parallel universes in a much larger metaverse.

Exoplanets (2009)

The Earth is not alone in the Universe. It is not even alone in our little neighborhood of the Milky Way. Within 50 light years it is estimated that there are about 1000 Earth-sized planets in the habitable zone of their respective stars. Why is 50 light years significant? It is because, within this century, the technology to explore those planets is likely to be developed. With the right designs, an unmanned probe could reach 50 light years from Earth within a century, and the time to call back home is only 50 years. So if a probe is launched in the year 2100, we could be receiving transmissions from the new planet by the year 2250.

This estimate of 1000 New Earths is the result of a quiet revolution in planetary science that has been unfolding over the past quarter century. The very first exoplanet was confirmed in 1995 by Michel Mayor and Didier Queloz. Today, as of the writing of this blog, there are 6,278 confirmed exoplanets. Most of these were disovered by the Kepler satellite that was launched in 2009.

Kepler exoplanet discoveries
Fig. 3. An artists rendition of several of the Earth-sized planets discovered by the Kepler satellite. From Ref.

By 2100, we will know where all the exoplanets are that are within 50 light years of Earth, and we will know which ones are potential inhabitable.  It may even happen that signs of life on one of these planets will have been discovered.  If so, then it is hard to imagine humankind NOT launching probes to visit those planets.  If the right propulsion technology is developed, then those probes could be signaling back information from those planets as early as the year 2250…if anyone is still here to listen.

The Higgs (2012)

The crowning achievement of high-energy physics may also have been the last nail in the coffin. Throughout the second half of the 20th century, high-energy physics took the lion’s share of money and attention showered on physics. Beginning in the aftermath of the Manhattan Project, the search for the fundamental constituents of our universe at first found more and more particles, creating a “zoo” that resisted easy classification, until quarks were proposed that simplified the whole thing down into what is now called the Standard Model of Physics.

But one piece of the puzzle was still missing–the explanation of why particles have the masses they do. This missing piece was supplied by the theoretical physicist Peter Higgs in 1964 who proposed that point-like massless particles interacted with a “field” that permeated space. The interaction energy was equivalent to mass through Einstein’s famous E = mc2, and the quantization of the field predicted the existence of a “Higgs Boson”. The search for the “Higgs”, as it is called for short, became the Holy Grail of Physics at the end of the last century.

Higgs production, decay and pair processes as Feynman diagrams
Fig. 4. Feynman diagrams that involve the generation of Higgs particles.

The discovery of the Higgs boson was announced on the 4th of July in 2012 [3]. It capped 80 years of progress in high-energy particle physics since the discovery of the positron in 1932. But it may also be the last. Since 2012, over the past 14 years, there have been no new “major” discoveries at the Large Hadron Collider (LHC). Most high-energy talks since then have been about speculative experiments seeking deviations from the Standard Model, but so far there is nothing new.

In the year 2100, looking back, the era of high-energy physics may be relegated to the 20th century, with the Higgs just a finishing touch that tipped over into the new millennium … Or sometime in the next 75 years there will be a discovery that goes beyond standard physics and opens a new chapter in the field. We will have to wait to see.

Gravitational Waves (2015)

Where were you on Nov. 11, 2015 at 10:30 am? Can you remember? I can! I was in a conference room in the Physics Building on the Purdue University Campus waiting with a small crowd of physicists for a news conference to begin. Everyone knew it would be something big. It was. They announced the first detection of a gravitational wave by the LIGO detector (the Laser Interferometric Gravitational Wave Observatory). In a way, it was anti-climactic because we all knew that LIGO would eventually see one. But it was also immensely dramatic, because it was the most sensitive measurement ever made by mankind. The displacement of the mirrors in the interferometer caused by the passing gravitational wave was a tiny fraction of a radius of a proton, yet the signal was as clear as a bell. It came from the merger of two 30 solar-mass black holes in a galaxy far, far away.

First detection of gravitational waves by LIGO
Fig. 5. The two LIGO recordings (at Hanfored and at Livingston) of the first detected gravitaitonal wave. From Ref.

By the year 2100, looking back, multi-messenger astronomy will have been a key part of the physics of the 21st century. Multi-messenger astronomy is when an astronomical event is detected across many detection modes, possibly including light, infrared, ultraviolet, x-ray, neutrino and gravitational wave detection. The field is just beginning and has a long way to go to integrate all these different ways of seeing into a complete picture of what happens out in the universe.

Topological physics (2016)

Of all the topics of this blog, this one is perhaps the most abstract. When we think of geometry, it is natural to think in terms of the symmetries that objects have. The last century was the pinnacle of geometric physics, where Einstein showed that gravity is a geometric property of warped space, where group theory classified all the ways that objects can be constructed and behave, and symmetry breaking was invoked to explain the hierarchy of physical forces.

The new century will be the time of topological physics, where symmetries of matter may not even matter, but the way that properties of matter are connected does. By “property of matter” I mean like the electronic states of a solid state material where the states are excluded from portions of state space, creating topology in abstract spaces. Such topological properties govern how freely currents can flow on surfaces but not in the bulk, or vice versa. In quantum systems, topological properties can protect quantum information from decoherence, which is the bane of most real-world implementations of quantum computers. For instance, by “braiding anyons” it is possible to create qubits that resist dephasing.

Braided anyons at Purdue
Fig. 6. Evidence for the braiding of anyons in the solid state. From Ref.

The importance of topology in physics was recognized with the 2016 Nobel Prize to David J. Thouless, F. Duncan M. Haldane, and J. Michael Kosterlitz for “Theoretical discoveries of topological phase transitions and topological phases of matter.”

Images of Black Holes (2019)

Why hasn’t this gotten a Nobel Prize yet? The imaging of black holes is a tour de force, requiring a telescope with the diameter of a planet, and requiring the collaboration of scientists from across that planet to make it all work.

The physics is straightforward. Everyone knows that bigger telescopes have better resolution, so the logical limit is a telescope the size of the Earth. This is accomplished by using interferometric detection, with data from widely spread millimeter-wave telescopes synchronized by an atomic clock in a network of telescopes known as the Event Horizon Telescope (EHT). The results are constructed numerically, as shown below.

Event Horizon Telescope (EHT) images of a black hole

Fig. 7. The EHT images (left) compared to the model (middle) and the blurred model (right) of the black hole in the M87 galaxy. From Ref.

The next logical step for this kind of imaging is a telescope array that is bigger than the Earth … much bigger! This could be accomplished with an array of Lagrange-point satellites, improving the resolution of the images. By the end of this century, we may be imaging the black holes in all the near-by galaxies.

More to Come?

What are the greatest outstanding problems of physics that may yet yield to solutions within this century? It is impossible to say for certain without a crystal ball, but there are some that are likely to be resolved in the next 75 years:

• Dark Matter: This is the 500 pound gorilla in the room. If most of the tangible universe is made of this stuff, then we had better get around to detecting it!

• Dark Energy: This is the other 500 pound gorilla in the room. If most of the intangible universe is made of this stuff, then we had better get a good understanding of it.

• Quantum Gravity: Of the four forces of physics (gravity, electro-magnetic, weak nuclear and strong nuclear) gravity stands apart in several ways, one of which is that there is no quantum theory for it. We have 75 years to fix this if it is to be a crowning achievement of 21st-Century physics.

• The Evolution of Life: I didn’t include any biophysics in my list of the best physics of the century mainly because I cannot point to a single revolutionary breakthrough of physics in this area. There has been a lot of good progress on the microphysics of biological systems, but nothing like discovering a Higgs boson. This could change if the origins of life turn out to be physics-based rather than just some chemistry.

• The Evolution of Intelligence: I think physics has more to say on the evolution of intelligence than on the evolution of life. Intelligence is the quintessential complex system, and the methods of theoretical physics may yet provide a clear answer to the question of “What is Intelligence?”.

• The Early Universe: This is just starting now with the James Webb Telescope peering into the dark depths of history–nearly to the Big Bang itself.

• Multiple Dimensions: String theory likes to live in 11-dimensional space, so what other parts of our physical universe live there too? Dark Matter? Dark Energy? Do all the extra dimensions need to be compact?

• The Arrow of Time: The physics of time is possibly the greatest unsolved problem in physics. Why does it only go one way?

• Singularity Physics: What happens at the center of a Black Hole? Do wormholes provide hyperspace bypasses? These questions may yet get answers from theoretical physics though likely not from the laboratory unless it is from an AMO analog.

References

[1] E. Knill, R. Laflamme and G. J. Milburn, A Scheme for Efficient Quantum Computation with Linear Optics, Nature 409 (6816), 46–52 (2001).

[2] D. NOLTE, A. LANGE and P. RICHARDS, Far-Infrared Dichroic Bandpass-Filters, Applied Optics 24 (10), 1541–1545 (1985).

[3] CERN. (2012, July 4). CERN experiments observe particle consistent with long-sought Higgs boson [Press release]. https://home.cern/news/press-release/cern/cern-experiments-observe-particle-consistent-long-sought-higgs-boson; ATLAS Collaboration. (2012). Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC. Physics Letters B, 716(1), 1–29. https://doi.org/10.1016/j.physletb.2012.08.020 Cited by: 13000+; CMS Collaboration. (2012). Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC. Physics Letters B, 716(1), 30–61. https://doi.org/10.1016/j.physletb.2012.08.021

by David D. Nolte

The Light in Einstein’s Elevator

Gravity bends light!

Of all the audacious proposals made by Einstein, and there were many, this one takes the cake because it should be impossible.

There can be no force of gravity on light because light has no mass.  Without mass, there is no gravitational “interaction”.  We all know Newton’s Law of gravity … it was one of the first equations of physics we ever learned

Newtonian gravitation

which shows the interaction between the masses M and m through their product.  For light, this is strictly zero. 

How, then did Einstein conclude, in 1907, only two years after he proposed his theory of special relativity, that gravity bends light? If it were us, we might take Newton’s other famous equation and equate the two

Newton's second law

and guess that somehow the little mass m (though it equals zero) cancels out to give

Acceleration

so that light would fall in gravity with the same acceleration as anything else, massive or not. 

But this is not how Einstein arrived at his proposal, because this derivation is wrong!  To do it right, you have to think like an Einstein.

“My Happiest Thought”

Towards the end of 1907, Einstein was asked by Johannes Stark to contribute a review article on the state of the relativity theory to the Jahrbuch of Radioactivity and Electronics. There had been a flurry of activity in the field in the two years since Einstein had published his groundbreaking paper in Annalen der Physik in September of 1905 [1]. Einstein himself had written several additional papers on the topic, along with others, so Stark felt it was time to put things into perspective.

Photo of Einstein around 1905 during his Annis Mirabalis.
Fig. 1 Einstein around 1905.

Einstein was still working at the Patent Office in Bern, Switzerland, which must not have been too taxing, because it gave him plenty of time think. It was while he was sitting in his armchair in his office in 1907 that he had what he later described as the happiest thought of his life. He had been struggling with the details of how to apply relativity theory to accelerating reference frames, a topic that is fraught with conceptual traps, when he had a flash of simplifying idea:

“Then there occurred to me the ‘glucklichste Gedanke meines Lebens,’ the happiest thought of my life, in the following form. The gravitational field has only a relative existence in a way similar to the electric field generated by magnetoelectric induction. Because for an observer falling freely from the roof of a house there exists —at least in his immediate surroundings— no gravitational field. Indeed, if the observer drops some bodies then these remain relative to him in a state of rest or of uniform motion… The observer therefore has the right to interpret his state as ‘at rest.'”[2]

In other words, the freely falling observer believes he is in an inertial frame rather than an accelerating one, and by the principle of relativity, this means that all the laws of physics in the accelerating frame must be the same as for an inertial frame. Hence, his great insight was that there must be complete equivalence between a mechanically accelerating frame and a gravitational field. This is the very first conception of his Equivalence Principle.

Cover of the Jahrbuch for Radioactivity and Electronics from 1907.
Fig. 2 Front page of the 1907 volume of the Jahrbuch. The editor list reads like a “Whos-Who” of early modern physics.

Title page to Einstein's 1907 Jahrbuch review article
Fig. 3 Title page to Einstein’s 1907 Jahrbuch review article “On the Relativity Principle and its Consequences” [3]

After completing his review of the consequences of special relativity in his Jahrbuch article, Einstein took the opportunity to launch into his speculations on the role of the relativity principle in gravitation. He is almost appologetic at the start, saying that:

“This is not the place for a detailed discussion of this question.  But as it will occur to anybody who has been following the applications of the principle of relativity, I will not refrain from taking a stand on this question here.”

But he then launches into his first foray into general relativity with keen insights.

The beginning of the section where Einstein first discusses the effects of accelerating frames and effects of gravity
Fig. 4 The beginning of the section where Einstein first discusses the effects of accelerating frames and effects of gravity.

He states early in his exposition:

“… in the discussion that follows, we shall therefore assume the complete physical equivalence of a gravitational field and a corresponding accelerated reference system.”

Here is his equivalence principle. And using it, in 1907, he derives the effect of acceleration (and gravity) on ticking clocks, on the energy density of electromagnetic radiation (photons) in a gravitational potential, and on the deflection of light by gravity.

Over the next several years, Einstein was distracted by other things, such as obtaining his first university position, and his continuing work on the early quantum theory. But by 1910 he was ready to tackle the general theory of relativity once again, when he discovered that his equivalence principle was missing a key element: the effects of spatial curvature, which launched him on a 5-year program into the world of tensors and metric spaces that culminated with his completed general theory of relativity that he published in November of 1915 [4].

The Observer in the Chest: There is no Elevator

Einstein was never a stone to gather moss. Shortly after delivering his triumphal exposition on the General Theory of Relativity, he wrote up a popular account of his Special and now General Theories to be published as a book in 1916, first in German [5] and then in English [6]. What passed for a “popular exposition” in 1916 is far from what is considered popular today. Einstein’s little book is full of equations that would be somewhat challenging even for specialists. But the book also showcases Einstein’s special talent to create simple analogies, like the falling observer, that can make difficult concepts of physics appear crystal clear.

In 1916, Einstein was not yet thinking in terms of an elevator. His mental image at this time, for a sequestered observer, was someone inside a spacious chest filled with measurement apparatus that the observer could use at will. This observer in his chest was either floating off in space far from any gravitating bodies, or the chest was being pulled by a rope hooked to the ceiling such that the chest accelerates constantly. Based on the measurement he makes, he cannot distinguish between gravitational fields and acceleration, and hence they are equivalent. A bit later in the book, Einstein describes what a ray of light would do in an accelerating frame, but he does not have his observer attempt any such measurement, even in principle, because the deflection of the ray of light from a linear path would be far too small to measure.

But Einstein does go on to say that any curvature of the path of the light ray requires that the speed of light changes with position. This is a shocking admission, because his fundamental postulate of relativity from 1905 was the invariance of the speed of light in all inertial frames. It was from this simple assertion that he was eventually able to derive E = mc2. Where, on the one hand, he was ready to posit the invariance of the speed of light, on the other hand, as soon as he understood the effects of gravity on light, Einstein did not hesitate to cast this postulate adrift.

Position-dependent speed of light in relativity.

Fig. 5 Einstein’s argument for the speed of light depending on position in a gravitational field.

(Einstein can be forgiven for taking so long to speak in terms of an elevator that could accelerate at a rate of one g, because it was not until 1946 that the rocket plane Bell X-1 achieved linear acceleration exceeding 1 g, and jet planes did not achieve 1 g linear acceleration until the F-15 Eagle in 1972.)

Aircraft with greater than 1:1 thrust to weight ratios
Fig. 6 Aircraft with greater than 1:1 thrust to weight ratios.

The Evolution of Physics: Enter Einstein’s Elevator

Years passed, and Einstein fled an increasingly autocratic and belligerent Germany for a position at Princeton’s Institute for Advanced Study. In 1938, at the instigation of his friend Leopold Infeld, they decided to write a general interest book on the new physics of relativity and quanta that had evolved so rapidly over the past 30 years.

Title page of "Evolution of Physics" 1938 written with his friend Leopold Infeld at Princeton's Institute for Advanced Study.
Fig. 7 Title page of “Evolution of Physics” 1938 written with his friend Leopold Infeld at Princeton’s Institute for Advanced Study.

Here, in this obscure book that no-one remembers today, we find Einstein’s elevator for the first time, and the exposition talks very explicitly about a small window that lets in a light ray, and what the observer sees (in principle) for the path of the ray.

One of the only figures in the Einstein and Infeld book: The origin of "Einstein's Elevator"!
Fig. 8 One of the only figures in the Einstein and Infeld book: The origin of “Einstein’s Elevator”!

By the equivalence principle, the observer cannot tell whether they are far out in space, being accelerated at the rate g, or whether they are statinary on the surface of the Earth subject to a gravitational field. In the first instance of the accelerating elevator, a photon moving in a straight line through space would appear to deflect downward in the elevator, as shown in Fig. 9, because the elevator is accelerating upwards as the photon transits the elevator. However, by the equivalence principle, the same physics should occur in the gravitational field. Hence, gravity must bend light. Furthermore, light falls inside the elevator with an acceleration g, just as any other object would.

The accelerating elevator and what an observer inside sees (From "Galileo Unbound" (Oxford, 2018).
Fig. 9 The accelerating elevator and what an observer inside sees (From “Galileo Unbound” (Oxford, 2018). [7])

Light Deflection in the Equivalence Principle

A photon enters an elevator at right angles to its acceleration vector g.  Use the geodesic equation and the elevator (Equivalence Principle) metric [8]

to show that the trajectory is parabolic. (This is a classic HW problem from Introduction to Modern Dynamics.)

Solution:

The geodesic equation with time as the dependent variable

This gives two coordinate equations

Note that x0 = ct and x1 = ct are both large relative to the y-motion of the photon.  The metric component that is relevant here is

and the others are unity.  The geodesic becomes (assuming dy/dt = 0)

The Christoffel symbols are

which give

Therefore

or

where the photon falls with acceleration g, as anticipated.

Light Deflection in the Schwarzschild Metric

Do the same problem of the light ray in Einstein’s Elevator, but now using the full Schwarzschild solution to the Einstein Field equations.

Schwarzschild metric

Solution: 

Einstein’s elevator is the classic test of virtually all heuristic questions related to the deflection of light by gravity.  In the previous Example, the deflection was attributed to the Equivalence Principal in which the observer in the elevator cannot discern whether they are in an acceleration rocket ship or standing stationary on Earth.  In that case, the time-like metric component is the sole cause of the free-fall of light in gravity.  In the Schwarzschild metric, on the other hand, the curvature of the field near a spherical gravitating body also contributes.  In this case, the geodesic equation, assuming that dr/dt = 0 for the incoming photon, is

where, as before, the Christoffel symbol for the radial displacements are

Evaluating one of these

The other Christoffel symbol that contributes to the radial motion is

and the geodesic equation becomes

with

The radial acceleration of the light ray in the elevator is thus

The first term on right is free-fall in gravity, just as was obtained from the Equivalence Principal.  The second term is a higher-order correction caused by curvature of spacetime.  The third term is the motion of the light ray relative to the curved ceiling of the elevator in this spherical geometry and hence is a kinematic (or geometric) artefact.  (It is interesting that the GR correction on the curved-ceiling correction is of the same order as the free-fall term, so one would need to be very careful doing such an experiment … if it were at all measurable.) Therefore, the second and third terms are curved-geometry effects while the first term is the free fall of the light ray.

  

Post-Script: The Importance of Library Collections

I was amused to see the library card of the scanned Internet Archive version of Einstein’s Jahrbuch article, shown below. The volume was checked out in August of 1981 from the UC Berkeley Physics Library. It was checked out again 7 years later in September of 1988. These dates coincide with when I arrived at Berkeley to start grad school in physics, and when I graduated from Berkeley to start my post-doc position at Bell Labs. Hence this library card serves as the book ends to my time in Berkeley, a truly exhilarating place that was the top-ranked physics department at that time, with 7 active Nobel Prize winners on its faculty.

During my years at Berkeley, I scoured the stacks of the Physics Library looking for books and journals of historical importance, and was amazed to find the original volumes of Annalen der Physik from 1905 where Einstein published his famous works. This was the same library where, ten years before me, John Clauser was browsing the stacks and found the obscure paper by John Bell on his inequalities that led to Clauser’s experiment on entanglement that won him the Nobel Prize of 2022.

That library at UC Berkeley was recently closed, as was the Physics Library in my department at Purdue University (see my recent Blog), where I also scoured the stacks for rare gems. Some ancient books that I used to be able to check out on a whim, just to soak up their vintage ambience and to get a tactile feel for the real thing held in my hands, are now not even available through Interlibrary Loan. I may be able to get scans from Internet Archive online, but the palpable magic of the moment of discovery is lost.

References:

[1] Einstein, A. (1905). Zur Elektrodynamik bewegter Körper. Annalen der Physik, 17(10), 891–921.

[2] Pais, A (2005). Subtle is the Lord: The Science and Life of Albert Einstein (Oxford University Press). pg. 178

[3] Einstein, A. (1907). Über das Relativitätsprinzip und die aus demselben gezogenen Folgerungen. Jahrbuch der Radioaktivität und Elektronik, 4, 411–462.

[4] A. Einstein (1915), “On the general theory of relativity,” Sitzungsberichte Der Koniglich Preussischen Akademie Der Wissenschaften, pp. 778-786, Nov.

[5] Einstein, A. (1916). Über die spezielle und die allgemeine Relativitätstheorie (Gemeinverständlich). Braunschweig: Friedr. Vieweg & Sohn.

[6] Einstein, A. (1920). Relativity: The Special and the General Theory (A Popular Exposition) (R. W. Lawson, Trans.). London: Methuen & Co. Ltd.

[7] Nolte, D. D. (2018). Galileo Unbound. A Path Across Life, the Universe and Everything. (Oxford University Press)

[8] Nolte, D. D. (2019). Introduction to Modern Dynamics: Chaos, Networks, Space and Time (Oxford University Press).

Read more in Books by David Nolte at Oxford University Press.
by David D. Nolte

The Many Worlds of the Quantum Beam Splitter

In one interpretation of quantum physics, when you snap your fingers, the trajectory you are riding through reality fragments into a cascade of alternative universes—one for each possible quantum outcome among all the different quantum states composing the molecules of your fingers. 

This is the Many-Worlds Interpretation (MWI) of quantum physics first proposed rigorously by Hugh Everett in his doctoral thesis in 1957 under the supervision of John Wheeler at Princeton University.  Everett had been drawn to this interpretation when he found inconsistencies between quantum physics and gravitation—topics which were supposed to have been his actual thesis topic.  But his side-trip into quantum philosophy turned out to be a one-way trip.  The reception of his theory was so hostile, no less than from Copenhagen and Bohr himself, that Everett left physics and spent a career at the Pentagon.

Resurrecting MWI in the Name of Quantum Information

Fast forward by 20 years, after Wheeler had left Princeton for the University of Texas at Austin, and once again a young physicist was struggling to reconcile quantum physics with gravity.  Once again the many worlds interpretation of quantum physics seemed the only sane way out of the dilemma, and once again a side-trip became a life-long obsession.

David Deutsch, visiting Wheeler in the early 1980’s, became convinced that the many worlds interpretation of quantum physics held the key to paradoxes in the theory of quantum information (For the full story of Wheeler, Everett and Deutsch, see Ref [1]).  He was so convinced, that he began a quest to find a physical system that operated on more information than could be present in one universe at a time.  If such a physical system existed, it would be because streams of information from more than one universe were coming together and combining in a way that allowed one of the universes to “borrow” the information from the other.

It took only a year or two before Deutsch found what he was looking for—a simple quantum algorithm that yielded twice as much information as would be possible if there were no parallel universes.  This is the now-famous Deutsch algorithm—the first quantum algorithm [2].  At the heart of the Deutsch algorithm is a simple quantum interference.  The algorithm did nothing useful—but it convinced Deutsch that two universes were interfering coherently in the measurement process, giving that extra bit of information that should not have been there otherwise.  A few years later, the Deutsch-Josza algorithm [2] expanded the argument to interfere an exponentially larger amount of information streams from an exponentially larger number of universes to create a result that was exponentially larger than any classical computer could produce.  This marked the beginning of the quest for the quantum computer that is running red-hot today.

Deutsch’s “proof” of the many-worlds interpretation of quantum mechanics is not a mathematical proof but is rather a philosophical proof.  It holds no sway over how physicists do the math to make their predictions.  The Copenhagen interpretation, with its “spooky” instantaneous wavefunction collapse, works just fine predicting the outcome of quantum algorithms and the exponential quantum advantage of quantum computing.  Therefore, the story of David Deutsch and the MWI may seem like a chimera—except for one fact—it inspired him to generate the first quantum algorithm that launched what may be the next revolution in the information revolution of modern society.  Inspiration is important in science, because it lets scientists create things that had been impossible before. 

But if quantum interference is the heart of quantum computing, then there is one physical system that has the ultimate simplicity that may yet inspire future generations of physicists to invent future impossible things—the quantum beam splitter.  Nothing in the study of quantum interference can be simpler than a sliver of dielectric material sending single photons one way or another.  Yet the outcome of this simple system challenges the mind and reminds us of why Everett and Deutsch embraced the MWI in the first place.

The Classical Beam Splitter

The so-called “beam splitter” is actually a misnomer.  Its name implies that it takes a light beam and splits it into two, as if there is only one input.  But every “beam splitter” has two inputs, which is clear by looking at the classical 50/50 beam splitter.  The actual action of the optical element is the combination of beams into superpositions in each of the outputs. It is only when one of the input fields is zero, a special case, that the optical element acts as a beam splitter.  In general, it is a beam combiner.

Given two input fields, the output fields are superpositions of the inputs

The square-root of two factor ensures that energy is conserved, because optical fluence is the square of the fields.  This relation is expressed more succinctly as a matrix input-output relation

The phase factors in these equations ensure that the matrix is unitary

reflecting energy conservation.

The Quantum Beam Splitter

A quantum beam splitter is just a classical beam splitter operating at the level of individual photons.  Rather than describing single photons entering or leaving the beam splitter, it is more practical to describe the properties of the fields through single-photon quantum operators

where the unitary matrix is the same as the classical case, but with fields replaced by the famous “a” operators.  The photon operators operate on single photon modes.  For instance, the two one-photon input cases are

where the creation operators operate on the vacuum state in each of the input modes.

The fundamental combinational properties of the beam splitter are even more evident in the quantum case, because there is no such thing as a single input to a quantum beam splitter.  Even if no photons are directed into one of the input ports, that port still receives a “vacuum” input, and this vacuum input contributes to the fluctuations observed in the outputs.

The input-output relations for the quantum beam splitter are

The beam splitter operating on a one-photon input converts the input-mode creation operator into a superposition of out-mode creation operators that generates

The resulting output is entangled: either the single photon exits one port, or it exits the other.  In the many worlds interpretation, the photon exits from one port in one universe, and it exits from the other port in a different universe.  On the other hand, in the Copenhagen interpretation, the two output ports of the beam splitter are perfectly anti-correlated.

Fig. 1  Quantum Operations of a Beam Splitter.  A beam splitter creates a quantum superposition of the input modes.  The a-symbols are quantum number operators that create and annihilate photons.  A single-photon input produces an entangled output that is a quantum superposition of the photon coming out of one output or the other.

The Hong-Ou-Mandel (HOM) Interferometer

When more than one photon is incident on a beam splitter, the fascinating effects of quantum interference come into play, creating unexpected outputs for simple inputs.  For instance, the simplest example is a two photon input where a single photon is present in each input port of the beam splitter.  The input state is represented with single creation operators operating on each vacuum state of each input port

creating a single photon in each of the input ports. The beam splitter operates on this input state by converting the input-mode creation operators into out-put mode creation operators to give

The important step in this process is the middle line of the equations: There is perfect destructive interference between the two single-photon operations.  Therefore, both photons always exit the beam splitter from the same port—never split.  Furthermore, the output is an entangled two-photon state, once more splitting universes.

Fig. 2  The HOM interferometer.  A two-photon input on a beam splitter generates an entangled superposition of the two photons exiting the beam splitter always together.

The two-photon interference experiment was performed in 1987 by Chung Ki Hong and Jeff Ou, students of Leonard Mandel at the Optics Institute at the University of Rochester [4], and this two-photon operation of the beam splitter is now called the HOM interferometer. The HOM interferometer has become a center-piece for optical and photonic implementations of quantum information processing and quantum computers.

N-Photons on a Beam Splitter

Of course, any number of photons can be input into a beam splitter.  For example, take the N-photon input state

The beam splitter acting on this state produces

The quantity on the right hand side can be re-expressed using the binomial theorem

where the permutations are defined by the binomial coefficient

The output state is given by

which is a “super” entangled state composed of N multi-photon states, involving N different universes.

Coherent States on a Quantum Beam Splitter

Surprisingly, there is a multi-photon input state that generates a non-entangled output—as if the input states were simply classical fields.  These are the so-called coherent states, introduced by Glauber and Sudarshan [5, 6].  Coherent states can be described as superpositions of multi-photon states, but when a beam splitter operates on these superpositions, the outputs are simply 50/50 mixtures of the states.  For instance, if the input scoherent tates are denoted by α and β, then the output states after the beam splitter are

This output is factorized and hence is NOT entangled.  This is one of the many reasons why coherent states in quantum optics are considered the “most classical” of quantum states.  In this case, a quantum beam splitter operates on the inputs just as if they were classical fields.

By David D. Nolte, May 8, 2022

Read more in “Interference” (New from Oxford University Press, 2023)

A popular account of the trials and toils of the scientists and engineers who tamed light and used it to probe the universe.

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and at Barnes & Noble

References

[1] David D. Nolte, Interference: The History of Optical Interferometry and the Scientists who Tamed Light, (Oxford, July 2023)

[2] D. Deutsch, “Quantum-theory, the church-turing principle and the universal quantum computer,” Proceedings of the Royal Society of London Series a-Mathematical Physical and Engineering Sciences, vol. 400, no. 1818, pp. 97-117, (1985)

[3] D. Deutsch and R. Jozsa, “Rapid solution of problems by quantum computation,” Proceedings of the Royal Society of London Series a-Mathematical Physical and Engineering Sciences, vol. 439, no. 1907, pp. 553-558, Dec (1992)

[4] C. K. Hong, Z. Y. Ou, and L. Mandel, “Measurement of subpicosecond time intervals between 2 photons by interference,” Physical Review Letters, vol. 59, no. 18, pp. 2044-2046, Nov (1987)

[5] Glauber, R. J. (1963). “Photon Correlations.” Physical Review Letters 10(3): 84.

[6] Sudarshan, E. C. G. (1963). “Equivalence of semiclassical and quantum mechanical descriptions of statistical light beams.” Physical Review Letters 10(7): 277-&.; Mehta, C. L. and E. C. Sudarshan (1965). “Relation between quantum and semiclassical description of optical coherence.” Physical Review 138(1B): B274.

by David D. Nolte

Who Invented the Quantum? Einstein vs. Planck

Albert Einstein defies condensation—it is impossible to condense his approach, his insight, his motivation—into a single word like “genius”.  He was complex, multifaceted, contradictory, revolutionary as well as conservative.  Some of his work was so simple that it is hard to understand why no-one else did it first, even when they were right in the middle of it.  Lorentz and Poincaré spring to mind—they had been circling the ideas of spacetime for decades—but never stepped back to see what the simplest explanation could be.  Einstein did, and his special relativity was simple and beautiful, and the math is just high-school algebra.  On the other hand, parts of his work—like gravitation—are so embroiled in mathematics and the religion of general covariance that it remains opaque to physics neophytes 100 years later and is usually reserved for graduate study. 

Yet there is a third thread in Einstein’s work that relies on pure intuition—neither simple nor complicated—but almost impossible to grasp how he made his leap.  This was the case when he proposed the real existence of the photon—the quantum particle of light.  For ten years after this proposal, it was considered by almost everyone to be his greatest blunder. It even came up when Planck was nominating Einstein for membership in the German Academy of Science. Planck said

That he may sometimes have missed the target of his speculations, as for example, in his hypothesis of light quanta, cannot really be held against him.

In this single statement, we have the father of the quantum being criticized by the father of the quantum discontinuity.

Max Planck’s Discontinuity

In histories of the development of quantum theory, the German physicist Max Planck (1858—1947) is characterized as an unlikely revolutionary.  He was an establishment man, in the stolid German tradition, who was already embedded in his career, in his forties, holding a coveted faculty position at the University of Berlin.  In his research, he was responding to a theoretical challenge issued by Kirchhoff many years ago in 1860 to find the function of temperature and wavelength that described and explained the observed spectrum of radiating bodies.  Planck was not looking for a revolution.  In fact, he was looking for the opposite.  One of his motivations in studying the thermodynamics of electromagnetic radiation was to rebut the statistical theories of Boltzmann.  Planck had never been convinced by the atomistic and discrete approach Boltzmann had used to explain entropy and the second law of thermodynamics.  With the continuum of light radiation he thought he had the perfect system that would show how entropy behaved in a continuous manner, without the need for discrete quantities. 

Therefore, Planck’s original intentions were to use blackbody radiation to argue against Boltzmann—to set back the clock.  For this reason, not only was Planck an unlikely revolutionary, he was a counter-revolutionary.  But Planck was a revolutionary because that is what he did, whatever his original intentions were, and he accepted his role as a revolutionary when he had the courage to stand in front of his scientific peers and propose a quantum hypothesis that lay at the heart of physics.

            Blackbody radiation, at the end of the nineteenth century, was a topic of keen interest and had been measured with high precision.  This was in part because it was such a “clean” system, having fundamental thermodynamic properties independent of any of the material properties of the black body, unlike the so-called ideal gases, which always showed some dependence on the molecular properties of the gas. The high-precision measurements of blackbody radiation were made possible by new developments in spectrometers at the end of the century, as well as infrared detectors that allowed very precise and repeatable measurements to be made of the spectrum across broad ranges of wavelengths. 

In 1893 the German physicist Wilhelm Wien (1864—1928) had used adiabatic expansion arguments to derive what became known as Wien’s Displacement Law that showed a simple linear relationship between the temperature of the blackbody and the peak wavelength.  Later, in 1896, he showed that the high-frequency behavior could be described by an exponential function of temperature and wavelength that required no other properties of the blackbody.  This was approaching the solution of Kirchhoff’s challenge of 1860 seeking a universal function.  However, at lower frequencies Wien’s approximation failed to match the measured spectrum.  In mid-year 1900, Planck was able to define a single functional expression that described the experimentally observed spectrum.  Planck had succeeded in describing black-body radiation, but he had not satisfied Kirchhoff’s second condition—to explain it. 

            Therefore, to describe the blackbody spectrum, Planck modeled the emitting body as a set of ideal oscillators.  As an expert in the Second Law, Planck derived the functional form for the radiation spectrum, from which he found the entropy of the oscillators that produced the spectrum.  However, once he had the form for the entropy, he needed to explain why it took that specific form.  In this sense, he was working backwards from a known solution rather than forwards from first principles.  Planck was at an impasse.  He struggled but failed to find any continuum theory that could work. 

Then Planck turned to Boltzmann’s statistical theory of entropy, the same theory that he had previously avoided and had hoped to discredit.  He described this as “an act of despair … I was ready to sacrifice any of my previous convictions about physics.”  In Boltzmann’s expression for entropy, it was necessary to “count” possible configurations of states.  But counting can only be done if the states are discrete.  Therefore, he lumped the energies of the oscillators into discrete ranges, or bins, that he called “quanta”.  The size of the bins was proportional to the frequency of the oscillator, and the proportionality constant had the units of Maupertuis’ quantity of action, so Planck called it the “quantum of action”. Finally, based on this quantum hypothesis, Planck derived the functional form of black-body radiation.

            Planck presented his findings at a meeting of the German Physical Society in Berlin on November 15, 1900, introducing the word quantum (plural quanta) into physics from the Latin word that means quantity [1].  It was a casual meeting, and while the attendees knew they were seeing an intriguing new physical theory, there was no sense of a revolution.  But Planck himself was aware that he had created something fundamentally new.  The radiation law of cavities depended on only two physical properties—the temperature and the wavelength—and on two constants—Boltzmann’s constant kB and a new constant that later became known as Planck’s constant h = ΔE/f = 6.6×10-34 J-sec.  By combining these two constants with other fundamental constants, such as the speed of light, Planck was able to establish accurate values for long-sought constants of nature, like Avogadro’s number and the charge of the electron.

            Although Planck’s quantum hypothesis in 1900 explained the blackbody radiation spectrum, his specific hypothesis was that it was the interaction of the atoms and the light field that was somehow quantized.  He certainly was not thinking in terms of individual quanta of the light field.

Figure. Einstein and Planck at a dinner held by Max von Laue in Berlin on Nov. 11, 1931.

Einstein’s Quantum

When Einstein analyzed the properties of the blackbody radiation in 1905, using his deep insight into statistical mechanics, he was led to the inescapable conclusion that light itself must be quantized in amounts E = hf, where h is Planck’s constant and f is the frequency of the light field.  Although this equation is exactly the same as Planck’s from 1900, the meaning was completely different.  For Planck, this was the discreteness of the interaction of light with matter.  For Einstein, this was the quantum of light energy—whole and indivisible—just as if the light quantum were a particle with particle properties.  For this reason, we can answer the question posed in the title of this Blog—Einstein takes the honor of being the inventor of the quantum.

            Einstein’s clarity of vision is a marvel to behold even to this day.  His special talent was to take simple principles, ones that are almost trivial and beyond reproach, and to derive something profound.  In Special Relativity, he simply assumed the constancy of the speed of light and derived Lorentz’s transformations that had originally been based on obtuse electromagnetic arguments about the electron.  In General Relativity, he assumed that free fall represented an inertial frame, and he concluded that gravity must bend light.  In quantum theory, he assumed that the low-density limit of Planck’s theory had to be consistent with light in thermal equilibrium in thermal equilibrium with the black body container, and he concluded that light itself must be quantized into packets of indivisible energy quanta [2].  One immediate consequence of this conclusion was his simple explanation of the photoelectric effect for which the energy of an electron ejected from a metal by ultraviolet irradiation is a linear function of the frequency of the radiation.  Einstein published his theory of the quanta of light [3] as one of his four famous 1905 articles in Annalen der Physik in his Annus Mirabilis. 

Figure. In the photoelectric effect a photon is absorbed by an electron state in a metal promoting the electron to a free electron that moves with a maximum kinetic energy given by the difference between the photon energy and the work function W of the metal. The energy of the photon is absorbed as a whole quantum, proving that light is composed of quantized corpuscles that are today called photons.

            Einstein’s theory of light quanta was controversial and was slow to be accepted.  It is ironic that in 1914 when Einstein was being considered for a position at the University in Berlin, Planck himself, as he championed Einstein’s case to the faculty, implored his colleagues to accept Einstein despite his ill-conceived theory of light quanta [4].  This comment by Planck goes far to show how Planck, father of the quantum revolution, did not fully grasp, even by 1914, the fundamental nature and consequences of his original quantum hypothesis.  That same year, the American physicist Robert Millikan (1868—1953) performed a precise experimental measurement of the photoelectric effect, with the ostensible intention of proving Einstein wrong, but he accomplished just the opposite—providing clean experimental evidence confirming Einstein’s theory of the photoelectric effect. 

The Stimulated Emission of Light

About a year after Millikan proved that the quantum of energy associated with light absorption was absorbed as a whole quantum of energy that was not divisible, Einstein took a step further in his theory of the light quantum. In 1916 he published a paper in the proceedings of the German Physical Society that explored how light would be in a state of thermodynamic equilibrium when interacting with atoms that had discrete energy levels. Once again he used simple arguments, this time using the principle of detailed balance, to derive a new and unanticipated property of light—stimulated emission!

Figure. The stimulated emission of light. An excited state is stimulated to emit an identical photon when the electron transitions to its ground state.

The stimulated emission of light occurs when an electron is in an excited state of a quantum system, like an atom, and an incident photon stimulates the emission of a second photon that has the same energy and phase as the first photon. If there are many atoms in the excited state, then this process leads to a chain reaction as 1 photon produces 2, and 2 produce 4, and 4 produce 8, etc. This exponential gain in photons with the same energy and phase is the origin of laser radiation. At the time that Einstein proposed this mechanism, lasers were half a century in the future, but he was led to this conclusion by extremely simple arguments about transition rates.

Figure. Section of Einstein’s 1916 paper that describes the absorption and emission of light by atoms with discrete energy levels [5].

Detailed balance is a principle that states that in thermal equilibrium all fluxes are balanced. In the case of atoms with ground states and excited states, this principle requires that as many transitions occur from the ground state to the excited state as from the excited state to the ground state. The crucial new element that Einstein introduced was to distinguish spontaneous emission from stimulated emission. Just as the probability to absorb a photon must be proportional to the photon density, there must be an equivalent process that de-excites the atom that also must be proportional the photon density. In addition, an electron must be able to spontaneously emit a photon with a rate that is independent of photon density. This leads to distinct coefficients in the transition rate equations that are today called the “Einstein A and B coefficients”. The B coefficients relate to the photon density, while the A coefficient relates to spontaneous emission.

Figure. Section of Einstein’s 1917 paper that derives the equilibrium properties of light interacting with matter. The “B”-coefficient for transition from state m to state n describes stimulated emission. [6]

Using the principle of detailed balance together with his A and B coefficients as well as Boltzmann factors describing the number of excited states relative to ground state atoms in equilibrium at a given temperature, Einstein was able to derive an early form of what is today called the Bose-Einstein occupancy function for photons.

Derivation of the Einstein A and B Coefficients

Detailed balance requires the rate from m to n to be the same as the rate from n to m

where the first term is the spontaneous emission rate from the excited state m to the ground state n, the second term is the stimulated emission rate, and the third term (on the right) is the absorption rate from n to m. The numbers in each state are Nm and Nn, and the density of photons is ρ. The relative numbers in the excited state relative to the ground state is given by the Boltzmann factor

By assuming that the stimulated transition coefficient from n to m is the same as m to n, and inserting the Boltzmann factor yields

The Planck density of photons for ΔE = hf is

which yields the final relation between the spontaneous emission coefficient and the stimulated emission coefficient

The total emission rate is

where the p-bar is the average photon number in the cavity. One of the striking aspects of this derivation is that no assumptions are made about the physical mechanisms that determine the coefficient B. Only arguments of detailed balance are required to arrive at these results.

Einstein’s Quantum Legacy

Einstein was awarded the Nobel Prize in 1921 for the photoelectric effect, not for the photon nor for any of Einstein’s other theoretical accomplishments.  Even in 1921, the quantum nature of light remained controversial.  It was only in 1923, after the American physicist Arthur Compton (1892—1962) showed that energy and momentum were conserved in the scattering of photons from electrons, that the quantum nature of light began to be accepted.  The very next year, in 1924, the quantum of light was named the “photon” by the American American chemical physicist Gilbert Lewis (1875—1946). 

            A blog article like this, that attributes the invention of the quantum to Einstein rather than Planck, must say something about the irony of this attribution.  If Einstein is the father of the quantum, he ultimately was led to disinherit his own brain child.  His final and strongest argument against the quantum properties inherent in the Copenhagen Interpretation was his famous EPR paper which, against his expectations, launched the concept of entanglement that underlies the coming generation of quantum computers.

By David D. Nolte, Jan. 13, 2020

Read more about the History of Light and Optics in

“Interference” (Oxford University Press, 2023)

Read the stories of the scientists and engineers who tamed light and used it to probe the universe.

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Available from Oxford U Press

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Einstein’s Quantum Timeline

1900 – Planck’s quantum discontinuity for the calculation of the entropy of blackbody radiation.

1905 – Einstein’s “Miracle Year”. Proposes the light quantum.

1911 – First Solvay Conference on the theory of radiation and quanta.

1913 – Bohr’s quantum theory of hydrogen.

1914 – Einstein becomes a member of the German Academy of Science.

1915 – Millikan measurement of the photoelectric effect.

1916 – Einstein proposes stimulated emission.

1921 – Einstein receives Nobel Prize for photoelectric effect and the light quantum. Third Solvay Conference on atoms and electrons.

1927 – Heisenberg’s uncertainty relation. Fifth Solvay International Conference on Electrons and Photons in Brussels. “First” Bohr-Einstein debate on indeterminancy in quantum theory.

1930 – Sixth Solvay Conference on magnetism. “Second” Bohr-Einstein debate.

1935 – Einstein-Podolsky-Rosen (EPR) paper on the completeness of quantum mechanics.

Selected Einstein Quantum Papers

Einstein, A. (1905). “Generation and conversion of light with regard to a heuristic point of view.” Annalen Der Physik 17(6): 132-148.

Einstein, A. (1907). “Die Plancksche Theorie der Strahlung und die Theorie der spezifischen W ̈arme.” Annalen der Physik 22: 180–190.

Einstein, A. (1909). “On the current state of radiation problems.” Physikalische Zeitschrift 10: 185-193.

Einstein, A. and O. Stern (1913). “An argument for the acceptance of molecular agitation at absolute zero.” Annalen Der Physik 40(3): 551-560.

Einstein, A. (1916). “Strahlungs-Emission un -Absorption nach der Quantentheorie.” Verh. Deutsch. Phys. Ges. 18: 318.

Einstein, A. (1917). “Quantum theory of radiation.” Physikalische Zeitschrift 18: 121-128.

Einstein, A., B. Podolsky and N. Rosen (1935). “Can quantum-mechanical description of physical reality be considered complete?” Physical Review 47(10): 0777-0780.

Notes

[1] M. Planck, “Elementary quanta of matter and electricity,” Annalen Der Physik, vol. 4, pp. 564-566, Mar 1901.

[2] Klein, M. J. (1964). Einstein’s First Paper on Quanta. The natural philosopher. D. A. Greenberg and D. E. Gershenson. New York, Blaidsdell. 3.

[3] A. Einstein, “Generation and conversion of light with regard to a heuristic point of view,” Annalen Der Physik, vol. 17, pp. 132-148, Jun 1905.

[4] Chap. 2 in “Mind at Light Speed“, by David Nolte (Free Press, 2001)

[5] Einstein, A. (1916). “Strahlungs-Emission un -Absorption nach der Quantentheorie.” Verh. Deutsch. Phys. Ges. 18: 318.

[6] Einstein, A. (1917). “Quantum theory of radiation.” Physikalische Zeitschrift 18: 121-128.