Einstein and the Quantum

by Stone, A. Douglas

  After the decisive year of 1926, in which he rejected the new quantum theory as the ultimate description of reality, he briefly sought to show, via his classic method of gedankenexperiments, that the theory contained internal contradictions. However, fairly soon he accepted the consistency of its logical structure with the comment “I know this business is free of contradictions, but in my view it contains a certain unreasonableness.” By September of 1931 he would graciously nominate both Heisenberg and Schrödinger for the Nobel Prize, with the comment “I am convinced that this theory undoubtedly contains a part of the ultimate truth.”

  But despite this grudging endorsement, Einstein himself never applied the quantum formalism to a specific physics problem for the rest of his career, except in the context of a famous critical paper written in 1935 with younger collaborators, Podolsky and Rosen. The article drew attention through a thought experiment to the “spooky action at a distance” implied by quantum theory, which the authors claimed made the theory an incomplete description of reality. Modern realizations of this “EPR” experiment have fully confirmed the existence of this effect, a counter-intuitive correlation between distant particles. Such effects are referred to as “entanglement”; they form the basis of much of the new field of quantum information science. Many now consider Einstein’s recognition and prediction of the EPR effect as his last major contribution to physics.

  Not only Einstein but also de Broglie and Schrödinger, the two quantum pioneers whom he had championed, made little contribution to the further application of quantum theory, and both ended up joining Einstein in rejecting it on philosophical grounds. As a consequence, the history of the discovery/invention of quantum theory was told from the perspective of Bohr, Heisenberg, Born, and their legions of students and collaborators. (Einstein, de Broglie, and Schrödinger had no students or collaborators in their works on quantum theory.) The matrix mechanicians, whose approach was instantly devalued following Schrödinger’s discovery of the “real quantum mechanics,” simply appropriated that work and gave it the interpretation that fit their understanding (and, it must be admitted, the experimental evidence). Ironically, Schrödinger was correct; his method was much more intuitive and visualizable than that of Heisenberg and Born, and it has become the overwhelmingly preferred method for presenting the subject. But with Born’s probabilistic interpretation of the wave-function, Heisenberg’s uncertainty principle, and Bohr’s mysterious complementarity principle,1 the “Copenhagen interpretation” reigned supreme, and the term “wave mechanics” disappeared; it was all quantum mechanics. The limitations on human knowledge of the physical world implied by these concepts were accepted by all practicing physicists. To this new generation Einstein became known primarily for relativity theory, admired by all, and secondarily for his stubborn refusal to accept the elegant new atomic theory of everything.

  However, if one takes stock of the conceptual pillars of the new theory, in light of the historical record, a rather different picture emerges. Einstein surely shares with Planck the discovery of quantization of energy, as Planck never accepted that the quantum of action implied quantization of mechanical energy until many years after Einstein had become the first to proclaim it. It was Einstein who first realized that quantized energy levels explained the specific heat of solids, which justified the Third Law of thermodynamics and brought chemists such as Nernst into the quantum arena. Einstein, in his paper on light quanta, discovered the first force-carrying particles, photons, now the paradigm for all the fundamental forces. Following up on this, he discovered the wave-particle duality of light and, in 1909, based on his rigorously correct fluctuation argument, predicted that a “fusion theory” must emerge to reconcile the two views. In 1916 his quantum theory of radiation combined the ideas of Bohr, Planck, and his own light quanta to put Planck’s blackbody law on a firm basis. Here he introduced, for the first time, the core concept of intrinsic randomness in atomic processes, which the mature theory would accept as fundamental. He also introduced the notion of the probability to make a quantum jump, and he distinguished between spontaneous and stimulated transitions, ideas fundamental to, for example, the invention of the laser. And during 1924–1925 he elevated Bose statistics from obscurity, explained what it meant and why it had to be correct, and derived the mind-boggling condensation phenomenon it implied, something undreamt of by Bose himself. Finally, without ever publishing it, he developed the rule of thumb that electromagnetic wave intensity could be thought of as determining a probability to find photons in a certain region of space, the idea that stimulated Born’s crucial interpretation of matter waves.

  In summary: quantization of energy, force-carrying particles (photons), wave-particle duality, intrinsic randomness in physical processes, indistinguishability of quantum particles, wave fields as probability densities—these are most of the key concepts of quantum mechanics. As Born would later say, “Einstein is therefore clearly involved in the foundation of wave mechanics and no alibi can disprove it.” The magnitude of these achievements? Four Nobel Prizes would be about right, instead of the one he received, grudgingly, in 1922. Not that Einstein cared much for such accolades.

  Why did Einstein, who clearly understood the structure of the new theory and the necessity of introducing radical concepts to explain the atom, refuse to accept that theory and hold out for a very different resolution of the quantum dilemma? In my opinion this was the result of both his life experiences in doing science and his fundamental motivation for choosing that life.

  Twice in his scientific career Einstein had wandered so far from the mainstream that even the many colleagues who already regarded him as an historic genius simply dismissed his views as wildly speculative and not to be taken seriously. Special relativity was not such a case, building as it did on the work of Lorentz and others, although certainly it unveiled a spectacular physical and epistemological insight that was uniquely Einsteinian. The first time was, of course, the light quantum “nonsense,” for which Planck felt compelled to apologize when nominating him to the Prussian Academy, and which Bohr still ridiculed a full two decades after it was proposed. The second time was with the theory of general relativity. In the latter case the idea did not elicit ridicule but simply incomprehension. There was no crisis in gravitation theory that required a radical resolution; what was this eccentric mastermind doing anyway?

  The development of general relativity had proceeded unevenly, with dead ends and backtracking, technical errors ultimately corrected, and then an epiphany as the beautiful final equations emerged and predicted correctly the precession of Mercury and the bending of starlight. Einstein recalled the struggle thus: “the years of searching in the dark for a truth that one feels but cannot express, the intense desire and the alternation of confidence and misgiving until one breaks through to clarity and understanding, are known only to him who has experienced them himself.” Much later, in rejecting the modern quantum theory, he remarked, “it is my experiences with the theory of gravitation which determines my expectations.”

  Moreover, just before the promulgation of the new quantum theory, in the summer of 1925, Einstein had experienced a similar vindication of his faith in the existence of light quanta. In 1924 Bohr and collaborators had put forth a new approach to the interaction of light and matter that sacrificed the principle of conservation of energy and momentum and introduced statistical considerations into the theory, although not in a manner that would turn out to agree with the final quantum theory. In print Bohr flatly stated that the theory of light quanta was “obviously not [a] satisfactory solution of the problem of light propagation.” Einstein staunchly opposed Bohr’s new theory, since he believed that the conservation laws must be exact or his beloved thermodynamics would be undermined. He also pointed to dramatic recent experiments by the American physicist Arthur Holly Compton that seemed to confirm the conservation laws for the collisions of an x-ray photon with an electron (treated as particles). However, it still could be argued that C
ompton’s experiments left open the possibility that momentum and energy were only conserved on average and not in each individual collision. This possibility was ruled out late in 1924 by landmark experiments of Bothe and Geiger in which the individual collisions were measured and shown conclusively to obey the conservation laws for two particles.

  In January of 1925 Born wrote to Bohr, “the other day I was in Berlin. There everybody is talking about the result of the Bothe-Geiger experiment, which decided in favor of light-quanta. Einstein was exultant.” In April of 1925, two months before Heisenberg’s coup de destin, Bohr conceded that it was time “to give our revolutionary efforts [to banish light quanta] as honorable a funeral as possible.” Einstein’s apparently infallible intuition had triumphed one last time. Thus when the newest statistical theory of the atom, the Heisenberg-Born-Schrödinger synthesis, commandeered the stage, Einstein must have felt a sense of déjà vu. Just hold out long enough, and again he would be proved right.

  Einstein’s most famous objection to the theory was the “dice complaint”: its insistence on the intrinsic randomness of individual events and the abandonment of rigid causality. But Schrödinger’s q-space picture had actually undermined Einstein’s objection to a probabilistic theory. Eugene Wigner, a leading figure in the second generation of quantum pioneers, was studying in Berlin in the early 1920s, and recalled that Einstein was quite “fond” of his guiding field concept, “[which] has a great similarity with the present picture of quantum mechanics,” but “he never published it … [because] it is in conflict with the conservation principles.” However, in the N-dimensional space of Schrödinger’s waves, the conservation laws survived, even if the outcomes were indeterminate. In quantum mechanics, if two particles collide, even if one has full knowledge of the particle properties before the collision, it is impossible to predict, in each individual case, in which directions the two particles will be traveling after the collision. One can only state the probability that they emerge from the collision in a certain pair of directions. Nonetheless, there is zero probability that the two particles emerge with a different total momentum and energy than they went in with. They are like a magic pair of coins, which when flipped individually give you heads or tails randomly and with equal probability, but when flipped as a pair always come up with opposite faces showing. So quantum indeterminacy still respects the conservation laws.

  Perhaps for this reason Einstein’s later critiques of quantum theory focused less on its indeterminacy and more on its strange epistemological status. In quantum mechanics the actual act of measurement is part of the theory; those magic coins just mentioned exist in a state of (heads, tails)-(tails, heads) uncertainty until they are measured, and then they are forced to “decide” which state they are in. This is true even if the coins are flipped very far apart, implying that obtaining knowledge of one coin, through measurement, “changes” the state of the other coin an arbitrary distance away. This is the “spooky action at a distance” that Einstein detested, now known as “quantum entanglement.” But beyond its apparent tension with relativity theory, the entire conceptual structure seems to break down the barrier between the “real world” of objective nature and the subjective world of human perception. “Do you really believe that the moon exists only if I look at it?” he used to say. Such a notion fundamentally challenged Einstein’s credo.

  In his autobiography he states, “Physics is an attempt to conceptually grasp reality as it is…, independently of its being observed.” In a letter to Born, late in his life, he amplified on this theme: “We have become Antipodean in our scientific expectations. You believe in the God who plays dice and I in complete law and order in a world which objectively exists, and which I, in a wildly speculative way, am trying to capture.” The importance of this dichotomy, the transitory, subjective, and ultimately insignificant individual versus the eternal order of the Cosmos, was central to his personal philosophy. As a very young man he rejected the “nothingness of the hopes and strivings which chases most men restlessly through life.” In this way one could “satisfy the stomach” but not the “thinking and feeling being.” But he soon realized that there was another way to live: “out yonder there was this huge world, which stands independently of us human beings and which stands before us like a great eternal riddle, at least partially accessible to our thinking and inspection. The contemplation of this world beckoned us like a liberation.” When he had risen to the apex of success in this pursuit, he spoke these words in tribute to Max Planck: “I believe … that one of the strongest motives that leads men to art and science is the escape from everyday life with its painful crudity and hopeless dreariness, from the fetters of one’s own everyday desires … a finely tempered nature longs to escape from personal life into the world of objective perception and thought.”

  In Beethoven’s Ninth Symphony, after three movements of breathtaking beauty, the composer interrupts the final movement with the baritone’s thunderous introduction to the chorale section, “Oh friends, not these notes” (nicht diese töne). As spectacular as his previous creations had been, the composer was searching for something different, something better. Similarly, Einstein could not hear the musicality of his quantum creations, and would spend the rest of his life in search of the final movement that would bring his atomic symphony to a harmonious resolution.

  1 A philosophical principle about the impossibility of a unified picture of the atomic world, the utility of which is controversial.

  APPENDIX 1: THE PHYSICISTS

  In order of appearance:

  Max Planck (1858–1947): German theorist, expert on thermodynamics, and Nobel laureate (1918) who introduced the first quantum ideas and his famous constant, h, in order to explain the blackbody radiation law.

  Wilhelm Wien (1864–1928): German Nobel laureate (1911) who did the first important theoretical work on the blackbody radiation law, leading in 1896 to Wien’s law, which is now known to be an approximation to the correct Planck law.

  Heinrich Weber (1843–1912): German experimentalist and researcher in thermodynamics. He was head of the Physics Department at the Zurich Polytechnic when Einstein was a student and clashed with him. His measurements of the temperature variation of specific heats influenced Einstein’s 1907 quantum theory of specific heat.

  Marcel Grossmann (1878–1936): Swiss mathematician and classmate of Einstein’s at the Zurich Poly. His family connections played the key role in Einstein’s receiving the patent office job in Bern. Later, in 1913, he became a professor at ETH and collaborated with Einstein on a fundamental paper in General Relativity Theory.

  Mileva Maric (1875–1948): Promising physics student who became Einstein’s first wife and, after failing to obtain her diploma, did not pursue a career in physics.

  Sir Isaac Newton (1642–1726): Founder of classical mechanics through Newton’s three laws and the invention of calculus. If you are reading this book you know who he is.

  Michael Faraday (1791–1867): English scientist whose experiments led to the concept of electric and magnetic fields; he was greatly admired by Einstein.

  James Clerk Maxwell (1831–1879): Scottish theoretical physicist who first found the complete equations of classical electromagnetism, which are named for him. He was also a pioneer of statistical mechanics.

  Ludwig Boltzmann (1844–1906): Austrian theoretical physicist who, along with Maxwell and Gibbs, founded the discipline of statistical mechanics. He discovered the fundamental microscopic law of entropy, S = k log W, where k is a fundamental constant of nature known as Boltzmann’s constant.

  Josiah Willard Gibbs (1839–1903): American physicist and mathematician who, along with Boltzmann and Maxwell, founded statistical mechanics.

  Hendrick Antoon Lorentz (1853–1928): Dutch theorist and Nobel laureate (1902) who initially doubted the validity of the Planck law. He became a close friend of, and father figure to Einstein, who regarded him as the greatest thinker he had ever met.

  Lord Rayleigh (184
2–1919): English mathematical physicist and Nobel laureate (1904); he was an expert on wave theory, particularly acoustics. He proposed the Rayleigh-Jeans law based on classical statistical mechanics, which leads to the incorrect prediction of the ultraviolet catastrophe.

  James Jeans (1877–1946): English theoretical physicist and astronomer who contributed to, and also championed, the Rayleigh-Jeans law.

  Svante Arrhenius (1859–1927): Swedish physicist and physical chemist, Nobel laureate (1903) for his work on electrolysis, who influenced the establishment and awarding of the Nobel Prizes in Physics and in Chemistry.

  Arnold Sommerfeld (1868–1951): German theoretical physicist and leader in the development of the Bohr-Sommerfeld approach to the quantum theory of atoms.

  Johannes Stark (1874–1957): German experimental physicist and Nobel laureate (1919), expert on the photoelectric effect, who led the anti-Semitic physics movement under the Nazis.