singularities in his gravitation theory, the density of matter becomes infinite and his field equations are no longer valid. By implication, Einstein was rejecting the prediction by his own gravity theory of black holes, which contain singularities lurking at their centres. Moreover, he was also rejecting the “Big Bang” model of cosmology also based on his gravity theory, in which a singularity at time t equal to zero must inevitably occur. What Einstein actually wrote to me about this was:
I only want to point out that Infeld’s objections are not justified. This is because they assume that even for non-gravitational interactions between systems, the areas of weak fields are dominant. The quantum facts teach [us] that in truth this cannot be. A complete field theory cannot allow any singularities.
Einstein’s reference to Leopold Infeld, his former collaborator at the institute at Princeton, concerns a paper published by Infeld criticizing Einstein’s unified field theory. The paper claimed that the theory cannot produce the correct motion of a charged particle in an electromagnetic field, otherwise known as the Lorentz equations of motion. In one of the papers that I had sent to Einstein, I had discussed this problem of the motion of charged particles in his unified field theory.
Einstein closed his letter with some insightful observations about quantum mechanics, which are very relevant to present-day attempts to understand the foundations of quantum mechanics and to quantize Einstein’s gravitation theory.
Naturally it is quite possible that it is not possible at all to do justice to reality with a field theory. Then, however, in my opinion, one is not allowed at all to introduce the continuum (also not the “space” ) and I see in this circumstance no concepts on which one can rely with some prospect of success.* At any rate, I do not put any hope in subsequent “quantization.” But all this does not claim to be objectively correct. I simply see it this way.
Einstein signed his letter “friendly greetings to you, Your A. Einstein.” Although he had not directly addressed my question about my abilities as an aspiring physicist, he wrote to me as an intellectual equal, which astonished me and certainly strengthened my motivation to become a physicist.
When the barber finished translating the letter as well as he could, he handed it back to me and said softly, “Well, John, it looks as if Herr Doktor Einstein is taking you seriously.”
In my next letter to Einstein, on July 21, 1953, I attempted to address some of his profound statements about how physics should be pursued. I wrote, in effect, an essay on the epistemology of physics and whether one should do physics from a top-down or a bottom-up approach. The top-down approach attempts to do physics based on a priori reasoning, with the aim of achieving an elegant, beautiful theory with the least number of fundamental assumptions; the bottom-up approach is based on experimental facts and builds up from these facts to a consistent theory. For example, modern particle physics usually takes a bottom-up approach, in that particle theories are developed on the basis of known experimental data. Current top-down theories are, for example, string theory and quantum gravity. In my letter to Einstein, I also mentioned the need for creative ideas in physics and described how a theory develops from imagination, while in the end it is necessary to confront it with experimental observations.
In his letter to me, Einstein had been concerned about whether quantum mechanics was indeed a complete description of reality; he had contended it could not provide a useful starting point for a more profound theory. Einstein held this view in spite of the empirical successes of quantum mechanics: the theory agrees with all the data from subatomic systems, and there is no known experiment that contradicts it.
In my answering letter, I discussed the pivotal issue of determinism versus non-determinism, where in classical physics the position and speed of a particle can both be determined with infinite accuracy, but through Heisenberg’s uncertainty principle, this cannot happen in quantum mechanics. Quantum mechanics is a non-deterministic system of physics, for it is based on statistical probability theory. I wrote:
I feel subjected to the same indecision as Buridan’s ass, which was unable to choose any specific bundle of hay.* This so with respect to the controversy Determinism versus Indeterminism. In spite of this, my intuition tells me which specific bundle of hay it is most propitious to decide on. The scientific minded youth of today see this dilemma in a different light to those who developed and lived with the problem. Consequently, they do not realize any problem whatsoever; they believe the aim of Scientific Comprehension is “the second principle” (Indeter-minism) in the limiting realm of the “quanta.” This conception (purely conventional) is typical of the age; owing to this, I do not believe in it as final.
What I was aiming to say to Einstein was that the younger physicists of the time simply accepted quantum mechanics without questioning whether it was a final and complete description of reality. However, today, more than fifty years later, the tide has turned, and many physicists are thinking about the foundations of quantum mechanics and questioning whether the present so-called Copenhagen interpretation of quantum mechanics is viable.
In my letter to Einstein, I also discussed the importance of empirical verification of a physics theory, quoting from Lord Rutherford:“It seems to me unscientific and also dangerous to draw far-flung deductions from a theoretical conception which is incapable of experimental verification, either directly or indirectly.” As a twenty-year-old, I anticipated a basic problem that faces physics today, namely the difficulty in obtaining sufficient experimental data to verify and test such theories as string theory, quantum gravity and other highly speculative theories in cosmology. The only way to obtain new data is through increasingly large and expensive high-energy accelerators, which is leading to a crisis in physics today.
I then wrote about theory versus experiment. “. . . It is always possible to modify a theoretical scheme (by additional artificial assumptions) in such a manner as to obtain immediate experimental verifications . . . One shall not modify the true aim of science (aim of complete comprehension) for the sake of momentary interests. However, if this is found necessary, the step shall only be understood as a temporary state of affairs . . .” Today, this problem of ad hoc physics is even worse than in Einstein’s day. Today we have the speculation that exotic “dark matter” and “dark energy” exist in order to explain astronomical and cosmological observations that do not follow from Einstein’s gravity theory.* Physicists today have “modified” Einstein’s gravity theory by adding in the “artificial assumption” of undetected exotic dark matter to “obtain immediate experimental verification.”
Later in my eight-page letter, I confronted the problem of singularities in gravitation theory, which Einstein had discussed in his letter. I speculated on whether there might be a possible criterion for when the solutions in field theory and gravity theory are regular or non-regular (that is, non-singular or singular, respectively). I also discussed the issue of the cosmological constant as “corresponding to a universal field density.” * I was proposing that this energy field associated with the cosmological constant, which today is interpreted as the universal vacuum energy, or “dark energy,” had to be included in a truly unified theory. Yet Einstein did not like his cosmological constant because it introduced what he called a “heterogeneous piece” into his basic gravity equations.
Finally, I wrote about how gravity theories should be purely geometrical in origin, avoiding a phenomenological description of matter such as Einstein had used in his gravity theory and in his first paper on cosmology, “Cosmological Considerations in the General Theory of Relativity,” published in 1917.** Einstein addressed the issue of a purely geometrical theory of gravity in a well-known quote:“Gravitational equations of empty space are the only rational well-founded case of a field theory.” He meant by this that the right-hand side of his field equations for gravity should be zero, not the phenomenological energy momentum tensor postulated in his papers on his general theory of relativity. Already early on in his research on gravity, Einstein was dissatisfied with the formulation of general relativity. Einstein was never entirely happy with the research he published. He was always looking ahead, ambitiously, to a more fundamental unified description of physics.
I