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I'm not simply referring to the notion that Einstein treated the discrete emission and transference of energy (and matter) as "real" physical phenomena, but rather his major continuous role in the development of QM all the way up to Heisenberg Schrodinger's formulation of it. In short, this isn't simply a query of "how Einstein's derivation of light quanta is different than Planck's" but rather why - until recently - people only associate Einstein with the explanation of the photoelectric effect and the Bohr debates when he did SO much more in the field of quantum theory. Even the Nobel committee's acknowledgement of his 1905 paper is a bit of a misnomer: he doesn't merely "explain the photoelectric effect" (although that is one its consequences) but he's the first to actually quantize the radiation field. As physicists, this isn't a small quibble but a substantive difference. It suggests that the committee hadn't fully understand the development of QM from genesis to its 1926 formalism - and with the benefit of hindsight, it's quite clear.

Here's a small exmaple of what I mean. In 1909 Einstein was the first to show that statistical fluctuations in thermal radiation fields display both particlelike and wavelike behaviour; his was the first demonstration of what would later become the principle of complementarity.

Later in 1916, after completing General Relativity, he turned to the interplay of matter and radiation to create a quantum theory of radiation, he once again based his arguments on statistics and fluctuations. Bohr introduced a crucial new concept called stationary states in his 1913 paper on hydrogen but major features of Bohr's model could be interpreted as absolute nonsense because, according to electromagnetic theory, the electron would radiate intensely, emitting a broad spectrum as it crashed into the nucleus. Here we see contradictions in classical laws, and yet major properties of Bohr's hydrogen model rested on those laws.

Einstein, always the original thinker, didn't take as his starting point the well-known field for thermal radiation given by the Planck radiation law. Instead, he assumed that the atoms are in thermal equilibrium and then deduced the properties of the radiation field required to maintain the equilibrium. Guess what? The field turned out to be given precisely by the Planck radiation law. He manages to create quantum effects (stimulated and spontaneous emission) from most classical principles. He uses Wien's displacement law, the canonical Boltzmann distribution, Poynting's theorem, and microscopic reversibility - all classical. The sole quantum idea was the concept of stationary states. And yet from these elements, he's the first to create a complete description of the basic radiation processes and a full description of the general properties of the photon. In his 1917 paper, he creates novel and elegant derivations of Planck's radiation law as well as a proof of Bohr's frequency rule. In it, among many other things, he answers the question of how a gas of atoms maintain the populations of its stationary states in equilibrium with a radiation field.

*The aforementioned novel concept of spontaneous emission, which embodies the FUNDAMENTAL interaction of matter with the vacuum, is a brilliant, Nobel-Prize worthy achievement. Why? Spontaneous emission sets the scale for ALL radiative interactions. The rates of absorption and stimulated emission, for instance, are proportional to the rate for spontaneous emission. Spontaneous emission can be viewed as the ultimate irreversible process and the fundamental source of noise in all of nature. With the development of cavity quantum electrodynamics - the study of atomic systems in close-to-ideal cavities - in the 1980s, the phystical situation was profoundly altered. In such cavities, spontaneous emission evolves into spontaneous-cavity oscillations. Although the dynamical behavior is totally altered, the atom-vacuum interaction that causes spontaneous emission sets the time scale for that evolution. It is first in Einstein's 1917 paper that the photon is demonstrated to possess all the properties of a fundamental excitation, and therefore it is quite clear that his radiation paper played a seminal role in the eventual creation of quantum electrodynamics.

*Apropos the second brilliant creation of his 1917 paper, stimulated emission of radiation, we see the first genesis of the laser. Stimulated emission underlies the basic mechanism of the laser and, by extension, laser cooling; his analysis of momentum transfer in a thermal radiation field can be immediately applied to atomic motion in a laser field. If the spectral width of a thermal field is replaced by the natural linewidth of the atom, Einstein's viscous damping force would give rise to the phenomenon known as optical molasses. This fundamental process of laser cooling was rediscovered by the atomic community in the 80's. Of course, you need Quantum Mechanics for a full realization of all the mechanisms of radiation, but papers like this are seminal contributions to what would eventually become QM.

Einstein's theory of radiaton provided a complete characterization of the particlelike properties of the light quantum and, in retrospect, he was within an arms grasp of working out the statistical mechanics of these particles. Given that his 1905 proposal for the energy quantization of radiation was based on the analogy between entropies of thermal radiation and a system of particles, it is surprising that Einstein didn't extend his method of reasoning to derive the Planck law by treating photons as indistinguishable particles. He was VERY close, and it is quite apparent that Bose himself did not realize he had done anything novel.

Fast forward to 1924 and Einstein, not Bose, applied the reasoning in Bose's treatment of photons as indistinguishable particle to a gas of indistuishable atoms thereby creating Bose-Einstein statistics. Subsequently, Einstein theorized Bose-Einstein condensation, a work for which 6 Nobel Prizes have been given.

I just finished reading A. Douglas Stone's book (Head of Applied Physics at Yale Univ.) - a great theorist in his own right - titled "Einstein and the Quantum: the Quest of the Valiant Swabian." It is a thrilling historical odyssey through the development of quantum mechanics, the best I've read since T.S. Kuhn's brilliant "Black Body Problem and the Quantum Discontinuity."

Stone convincingly argues that Einstein, not Planck, should be regarded as the true father of quantum theory. In the book Stone argues that:

Einstein is well known for his rejection of quantum mechanics in the form it emerged from the work of Heisenberg, Born and Schrodinger in 1926. Much less appreciated are the many seminal contributions he made to quantum theory prior to his final scientific verdict, that the theory was at best incomplete. Einstein’s many conceptual breakthroughs need to be placed in historical context. Einstein, much more than Planck, introduced the concept of quantization of energy in atomic mechanics.

Einstein proposed the photon, the first force-carrying particle discovered for a fundamental interaction, and put forward the notion of wave-particle duality, based on sound statistical arguments 14 years before De Broglie’s work. In fact, after reading the literature, De Broglie's contributions are a bit overrated in my estimation.

As I've pointed out above, Einstein was the first to recognize the intrinsic randomness in atomic processes, and introduced the notion of transition probabilities, embodied in the A and B coefficients for atomic emission and absorption.

Einstein also preceded Born in suggesting the interpretation of wave fields as probability densities for particles, photons, in the case of the electromagnetic field.

As I've already stated above, Einstein, stimulated by Bose, introduced the notion of indistinguishable particles in the quantum sense and derived the condensed phase of bosons, which is one of the fundamental states of matter at low temperatures. His work on quantum statistics in turn directly stimulated Schrodinger towards his discovery of the wave equation of quantum mechanics - a fact that Schrodinger always acknowledged.

Einstein, in the EPR Paradox paper, and intending of course to poke holes in the modern iteration of QM (Schrodinger-Heisenberg-Born-Dirac), was the first to imply the phenomenon of quantum entanglement. Yes, Schrodinger fleshed it out after the fact, but it was the EPR paper which really highlighted that entanglement as the truly bizarre property of QM.

Stone cogently argues that it was only due to his rejection of the final theory that he is not generally recognized as the most central figure in this historic achievement of human civilization.

You can check out the interview on youtube here: https://www.youtube.com/watch?v=anP54GxKgEQ

Here's the Einstein paper Stone stumbled upon that precipitated his investigations: lptms.u-psud.fr/nicolas_pavloff/files/2010/03/Stone-phys_today1

Here's the book's summary (from his interview on NPR with Ira Flatow): http://www.npr.org/2013/11/01/242356997/einsteins-real-breakthrough-quantum-theory

Check this out, it's a great book and it reveals with historical veracity how integral Einstein was in the development of QM. It wasn't just the photoelectric effect, he clearly did much more in QM theory than most people know. His 1906 work on the Specific Heat of Solids is also quite impressive.

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    $\begingroup$ Einstein's got a Nobel prize for quantum mechanics. What "more credit" do you recommend? Quantum mechanics, unlike general relativity, is a creation of many people. $\endgroup$ – Alexandre Eremenko Jun 21 '16 at 9:47
  • $\begingroup$ History of quantum entanglement makes it clear that Schrödinger invented the term, and did the first detailed analysis, though it was in response to the EPR paper. EPR simply used the conserved properties, but did not explore entanglement. So it seems unfair to give Einstein most of the credit, when he seems to deserve very little on this topic. $\endgroup$ – Peter Diehr Jun 21 '16 at 11:59
  • $\begingroup$ Possible duplicate of What was different about Planck's quantization of light compared to Einstein's? $\endgroup$ – Geremia Jun 21 '16 at 16:07
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    $\begingroup$ It also strikes me odd that Max Born explicitly states that Einstein was the first to interpret wave fields as probability densities for particles (specifically photons). Born simply took Einstein's idea and applied it to electrons (and this helped Born get a Nobel). Born always acknowledged this. $\endgroup$ – Albert Heisenberg Jun 21 '16 at 17:20
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    $\begingroup$ Einstein is sort of interesting in that he's both a victim and beneficiary of the "Great Man fallacy" of hist-sci, and its tendency to group a large number of discoveries by different people under one or two figures. Einstein gets over-credited for special relativity, at the expense of Poincare and Lorentz, but under-credited for early quantum, to the benefit of Born and DeBroglie $\endgroup$ – simplicio Jun 24 '16 at 16:01

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