Unfortunately, none of the notes containing Einstein’s failed attempts to quantize radiation have survived, and we know very little about the mathematical structures he played with and discarded during this period. This letter is, however, the last time that Einstein suggests he knows how or is close to solving the quantum puzzle for radiation. In December of 1910, again he expresses frustration: “the riddle of radiation will not yield … the secret remains unsolved.”
In hindsight we know that Einstein was on the wrong track in trying to change Maxwell’s equation to encompass quanta. Einstein was trying to do the most natural thing: find a new set of electromagnetic equations that contained the fundamental quantum constant, h, either explicitly or perhaps, he thought, implicitly, through the ratio e2/c (the electron charge squared divided by the speed of light), which has the same units as Planck’s constant. All the other known constants of nature at the time (except h and e) appeared in the known laws of nature. The speed of light appears directly in Maxwell’s equations; the gravitational constant, G, in the Newtonian law of gravity; Boltzmann’s constant, k, in the entropy principle, S = k log W. As these constants appear in the fundamental laws, one can calculate from these laws consequences that depend on the values of c or G or k.
Planck’s constant was not introduced in connection with a new physical law; its introduction was an ad hoc insertion in the midst of evaluating the blackbody entropy from Boltzmann’s principle. Einstein’s hypothesis of light quanta had the same ad hoc character, essentially inherited from Planck. That is why Einstein repeatedly emphasized that “the so-called quantum theory of today is, indeed, a helpful tool but … it is not a theory in the usual sense of the word.” He naturally assumed that a quantum theory of radiation would require a generalization of Maxwell’s equations, which would introduce Planck’s constant but would reduce to the original equations in contexts where no hint of quantum behavior was observed.
But the deck was stacked against him, and his assumption was wrong for a most subtle reason. Maxwell’s equations remain true and unchanged in quantum theory; it is only their interpretation that changes: they are the wave equation governing the dynamics of the photon, in the same sense that eventually the Austrian physicist Erwin Schrödinger would discover the quantum wave equation describing the dynamics of the electron. But there is a decisive difference between the two equations: right in the middle of Schrödinger’s equation for the electron, planted like a flag, is Planck’s constant, just as Einstein had expected in an analogous equation for photons. Einstein had picked the short straw. In the radiation problem the “quantum of action,” h, was hidden in plain sight, invisible because of the principle of relativity, Einstein’s own creation!
If there were indeed particles of light, they could have no inertial mass, as no massive object can reach the full speed of light. Nonetheless, as we have seen, radiation can exert pressure (i.e., it can transfer momentum) even though it is massless.3 The relativistic relation between the energy, E, of a light wave and its momentum, p, is E = pc; this relationship is embedded in Maxwell’s differential equations. In quantum theory, as we now understand it, photon energy is quantized and proportional to h, but so is momentum; so the factor h cancels in the equation relating the two. This is the essential reason that h does not appear in Maxwell’s equations. It “should” be there, but it cancels because photons are massless. This does not happen for massive particles, which thus are governed by quantum equations in which h sticks out like a sore thumb. We now believe that photons are the only freely propagating massless particles in our universe, so Maxwell’s equations are the only quantum equations where h does not appear explicitly. How’s that for bad luck? If Einstein had instead decided to focus on the mechanics of electrons in atoms, as would Niels Bohr in a just a couple of years, perhaps the history of physics would have been different. But his quixotic search for the quantum version of Maxwell’s equations defeated him, and he soon would lay down his lance.
By May of 1911, writing from Prague, a new note of resignation appears in a letter to Besso. “I no longer ask whether these quanta really exist. Nor do I try to construct them any longer, for I now know that my brain cannot get through in this way. But I rummage through the consequences as carefully as possible so as to learn the range of applicability of this conception.” And then, just as Einstein is abandoning his four-year struggle, comes the invitation:
Dear Sir,
To all appearances, we are at the moment in the midst of new developments regarding the principles on which the classical molecular and kinetic theory of matter has been based…. Messrs. Planck and Einstein have demonstrated that … contradictions disappear if one imposes certain limitations on the movement of electrons and atoms, … but this interpretation in turn … would necessarily and indisputably entail a vast reform of our current fundamental theories.
To that end, the undersigned proposes to you to participate in a “Scientific Congress” which will … bring together in a small meeting, several eminent scientists…. I hope that I can count on your collaboration, and I beg to assure you, dear, Sir, of my highest esteem.
Signed: Ernest Solvay, June 9, 1911
One can just imagine Einstein’s reaction as he read the letter: Tell me about it, buddy. The invitation was of course too prestigious to turn down, and he feigns great interest in his reply to Nernst a few days later. He has been asked to give the report on the current status of the problem of specific heat, and he accepts. But his heart, and his fertile scientific imagination, are elsewhere. By August 1911 his correspondence with Laub contains the first hints of a new passion: “The relativistic treatment of gravitation is causing serious difficulties. I consider it probable that … the principle of the constancy of the velocity of light holds only for spaces of constant gravitational potential.” Within two weeks of that letter he is corresponding with the astronomer Willem Julius about the redshift of the wavelength of light rays from the sun due to its gravitational4 field. In September, with the Solvay Congress looming in less than two months, he replies irritably to a letter from Besso: “If my answer is not … thorough, it’s because my drivel for the Brussels congress weighs down on me.”
Thus, while the First Solvay Congress was a point of departure for the field, the quantum problems it addressed would henceforth be the central problems of physics, it marked a temporary surrender for its youngest participant. Einstein’s report was thorough and scholarly and explained how sharply contradictory the various modes of reasoning were, as revealed, for example, by the fluctuations in the energy of radiation: “We stand here before an unsolved puzzle, just as in the study of thermal motion in a solid…. Who would have the audacity to give a categorical answer to these questions? I only intended to show here how fundamental and deep-rooted the difficulties are in which the radiation formula enmeshes us.” He presented no new ideas for how to get out of these difficulties; the optimism of Salzburg had dissipated.
On a personal level Einstein enjoyed the conference greatly; he described how he was “enchanted” with the French trio of Jean Perrin, Paul Langevin, and Madame Curie. Lorentz, whom he had already met for the first time earlier that year, again awed him: “H. A. Lorentz chaired the conference with incomparable tact and unbelievable virtuosity.” Planck’s integrity won him over: “he is a completely honest man who shows no consideration for himself.” But as for science, everyone there was just discovering the forbidding territory he had been surveying for years. His final verdict was delivered to his old friend Besso, for whom diplomacy was not required: “In Brussels, too, they acknowledged the failure of the theory … but without finding a remedy. In general the Congress … resembled the lamentations on the ruins of Jerusalem. Nothing positive has come out it…. I did not find it very stimulating because I heard nothing that I had not known before.” In the aftermath he seems to have suspected that his focus on radiation was the wrong path, writing to Lorentz a month later, “the h-disease5 looks ever more hopeless. Stil
l I believe that the purely mechanical side will be the first to be cleared up.” In this he would be proved right.
There was one claim enunciated at Brussels that Einstein alone of all present might have found particularly interesting and worthy of dispute, although he would never have done so in public, because that claim was made by Solvay himself. In the midst of his incomprehensible lecture on “positive and negative ether” Solvay had included the statement, “I took as my starting point Newton’s wonderful law [of gravity], which is uncontested and therefore able to satisfy the most rigorous scientific mind.” In fact it was just this law that Einstein had now begun to question seriously. By March of 1912 he wrote to a friend, “I’m working at full speed on a problem (gravitation). You should forgive me my long silence.” In October of 1912, having returned to Zurich, he declined an invitation from Sommerfeld to speak on quantum theory with the words, “I assure you that I have nothing new to add to the question of quanta that might be of any interest…. I am now working exclusively on the gravitation problem.” Sommerfeld, who had contacted Einstein with the speaking invitation on behalf of the famous mathematician David Hilbert, wrote in despair to Hilbert, “My letter to Einstein proved useless…. Apparently he is so deeply involved in the problem of gravitation that he turns a deaf ear to all else.”
Einstein, at least temporarily, had put up a metaphorical sign over the door to the atom: this way lies madness. He admitted as much with a joke he told to a friend and colleague, Philipp Frank, whom he had met during his year in Prague. Frank had quickly been captivated by Einstein’s wit and whimsy: “his sense of humor was readily apparent … when someone said something funny … the laughter that welled up from the very depth of his being was one of his characteristics which immediately attracted one’s attention.” As Frank tells the story, “about that time Einstein began to be much troubled by the paradoxes arising from the dual nature of light6 [wave and particle]…. his state of mind over this problem can be described by this [the following] incident.” Einstein’s office in Prague looked over a park, whose patrons had odd characteristics: only women appeared in the morning, only men in the afternoon, sometimes alone and talking to themselves, other times in groups engaged in vehement discussions. The explanation for these patterns turned out to be that the park belonged to the mental asylum of Bohemia, whose less violent patients were allowed its use. Einstein led Frank to his window, and then remarked playfully, “there are the madmen who do not occupy themselves with the quantum theory.”
1 The letter from Fischer mentioned only Einstein’s “great theoretical papers in the area of thermodynamics” and not relativity theory, indicating the input of Nernst.
2 The Zurich Polytechnic had just been raised to the status of a technical university capable of granting doctorates and renamed ETH Zurich.
3 In Newtonian physics the momentum of an object is its mass times its velocity (p = mv), and would be zero for a massless object.
4 The correspondence was actually initiated by a job feeler from Julius’s University of Utrecht, which Einstein ultimately received and turned down in favor of ETH Zurich.
5 Einsteinian synecdoche: Planck’s constant, h, stands for the entire quantum conundrum.
6 Frank was of course wrong here; Einstein had been concerned about this paradox for at least four years prior to moving to Prague.
CHAPTER 19
A COSMIC INTERLUDE
Scientific endeavors are quite extraordinary; often nothing is more important than seeing where it is not advisable to expend time and effort…. an instinct must be developed for what is just barely attainable upon the exertion of the utmost effort. [My recent] magnetic experiment, for example, could have been done by any old lout. But general relativity is of another kind. Having actually arrived at this goal gives me the greatest satisfaction of my life, even though up to now not a single colleague in the field has recognized the depth and necessity of this path.
—ALBERT EINSTEIN, MAY 31, 1915
Having decided that a true quantum theory was not yet attainable in 1911, even with his utmost exertion, Einstein devoted himself for the next four years primarily to his new theory of gravity, which arose as a natural generalization of his special theory of relativity and is hence termed the general relativity theory. The inspiration for his first work in this area, the special theory, had come from the properties of electromagnetic waves, arising from Maxwell’s equations. Gravity played no role at all in his thinking, and in fact prior to 1907, in contrast to his well-documented interest in atoms, there is no evidence Einstein was particularly interested in gravitational phenomena. Gravitational effects were of primary interest in astronomy, as it is only on the celestial scale that gravitational forces dominate over electromagnetic and nuclear forces. However, Einstein was nothing if not dogged in pursuit of conceptual clarity. Upon enunciation of the principle of relativity, the statement that the laws of physics should appear the same to all observers in uniform relative motion, he quickly noted that “the question arises whether this statement should not also be extended to non-uniform [i.e., accelerated] motion.” When in accelerated motion, you feel forces not present in uniform motion. For example, when you go from zero to sixty in four seconds, you are pressed back in your seat; you cannot say you are standing still and the world around you is accelerating backward, because people outside your car are not pushed forward. The conclusion that you are “really accelerating” and they are not seems unavoidable. Thus it appears that one can at least define absolute acceleration, if not absolute velocity.
However, in 1907, Einstein got the idea that pointed the way to a theory in which all motion, even that involving acceleration, is relative—a general theory of relativity. The hint to his idea is contained in a phrase used by the zero-to-sixty crowd: “pulling gs.” The force you feel pushing you back in your seat feels sort of like gravity; in fact, if your acceleration were constant and exactly the same as that due to gravity at the earth’s surface (9.8 meters per second squared, denoted by the letter g), you would “weigh” exactly the same with respect to a scale placed in the back of your seat as you do with a scale standing upright. Einstein surmised that the inertial force experienced during acceleration is completely indistinguishable from the force of gravity. It followed that a general theory of relativity, with no special, privileged states of motion, could perhaps be achieved if it were also combined with a new theory of gravitation. He sketched the earliest, most primitive outline of such a theory in 1907 but did nothing more on it until 1911, as he began to relinquish his single-minded focus on quantum theory and the nature of radiation. For the next four years almost all his original research papers were on the theory of gravitation, and his few works pertaining to atoms and/or quantum phenomena were not of a groundbreaking nature. His final success did not come until November of 1915, six months after his premature declaration of success (quoted above).
This episode in his scientific life was a departure from his earlier modus operandi. Contrary to some depictions, Einstein had been very interested in and aware of experiments in all his previous work; in fact, during this very same year, 1915, he had published his only experimental paper, an attempt to determine the origin of atomic magnetism in collaboration with Lorentz’s son-in-law, Wander J. de Haas.1 Moreover, ever since his student days he had not been much excited about higher mathematics, which he dismissed as needless erudition. He wanted to explain nature, not impress his fellow physicists with his mathematical prowess. General relativity changed his outlook. He quickly realized that he would need more sophisticated mathematical tools than previously, and his theory building was not motivated by any puzzling experiments or even community consensus about fundamental questions, but rather by his own conviction that a consistent framework for physical laws must exist in which all motion is relative. The fact that at the end of a herculean struggle he ended up with a beautiful mathematical construction, which also predicted and explained a few observable astronomical phenomena,
created a paradigm of supreme theoretical insight for all who followed.
Nothing quite like this had transpired before in natural science. As early as 1919 J. J. Thomson, the British Nobel laureate. pronounced it “one of the highest achievements of human thought.” Quantum pioneers and Nobel laureates Paul Dirac and Max Born went one step further: Dirac called general relativity “probably the greatest scientific discovery ever made,” and Born pronounced it “the greatest feat of human thinking about nature.” Einstein himself was transported by his breakthrough: “The theory is of incomparable beauty,” he told his friend Zangger; to Besso he wrote, “my boldest dreams have now come true.” The die was cast; henceforth this achievement would overshadow everything he had done or would do in theoretical physics, not just to the public, who went crazy over curved space and bent light rays when news of the theory’s confirmation emerged in 1919, but eventually to Einstein himself. His autobiographical notes, written at his seventieth birthday, present a view of his scientific career in which all his earlier work was the prelude to general relativity and all his subsequent work flowed from it. His quantum mania is barely mentioned.
Einstein and the Quantum Page 18
