Einstein Wrote Back. John W. Moffat

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      “All right, John,” Hans said, wiping his hands on his apron and turning to me. “What’s this you have here?”

      I pulled the letter out of my pocket and handed it over. It was written on two sides of a piece of stationery. Hans perused it quickly and stopped at the end, peering at it intently. “Well, indeed, this letter has Albert Einstein’s signature!” The other customers stood up and gathered round to stare at the signature too. The barber said, “What have you been up to, John?” and he smiled. I gave him, and our audience, a brief summary of how I had spent my spare time during the past year, the talk I’d given at the Niels Bohr Institute, and why I had written a letter to Einstein.

      Hans proceeded to translate the letter into Danish orally, despite some difficulties with the technical terms in German, while we all stood listening attentively. According to the translation, Einstein made constructive comments and criticisms on my manuscripts, and attempted to answer my criticisms of his mathematical formulation. He also had some things to say about my audience at the institute.

      “‘I can understand very well that your work has not found a favourable reception in Bohr’s circle,’” Hans translated. “‘For every individual and every study circle has to retain its own way of thinking, if he does not want to get lost in the maze of possibilities. However, nobody is sure of having taken the right road, me the least.’” *

      Einstein went on to make some profound comments about physics as it was at that time. Later, I was able to obtain an English translation of the letter, and had more time to contemplate Einstein’s ideas. Indeed, his comments still have significance for many of the endeavours of physicists today:

      I do not believe that one achieves one’s objectives by first setting up a classical theory and then quantizing it. Although this, of course, has been successful in the interpretation of classical mechanics and in the interpretation of quantum facts by modifying this theory according to the principles of statistics. But I believe that in the attempts to carry over this method to field theories, one encounters ever increasing complications and the necessity to increase the number of independent assumptions monstrously. For generally covariant field theories* this will be even worse.

      I even think that the mechanics based on the quantum theory cannot provide a useful starting point for a more profound theory, despite its significant successes, because I can see by looking at it that it has accepted the understanding of the “quantum jumps” in an “illegal” fashion by raising probability to a reality and in doing so giving up the reality of the quantum states (in the old sense). Thus one wants to explain why an apparent arbitrarily small perturbation can change the energy of an atomistic system by a finite amount [Einstein’s italics].

      I understood from Einstein’s words that he believed that the old quantum physics that he had been involved with, in the early days of the birth of quantum mechanics, represented a complete description of reality, whereas the later quantum mechanics and quantum field theory, which were accepted in the 1950s, were based purely on probability theory and statistics, and did not constitute a complete and real description of nature.

      Einstein continued:

      In view of this state of affairs I see myself urged to consider the logical simplicity as the sole guide using general relativity. This leads me to the attempt (but not to the conviction) to seek the future in a field theory (in the old sense) (generalization of the theory of the gravitational field). The point of view that one is not allowed to construct the Lagrangian function from logically independent terms appears essential to me. I send you my latest research from which you can see what I mean by that.

      I was overwhelmed by the amount of obviously pertinent information one of the world’s greatest physicists had imparted to me, and I understood the significance of Einstein’s comments for the future of physics. It is clear from his comments on quantum mechanics and the way it was applied at the time that he had not wavered in his opposition to Bohr’s interpretation. The famous discourses on the meaning of quantum mechanics between Bohr and Einstein, initiated at the 1927 Solvay conference and pursued over several years, had not persuaded Einstein to join the herd of physicists who were convinced that the probabilistic interpretation of quantum mechanics was here to stay.

      Einstein went on in his letter to make an important statement about singularities in field theory, and emphatically rejected the existence of singularities. At these mathematical 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.

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