Читать книгу Einstein Wrote Back - John W. Moffat - Страница 13
ОглавлениеTWO WEEKS LATER, I gave my talk in the seminar room on the ground floor of the Niels Bohr Institute, with its pleasant view of the adjoining park. The audience, consisting of Professor Møller and other professors and their students, was hostile, just as Professor Bohr had predicted. They made rude comments to me about Einstein’s unified field theory research and my attempts to defend it. I felt disappointed that Professor Bohr himself had not attended my talk.
Afterwards, Professor Rudolf Haag, who was visiting the institute from Germany, came up to speak to me. He advised me to enter the university and go through a conventional academic training to obtain an undergraduate degree. He agreed that it would be best to do this in a British university. Haag was the one person at the institute that day who showed any interest in my research and my future.
Disturbed by my overall reception at the seminar, I returned home, and with the rashness of youth, I wrote a letter by hand to Albert Einstein, describing the negative reaction of the audience towards his goal of unifying gravity and electromagnetism in one geometrical scheme. I also included the two manuscripts that I had written on his unified field theory. “. . . I have today held a talk on my work with regard to your theory at the Niels Bohr Institute, Copenhagen,” I wrote, “and there found only complete misunderstanding. In fact, it appeared that the main purpose was to undermine my personal confidence as to my ability. I would be eternally indebted if you could find time to read my work, and should you find yourself satisfied with my interpretation, mathematical ability, and conceptions, that you return same to me with your opinion . . . I found the Personel [sic] at the Bohr Institute completely without the fundamental knowledge necessary for the understanding of your Theory of Generalized Gravitation, and need I state how great a disappointment this was to me.
“Moreover,” I continued helpfully, “I found the attitude of the persons concerned contrary to all aesthetic feeling and conceptions, and I feel that you should become aware of what is really going in the opposite camp.”
I posted the letter, along with my two manuscripts, one of which pointed out a potential problem in his unified field theory, to Einstein at the Institute for Advanced Study at Princeton University, New Jersey. My manuscripts were titled “Theory of Quantized Unified Fields” and “On Unified Field Theory and the Equations of Motion.”
The year was 1953. I never expected a response. It had been a valuable learning experience for me just to write the papers and to give the seminar. Why would I anticipate that Einstein would have time, great physicist that he was, to read and respond to my letter and manuscripts? Perhaps he would be offended that an unknown, unschooled young man in Copenhagen dared to criticize his published theory.
Three weeks later, an airmail letter with U. S. stamps arrived for me at my parents’ apartment. The return address was Einstein’s home at 112 Mercer Street, Princeton, New Jersey. Even then, in my excitement, I reflected on the fact that Einstein did not use the Institute for Advanced Study as his official address. I tore open the envelope and found that Einstein had written back to me in his own handwriting! He had also included a reprint of the appendix to his latest edition of The Meaning of Relativity, which I had not yet read. The book I had borrowed from the university library was an earlier edition.
But unfortunately, Einstein’s handwritten letter was in German, and my German from two years of study in two different Danish schools was not up to the task of understanding it.
I immediately thought of my barber, Hans Busch, who was of German extraction. I rushed down the street on that warm June afternoon and burst into Hans’s shop shouting, “I just received a letter from Albert Einstein in America! It’s written in German. Can you please help me translate it?”
It was midmorning, a busy time in the small shop, and the men sitting and waiting for their haircuts stared at me in astonishment. The barber looked at me, his scissors clipping at a customer’s hair, and said, “Just a minute, John. I need to finish with this gentleman.”
I curbed my impatience and sat down to wait, feeling exhilarated. Finally, Hans Busch’s elderly client rose from the barber chair, brushing stray hairs off his jacket, and paid for his haircut. He joined the other customers seated around me to watch the show.
“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.
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 didn’t wait to hear back from Einstein, but I wrote to him again, on August 12, and this time my letter was much more technical. I also enclosed a manuscript I had just completed, entitled “Unified Field Theory.” In the letter and in my paper, I discussed the fact that in Einstein’s attempts to construct a unified field theory, he had not included a field associated with the strong and weak nuclear forces. These forces were already known to be important in the early 1950s, and had been discovered by observing particle collisions in early accelerators. I really felt that Einstein needed to include these forces in his theory. It was clear to me that without them, he could never hope to achieve a correct and complete unified field theory.
Einstein must have responded almost immediately to this letter, for his next one to me was dated August 24. “Dear Mr. Moffat!” he began, in another handwritten letter:
Our situation is the following. We are standing in front of a closed box which we cannot open, and we try hard to discuss what is inside and what is not. The similarity of the theory [his unified field theory] with the one by Maxwell [electromagnetism] is only superficial. Thus we cannot simply take over the concept of a “force” from this theory to the asymmetric field theory. If this theory is useful at all, then one cannot separate the particle from the field of interaction. Also there is no concept at all of the motion of something that is more or less rigid. The question here is exclusively: Are there solutions without singularities? Is there energy preferably localized in such a way as it is required by our knowledge of the atomic and quantum character of reality? The answer to these questions is indeed not achievable with present mathematical means. Thus I do not see how one should suspect whether some remote action and some objects, as far as we have gained a semi-empirical knowledge of them, are represented by the theory. Thus our pertinent complete ignorance does not begin with “nuclear forces.” Here the situation is different from the pure theory of gravitation, where one can approximate the masses through singularities.
Einstein was willing to accept that he was ignoring the nuclear forces. However, he was trying to justify this omission by saying that we are not able to understand these nuclear forces with the mathematical tools available at that time.
“The only thing that is in favor of the new theory,” he continued, still referring to his unified field theory, “is the fact that it appears to be the only natural generalization of the equations of the pure gravitational field.”
I wrote two more letters to Einstein, enclosing further calculations based on his nonsymmetric unified field theory. I discussed some critical aspects of his field equations. He responded in October 1953 with a short note, advising me to be careful about publishing this work prematurely. I took his advice and continued developing his theory.
When I wrote to Einstein in 1953, he was one of the most celebrated physicists in the world, and had won the Nobel Prize long before, in 1921.* But he had isolated himself from the rest of the physics community by his problematic stand on quantum mechanics. He felt that “God does not play dice with the universe,” a metaphorical swipe at the random, probabilistic nature of quantum mechanics. His disagreements with Niels Bohr on the interpretation of quantum mechanics were legendary. His work on unified field theory and gravitation was disconnected from the mainstream of physics, which at that time was concentrating on developing nuclear physics and atomic physics. Most other physicists dismissed Einstein’s attempts to find a generalization of his gravity theory that unified it in a geometrical framework with James Clerk Maxwell’s equations for electromagnetism. Indeed, Einstein was ostracized by his physicist peers.
This ostracism began as early as the 1930s, when Einstein appeared before a committee at the Institute for Advanced Study, requesting financial assistance to bring Leopold Infeld from Poland to the institute to assist Einstein in his calculations of the motion of particles in his gravitation theory. He was denied this request. This prompted Einstein and Infeld to write a bestselling popular book together, titled The Evolution of Physics.Money from the sales of this book paid for Infeld to travel to Princeton and begin the collaboration. Much later, in the late 1940s and early 1950s, when Robert Oppenheimer was director of the institute, he dissuaded the young physicists there from associating with Einstein because he believed that Einstein would be wasting their time; he didn’t want Einstein influencing the younger generation.
Is it possible that Albert Einstein showed interest in corresponding with me, an unknown, self-taught student of physics in Denmark, because I had shown critical interest in his work? Unlike his esteemed peers, I, a young aspiring physicist, was taking him and his recent work seriously. Also, in opposing the consensus view of what physics was worth doing and what was not, I had positioned myself as an outsider at the Niels Bohr Institute circle, just as Einstein himself had become an outsider.
