Einstein Versus the Physical Review

Einstein introduced gravitational waves into his theory of general relativity in 1916, within a few months of finding the correct form of the field equations for it. Although the concept of gravitational radiation was then relatively new and no experimental evidence existed to support it, the analogy with the case of the electromagnetic field was so compelling that by the 1930s most scientists thought that gravitational waves must exist in principle. Nevertheless, in 1936 Einstein wrote to his friend Max Born:

Einstein submitted this research to the Physical Review under the title “Do Gravitational Waves Exist?” with Rosen as coauthor. Although the original version of the paper no longer exists, Einstein’s answer to the title question, to judge from his letter to Born, was “No.” It is remarkable that at this stage in his career Einstein was prepared to believe that gravitational waves did not exist, but he also managed to convince his new assistant, Leopold Infeld, who replaced Rosen in 1936, that his argument was valid. ⁵ Infeld is shown with Einstein in figure 2.

But not everyone was so easily convinced. The Physical Review received Einstein’s submission on 1 June 1936, according to the journal’s logbook. Tate returned the manuscript to Einstein on 23 July with a critical review and the mild request that he “would be glad to have [Einstein’s] reaction to the various comments and criticisms the referee has made.” Einstein wrote back on 27 July in high dudgeon, withdrawing the paper and dismissing out of hand the referee’s comments:

On 30 July, Tate replied that he regretted Einstein’s decision to withdraw the paper, but stated that he would not set aside the journal’s review procedure. In particular, he wrote, “I could not accept for publication in THE PHYSICAL REVIEW a paper which the author was unwilling I should show to our Editorial Board before publication.”

The paper was, however, subsequently accepted for publication by the Journal of the Franklin Institute in Philadelphia, ⁶ a periodical in which Einstein had already published. The paper appeared with radically altered conclusions in early 1937. A letter dated 13 November 1936, from Einstein to the journal’s editor, indicates that the institute had accepted the paper in its original form: Einstein simply explained why “fundamental” changes in the paper were required because the “consequences” of the equations derived in the paper had previously been incorrectly inferred.

What originally led Einstein to the conclusion that gravitational waves do not exist? Having set out to find an exact solution for plane gravitational waves, he and Rosen found themselves unable to do so without introducing singularities into the components of the metric that describes the waves. This was surely not at all what they had hoped for. But, like good physicists confronted with the unexpected, they attempted to turn it to their advantage. In fact, they felt they could show that no regular periodic wavelike solutions to the equations were possible. ⁷ Instead of a solution to the Einstein equations, they had a nonexistence proof for solutions representing gravitational waves—a far more important and breathtaking result.

Today it is well known that one cannot construct a single coordinate system to describe plane gravitational waves without encountering a singularity somewhere in spacetime. But it is also understood that such a singularity is merely apparent and not real. It is a coordinate singularity, analogous to the problem one encounters when attempting to find the longitude of the North Pole. Einstein was one of the first to understand the critical difference between coordinate and physical singularities, but in the 1930s there was still no mathematical formalism for distinguishing between the two. It was something that had to be worked out by trial and, frequently, error. Only after World War II did the identification of singularities become rigorous. In 1936 Einstein and Rosen were too cautious, treating a harmless coordinate effect as a real physical pathology. It simply did not occur to them that trying to cover the whole of their spacetime with a single coordinate system was asking too much.

In the summer of 1936, the relativist Howard Percy Robertson (pictured in figure 3) returned to Princeton from a sabbatical in Pasadena, and later that year struck up a friendship with Einstein’s then newly arrived assistant Infeld. One of the most distinguished figures in the new field of cosmology, Robertson was a colorful, jovial character who enjoyed cultivating enemies as much as he, in Infeld’s words, “enjoyed spiteful gossip” about his colleagues.

He told Infeld that he did not believe Einstein’s result, and his skepticism was unshakable. Robertson went over Infeld’s version of the argument with him, and they discovered an error. ⁵ Infeld related the conversation to Einstein, who concurred and drastically changed the Franklin Institute paper in proofs.

Curiously, Infeld states that when he told Einstein he and Robertson had uncovered an error in his (Infeld’s) version of the proof, Einstein replied that he had coincidentally and independently uncovered an error in his own proof the night before. ⁵ Unfortunately Infeld gives no details about those errors in his autobiography. He writes that Einstein had only realized that his proof was incorrect and had still not managed to find the gravitational wave solution he had been looking for.

But Einstein had been closer to a solution than he thought and it was here that Robertson made his key contribution, at least according to remarks made by Rosen in a later paper of 1955. ⁸ Robertson observed that the singularity could be dealt with by a change of coordinates, an approach that revealed that Einstein and Rosen were dealing with a solution representing cylindrical waves. With the coordinate change the worrisome singularities were relegated to the central axis of the spacetime, where one would expect to find the source of the cylindrical waves.

Associating singularities with a material source was relatively common and widely accepted, although Einstein and some others had often expressed serious reservations about the practice. But any port in a storm will do, and Einstein was happy to retitle his paper “On Gravitational Waves,” as shown in figure 4, and present those cylindrical waves, which he had stumbled upon unwittingly.

The irony, of course, is that Einstein could have found that escape route months earlier, simply by reading the referee’s report that he had dismissed so hastily. The referee had also observed that casting the Einstein–Rosen metric (as we now call this solution of the Einstein equations) in cylindrical coordinates removes the apparent difficulty.

Coincidentally, in the Soviet Union, Rosen was also having second thoughts, and wrote back to Einstein that he, too, thought there was an error in the paper. But Rosen was not completely happy with the Franklin Institute version, so in 1937 he published his own revised treatment—one that proves only the nonexistence of plane gravitational waves—in a Soviet journal. ⁷ That paper is the closest account we have to the original manuscript submitted to the Physical Review. After the war, Ivor Robinson, Hermann Bondi, and Felix Pirani showed that Rosen’s argument was incorrect because the singularities involved were merely coordinate in nature.

Meanwhile, Einstein was not a man to waste time on embarrassment. Infeld relates the amusing detail that Einstein was due to give a lecture in Princeton on his new nonexistence proof, just one day after his discovery of its errors. He had not yet spoken to Robertson and discovered the way out of his difficulty, and so was obliged to lecture on the invalidity of his own proof. He concluded the talk by saying “If you ask me whether there are gravitational waves or not, I must answer that I do not know. But it is a highly interesting problem.” ⁵  

Einstein rarely let personal pride interfere with his work. While they were working on the popular book, Evolution of Physics: The Growth of Ideas from Early Concepts to Relativity and Quanta, which they wrote together, Infeld told Einstein that he took special care because he could not “forget that your name will appear on it.”

Although it now bears Einstein and Rosen’s names, the solution for cylindrical gravitational waves had been previously published by the Austrian physicist Guido Beck in 1925. But Beck’s paper was completely unknown to relativists with the single exception of his student Peter Havas, who entered the field in the late 1950s. In a 1926 paper by the English mathematicians O. R. Baldwin and George B. Jeffery, and in the referee’s report on Einstein’s paper, there was discussion of the fact that singularities in the metric coefficients are unavoidable when describing plane waves with infinite wavefronts. But although such a wave shows some distortion, in the words of the referee, “the field itself is flat” at infinity. ⁹  

Clearly, the referee’s familiarity with the literature exceeded Einstein’s, but then Einstein was notoriously lax in that regard. The published Einstein–Rosen paper contains no direct reference to any other paper whatsoever and only two other authors are even mentioned by name. In response to Infeld’s suggestion that he search the literature for previous work, Einstein laughed and said, “Oh yes. Do it by all means. Already I have sinned too often in this respect.” ⁵  

So who was the referee? The report is 10 pages long and shows a deep, if not total, familiarity with the literature on gravitational waves; the referee knew of the 1926 paper by Baldwin and Jeffery, but not Beck’s of 1925. The copy forwarded to Einstein was typewritten and the spelling followed American practices. That points to an American author with a strong interest in general relativity. Few people at the time—among them Robert Oppenheimer and Richard Chase Tolman, both based in California—fit that description. Suspicion naturally falls on Robertson too, of course. After all, he appeared to have the solution to the paper’s flaws at his fingertips in the fall of 1936 when he spoke with Infeld.

In the first half of 1936, Robertson was on sabbatical at Caltech, and therefore absent from Princeton when the gravitational-wave paper was presumably written. (Rosen did not leave for the Soviet Union until near the end of July, according to a letter written on his behalf by Einstein to Vyacheslav Molotov on 4 July.) Robertson apparently did not return to Princeton until mid-August. Einstein was on vacation in upstate New York until late August; the angry letter to Tate, dated 27 July, was sent from Saranac Lake. Therefore Robertson’s encounter with Infeld, which probably took place in early October, may have been his first opening to approach the great man in person about the difficulties with his paper.

Robertson’s own papers are preserved in the Caltech archives. Among them, when I first browsed the collection ten years ago, was a letter to Tate, written on 18 February 1937. Robertson writes,

Therefore, it seems clear that Robertson was the referee. Finding that Einstein had completely ignored his written critique, he took the opportunity of their collegial closeness at Princeton to correct the great man in a less confrontational fashion. Blume’s release of the logbook records—a decision made because 69 years have passed and no one involved is still living—confirms the identity (see figure 5).

Inspired by this discovery, I returned to the Robertson archives to check on his movements that summer. To my surprise, further material had been added to the archive: Sitting in the middle of the Tate correspondence was most of the immediate exchange between Robertson and Tate concerning the Einstein–Rosen manuscript. Here is what Robertson had to say in his reply (dated 14 July) to Tate’s still-missing original letter:

Tate thanked Robertson and rewarded his diligent referee in the usual manner—by sending him another tricky assignment.

We are probably justified in assuming that Einstein, over-come with the novelty of receiving such a report, barely glanced at the 10-page set of referee comments he was sent. German journals in the early part of the 20th century were considerably less fastidious than the Physical Review about what they published. Infeld claimed that the German attitude, in contrast to that prevailing in Britain and America, was “better a wrong paper than no paper at all.” ⁵ In a March 1936 letter to Einstein, the relativist and fellow European exile Cornelius Lanczos, who had himself been on the receiving end of one of Robertson’s reports, remarked on “the rigorous criticism common for American journals” such as the Physical Review.  ¹⁰  

Historians Christa Jungnickel and Russel McCormmach have studied in some detail the editorial policies of Annalen der Physik, the leading German journal of the early 1900s, and note that “the rejection rate of the journal was remarkably low, no higher than five or ten percent.” ¹¹ They describe the editors’ reluctance to reject papers from established physicists, even relatively junior ones. As they put it, “Now and then the journal published bad papers by good physicists.” In one specific example, editor Paul Drude annoyed Max Planck by printing what Planck considered a worthless paper, whose author had “appealed to [Drude] personally, and Drude lacked the heart to refuse him.” ¹¹  

Planck’s own editorial philosophy was to “shun much more the reproach of having suppressed strange opinions than that of having been too gentle in evaluating them.” ¹⁰ In America things were different, although Robertson and Tate surely treated Einstein more gently than they would have many others. Indeed, Robertson, in his very next report to Tate, commented that the author “is a man of good scientific standing, and it would seem to me that if he insists, he has more right to be heard than any single referee has to throttle!” That dispute turned more on matters of interpretation, though, and when it came to a paper that might actually be wrong, even an Einstein had to be queried, however gently.

Doubtless the rigorous criticism may have come as something of a shock to Einstein, who was accustomed to gentler treatment early in his career. However, Einstein could be very frank and direct in his criticism of others’ work. From 1914 on, as a member of the Prussian Academy of Sciences, he was regularly called on to review articles submitted to the academy’s proceedings. The German word for worthless frequently occurs in those brief reviews. As a member of the academy, Einstein had his papers published without question or revision. Anything less must have seemed to him a tremendous slight.

In his letter to Einstein, Tate had carefully avoided stating that anonymous review by the editorial board or others was a necessary step in the acceptance of a paper by the journal. In fact, the Physical Review logbook suggests that neither of the two previous papers by Einstein and Rosen, including the one with Podolsky, had been sent to a referee: In both cases the field for the referee’s name was left blank, and the EPR paper was sent for publication the day after its receipt at the journal. Therefore it is likely that the gravitational wave paper was Einstein’s first encounter with the anonymous peer-review system practiced in American journals at the time.

That Tate chose to have the 1936 paper refereed is interesting. After all, Einstein’s two previous submissions were certainly controversial. EPR is arguably the most controversial paper Einstein ever published, and the Einstein–Rosen bridge paper was part of an ongoing controversy with Ludwig Silberstein. ¹⁰ Einstein and Rosen’s letter to the Physical Review in 1935 was part of this same debate. Tate published both of those papers without outside advice.

A paper purporting to prove that gravitational waves did not exist, though, apparently sounded alarms with him. Nowadays one imagines that most physicists of the time knew little and cared even less about general relativity. But apparently gravitational waves were already such a well-accepted prediction of the theory, despite the absence of experimental support, that such a surprising result warranted some scrutiny. More than a month elapsed between receipt of the paper and its referral to Robertson. The delay certainly suggests hesitation on Tate’s part, and may even be evidence of an initial round of editorial discussion.

In general Tate did not like to slow the publication of important work and often relied on his own editorial instincts, ¹² which certainly served Einstein well. Tate published the better-known papers expeditiously and, by consulting Robertson for the third, saved Einstein from what would have been a very public embarrassment. The relatively innocuous Franklin Institute paper still attracted newspaper attention. Indeed, Rosen learned that the paper had appeared only when he received a newspaper clipping about it from a friend. The price for Tate was that he would never again receive a submission from “his most distinguished contributor.”

Special thanks go to Martin Blume and the Physical Review for permission to see and publish the critical line and details from the logbook. Also thanks to Diana Buchwald for translation of Einstein’s letter to Tate, and to John T. Tate Jr for permission to quote from his father’s correspondence. I am grateful to the Caltech Archives for permission to quote from the correspondence of H. P. Robertson and to the Hebrew University of Jerusalem for permission to quote from Einstein’s correspondence.

Daniel Kennefick is a visiting assistant professor of physics at the University of Arkansas at Fayetteville and an editor with the Einstein Papers Project at the California Institute of Technology.