Einstein’s annus mirabilis of 1905 is rightly a cause for celebration. In less than seven months, Einstein wrote five history-making papers. He proposed the particle theory of light, developed a method to measure molecular dimensions, explained the long-puzzling Brownian motion, developed the theory of special relativity, and he finished his intellectual sprint by producing the world’s most famous equation, E = mc².

The creative outpouring that Einstein exhibited in 1905 stands alone in the history of physics. After 100 years of sweeping advances in the subject since then, the content of these papers remains at the bedrock of our discipline (see Five papers that shook the world Physics World January 2005 pp16-17). But although all of Einstein’s 1905 papers were fundamental, only one paper was truly revolutionary.

What makes a physics paper revolutionary? Perhaps the most important requirement is that it contains a “big idea”. Next, the big idea must contradict the accepted wisdom of its time. Third, physicists capable of judging the intrinsic merit of the big idea typically reject it until they are forced to accept it. Finally, the big idea must survive and eventually become part of the woodwork of physics.

Only Einstein’s March paper “On a heuristic point of view concerning the production and transformation of light” (Ann. Phys., Lpz 17 132-148) meets these criteria.

Quantum beginnings

The big idea in Einstein’s March paper was his gentle suggestion that light consists of individual, discrete, localized and indivisible quantum particles. This blithely made, audacious claim contradicted a century of compelling empirical evidence, and it challenged the crowning achievement of 19th-century theoretical physics: the electromagnetic theory of light. It can be argued persuasively that Einstein’s March paper was the start of quantum physics.

The quantum idea had been introduced by Max Planck in 1900; however, he did this tentatively and under duress (see “Max Planck: the reluctant revolutionary” by Helge Kragh Physics World December 2000 pp31-35). Planck’s quantum had nothing whatsoever to do with the radiation he sought to explain. Rather, he divided the energies of the vibrating charged oscillators (the source of the black-body radiation) into finite energy elements so that he could find the entropy of the oscillators via Boltzmann’s probabilistic approach. For Planck, the “energy elements” were not physically real, but a mathematical means to his objective. Planck was adamantly opposed to the concept of light quanta.

Einstein’s path to the light quantum was not guided by experimental data: there were no data in 1905 that required light to be particulate. Einstein’s starting point was the obvious contradiction between continuity and discontinuity. Physicists were pleased with their electromagnetic wave theory of light, and were intrigued by atoms and the evidence for subatomic particles. But even the cleverest among Einstein’s contemporaries were not troubled by the continuity of light and the discontinuity of atoms. Einstein, however, was concerned. He recognized the fundamental problems that occur when extended light waves and point-like atoms are brought together – for example, when atoms emit or absorb light. It was this juxtaposition of light and atoms that he addressed in his March paper.

After acknowledging that the wave theory of light had “proved itself splendidly in describing purely optical phenomena”, Einstein immediately points out that “optical observations apply to time averages and not to momentary values”. However, he continues, observations associated with”the production [emission] or conversion [absorption] of light” are not time averages, but involve “momentary values”. Einstein then writes what the science journalist Albrecht Fölsing has called the most “revolutionary” sentence written by a physicist in the 20th century.

“According to the assumption to be contemplated here, when a light ray is spreading from a point, the energy is not distributed continuously over ever-increasing spaces, but consists of a finite number of energy quanta that are localized in points in space, move without dividing, and can be absorbed or generated only as a whole.”

Einstein’s light quantum does not come from a theory that ends with quod est demonstratum. The first two sections of his March paper are tangential to his purpose, and what follows comes from Einstein’s deep well of intuition; specifically, his quantum postulate emerges from an analogy between radiation and an ideal gas. Einstein derives the entropy change at constant temperature of both an ideal gas and radiation when each is compressed from a volume V₀ to a lesser volume V. Employing the Boltzmann principle S = (R/N)lnW – where S is entropy, R is the ideal-gas constant, N is Avogadro’s number and W is the “relative probability” of a state – Einstein extends, by analogy, his results for a sample of an ideal gas to a sample of radiation. He concludes that “radiation…behaves thermodynamically as if it consisted of mutually independent energy quanta of magnitude Rβν/N“, where β is a constant and ν is the frequency of the quanta. The ratio Rβ/N is what we now call the Planck constant, h.

Einstein’s “revolutionary” paper has the strange word “heuristic” in the title. This word means that the “point of view” developed – that is, the light particle – is not in itself justified except as it guides thinking in productive ways. Therefore, at the end of his paper, Einstein demonstrated the efficacy of light quanta by applying them to three different phenomena. These were the photoelectric effect, the ionization of gases by ultraviolet light, and Stokes’ rule, which says that when light of frequency n1 is converted through photoluminescence to light of frequency ν₂ then ν₂≤ν₁. But the phenomenon that demonstrated the efficacy of Einstein’s light quantum most compellingly was (and is) the photoelectric effect.

In time, the photoelectric effect became a staple of physics textbooks. Teachers like it because given all the experimental data, only part of which was known in 1905, the photoelectric effect provides the basis for a simple-minded step to the hypothesis of light quanta. The pedagogical prominence given to the photoelectric effect, as well as the oft-made assumption that Planck proposed the light quantum in his earlier black-body work, have led many physicists to refer to the March paper as the “photoelectric-effect paper”. The fact that Einstein won the Nobel prize for the photoelectric effect has also played a role; in truth, the photoelectric effect was a compromise solution because the Royal Swedish Academy of Sciences did not accept the quantization of light and would not recognize the theory of relativity.

All of this trivializes Einstein’s only revolutionary 1905 paper. Indeed, three reputable physicists who recently debated Einstein’s miracle year on Science Friday – a US radio show – did not once refer to his March paper during the one-hour programme.

Waiting for acceptance

Einstein’s big idea was universally rejected by contemporary physicists; in fact, Einstein’s light quantum was derisively rejected. When Max Planck, in 1913, nominated Einstein for membership of the Prussian Academy of Science in Berlin, he apologized for Einstein by saying, “That sometimes, as for instance in his hypothesis on light quanta, he may have gone overboard in his speculations should not be held against him.” Moreover, Robert Millikan, whose 1916 experimental data points almost literally fell on top of the straight line predicted for the photoelectric effect by Einstein’s quantum paper, could not accept a corpuscular view of light. He characterized Einstein’s paper as a “bold, not to say reckless, hypothesis of an electro-magnetic light corpuscle of energy hν, which…flies in the face of thoroughly established facts of interference” (1916 Phys. Rev. 7 355-358). About the time Millikan wrote these words, Einstein wrote a letter to his friend Michele Besso and said that the existence of “the light quanta is practically certain”.

In his 1922 Nobel address, Niels Bohr rejected Einstein’s light particle. “The hypothesis of light-quanta”, he said, “is not able to throw light on the nature of radiation.” It was not until Arthur Compton’s 1923 X-ray scattering experiment, which showed light bouncing off electrons like colliding billiard balls, that physicists finally accepted Einstein’s idea. Bohr, however, continued to reject the light particle until mid-1925, and had even been willing to sacrifice the conservation of energy to keep the light quantum off the stage of physics.

In 1926 Einstein’s light particle became the photon, named by Gilbert Lewis. Since then, the photon has become omnipresent in physics. Gone is the electromagnetic field spreading continuously through space, and in its place is a quantized field. Gone is Coulomb’s force continuously filling the space between two charges; in its place are two charges exchanging localized photons. With Einstein’s light particle leading the way, the other basic interactions now have their own “photons” that transmit forces through exchanges of specific field quanta. The photon is now ingrained in the woodwork of physics.

Revolutionary thoughts

In 1909, while Einstein’s light quantum was being ignored by physicists, he wrote a paper entitled “On the present status of the radiation problem” (Physikalische. Zeitschrift 10 185-193). In this paper, Einstein acknowledges Planck’s radiation law and writes that it “can be understood if one uses the assumption that the oscillation energy of frequency n can occur only in quanta of magnitude hn”. However, Einstein continues, “it is not sufficient to assume that radiation can only be emitted and absorbed in quanta of this magnitude, i.e. that we are dealing with a property of the emitting or absorbing matter only”.

Then, referring to results mentioned earlier in the paper, Einstein points out that those results are valid “if the radiation consisted of quanta of the indicated magnitude [hn]…The consequences of the theory of light quanta is, in my opinion, one of the most important tasks that the experimental physics of today must solve”.

In his “autobiographical notes” of 1951 – Albert Einstein: Philosopher-Scientist (edited by Paul Schillp) – Einstein said that when Planck introduced the quantum, it “was as if the ground had been pulled out from one, with no firm foundation to be seen anywhere, upon which one could have built”. In the years immediately following 1900, Einstein may well have been the only physicist to fathom the deep significance of Planck’s quantum. Einstein’s light particle forever changed physics by transforming Planck’s quantum from a mathematical convenience to a basic physical concept. That was a revolution.