He is concerned with the geometry of curved space, and discusses the mathematics behind his work in a letter sent to a soldier fighting in World War II; He sheds light on his approach to scientific inquiry in his quest for a Unified Theory
In 1905, while a young patent clerk and physicist in Bern, Switzerland, Albert Einstein obtained his doctorate and published a paper that explained his newly developed Special Theory of Relativity. This unlocked many mysteries of the universe, and introduced the world to "e=mc2," equating mass and the speed of light with energy. It established that time and space are not fixed, and in fact change to maintain a constant speed of light regardless of the relative motions of sources and observers. Just 10 years later, in 1915, Einstein published his General Theory of Relativity, which describes the universe as a four-dimensional continuum (with time added as the fourth dimension), where gravitational effects are explained by the warping of space-time. In this theory, Einstein incorporated gravity as a geometric property of space-time.
The impact of Einstein's work between 1905 and 1915 challenged many principles of physics that had been accepted for centuries. In 1921, he won the Nobel Prize for his work. Time Magazine named him the Person of the Century for the 20th century for his discoveries in relativity and space-time. Einstein is the most important scientist since Isaac Newton, and probably the most famous in history.
When Einstein fled Europe in 1933, he settled in Princeton, New Jersey. He came to work at the Institute for Advanced Study at the School of Mathematics. From there he continued the gravitational work he had done on relativity, and searched to expand its application by developing its relationship to electromagnetism. His overall goal: to unify these two forces of nature under one umbrella and into one theory that would explain all natural phenomena. “The intellect seeking after an integrated theory cannot rest content with the assumption that there exist two distinct fields totally independent of each other by their nature,” Einstein said. This attempt to unify his relativity work with electromagnetism occupied him until the moment he died. "The generalization of the theory of gravitation has occupied me unceasingly since 1916," he once wrote. Einstein saw systems within systems, equations within equations, and ultimately a profound sense of unity among all things infinitely large and small.
In 1943 and 1944, Einstein, concerned with the geometry of curved space, turned to a new theory called bivectors based on mathematical equations not of the standard differential variety he had used with General Relativity, but rather a more algebraic approach in which he wrapped in more variables. He assumed the four-dimensionality of space, but the bivectors mathematical construct depended on two distinct points of the four-dimensional continuum to measure distance in space. Each point was a different mark in space not infinitesimally close to the other. Since each point is four dimensional, this requires 8 variables for two points. It becomes a more complex algebraic equation. He wrote two papers on this subject in 1943 and 1944; this was to be his last major new scientific model. After 1945, while still believing in the unified forces of nature, his method of determining them would revert to his earlier methods of calculation with four variables.
In January of 1945, in the Pacific Theater of World War II, the Americans landed in a bay near Luzon on the Philippine Islands, which they took in near entirety by April. These men in the northern Philippines would help launch the assault on Okinawa. The action in the Pacific Theater would close out the war in the coming months. The 26th Photographic Reconnaissance Squadron, called the Lightening Bugs after the planes they sent to spy on the enemy, supported the successful American island-hopping campaign in the East Indies, then flew missions in support of the 1944-1945 Philippines Campaign. Later it moved to Okinawa in August 1945 after the Japanese capitulation and flew aerial reconnaissance over occupied Japan and Korea.
While Einstein was toiling on his relativity work, far away in the Philippine Islands, a group of American soldiers, the Lightening Bugs, were recovering from the campaign on Luzon. They were interested in science, but found themselves puzzled by an article they read in Science Digest, which they interpreted to read that Einstein was suggesting that instead of the four-dimensional universe that he had postulated in 1915, there were in fact more, perhaps eight. This article reported on Einstein's new bivector approach.
As a 1945 issue of the military's "Stars and Stripes" publication wrote, "Army 'bull-sessions' are usually noteworthy only for the noise that accompanies them, but in the case of Sgt Frank K. Pfleegor of the Lightning Bugs such a session led to correspondence with no less a figure than the great Albert Einstein. Sgt. Pfleegor was reading a well-known science magazine in which an article by the world-renowned mathematician appeared. He understood that Dr. Einstein now believed there are eight dimensions instead of four. Thinking that four were enough to give him headaches, he called the matter to the attention of his tentmates. There was much arguing and shaking of heads, and the other fellows finally decided that Dr. Einstein must know what he was talking about. But Sgt Pfleegor was not satisfied, so he V-mailed a query to the scientist.”
Pfleegor was an engineer and had a scientific background. The original of Pfleegor's letter to Einstein is published and is in the Einstein Papers at Jerusalem University. It is dated April 17, 1945, and reads: "In our tent we usually spend our evenings discussing various scientific topics. Tonight we attempted to tackle a problem from the Nov. 1944 issue of Science Digest, entitled "Einstein's At It Again." By your theory, space is composed of two spaces of four dimensions each. Space is composed of the whole extent of the universe. According to the law of impenetrability: two objects cannot occupy the same space at the same time. Can space be divided? The article was not very enlightening. Some of us stick by the single four dimensional space. The rest say it is made up of two spaces of four dimensions. Why not three of four dimensions etc.? We would appreciate an answer."
This soldier's letter from the front lines touched Einstein, and he did answer. Below is Einstein's reply. Although it was considered important enough at the time that it was referenced in Stars & Stripes, record of it was soon lost. It went unpublished, and completely unknown (the Einstein Papers had never seen or heard of it) except by the Pfleegor family until we obtained it from the heirs of Sgt. Pfleegor. It is interesting enough that Einstein responded, but what is extraordinary is that he provided such significant information in such a concise and complete way. In the letter we can see Einstein's frame of mind at that time, and his view of where his work stood then. He related that he was coming back to his core belief in four dimensions, even as he maintained his quest for a unifying theory for all phenomena.
Typed letter signed, on his Institute for Advanced Study at the School of Mathematics letterhead, in English, May 11, 1945, to Sgt. Pfleegor in the Phillippines, with the original envelope and article from Star and Stripes. In this letter, Einstein succinctly describes his new scientific inquiry, reports on the status of this inquiry, explains his methods, and maintains the primacy of General Relativity. We do not ever recall seeing a similar statement in a letter of Einstein, let alone in this context and in English. This letter has never before been seen by the public and has never before been offered for sale.
"Dear Sir: I see from your letter of April 17th that the attempt of my last publication was not reported in an adequate way. I have not questioned there that space should be at as a four dimensional continuum. The question is only whether the relevant theoretical concepts describing physical properties of this space can or will be functions of four variables. If, f.i., the relevant entity is something like the distance of two points which are not infinitesimal near to each other, then such distance has to be a function of the coordinates of two points. This means a function of eight variables. I have investigated the possibilities of this kind in the last years but my respective results seem to me not very encouraging. For the time being I have returned to ordinary differential equations [from General Relativity] with dependent variables being simply functions of the four coordinates [space-time]. What the future has in store for us nobody can foretell. It is a question of success."
In this letter, Einstein re-iterates the primacy of his great space-time theory, the General Theory of Relativity. He explains how the main question in his opinion is whether the properties of space will have four variables or eight, explaining this in mathematical terms. He discloses, with great frankness under the circumstances, that his investigation of the use of a eight variables has not yielded results. He is therefore returning to his basic concept of four variables. He did not, however, give up his idea of reconciling the two theories into one unified one. Thus, in the end, Einstein closes no doors and shows how he viewed the ongoing progress of science: "What the future has in store for us nobody can foretell. It is a question of success."
For years after his death, physicists considered Einstein's search for one unified field as simply unsuccessful. However, that began changing in the 1970s, when physicists successfully unified the strong nuclear interaction and weak nuclear interactions together with quantum electrodynamics to form the standard model of quantum physics. More recently, many physicists have taken up the search where Einstein left off. The current quest for a unified field theory is largely focused on superstring theory. So ultimately, Einstein may well end up as right, and be considered as a prophet.
Letters of Einstein discussing science are increasingly uncommon, and those in English are even more so. Letters mentioning space/time, let alone discussing another theory on which he is working, are extremely difficult to find. We have never had another.