The Editors of the Z. Naturforsch. kindly asked us to comment on the article by Prof. Winterberg that they recently published (Z. Naturforsch., 59a, 715-719, 2004). We have prepared and submitted a detailed reply, but the Editors have declined to publish it as it stands, instead suggesting changes that we find unacceptable. We hope to publish this reply elsewhere.
Leo Corry, Jürgen Renn, John Stachel
As suggested in his "Final Comment," Prof. Winterberg's paper has a long history. Since he has mentioned it, and since this history has a direct bearing on some of the issues raised in the current version of his paper, we feel free to recount some of this history before getting to the substance of his paper.
Prof. Winterberg is not quite accurate in stating that "This [our emphasis] paper was on Nov. 21, 2002 originally submitted to Science ". The paper submitted to Science differs substantially from the current version. Prof. Winterberg is also less than candid in stating that " Science refused to publish my criticism paper, with the argument that my paper was allegedly of low priority for Science ." He omits to mention that the Editors of Science submitted his paper to us for comment, and that we prepared a substantial set of comments that he received. It was on the basis of these comments that his paper was rejected. We quote from the letter of Stewart Wills, Online Editor, Science , dated 9 January 2003.
We have now received a response from the authors of the original paper, which is enclosed for your information. On evaluation of the comment and response, we regret to say that your comment received a lower priority rating than other technical comments under consideration. As a result, we won't be able to publish it. We believe that, at this point- particularly in view of the age of the original article- this discussion is best pursued through new papers and contributions in the specialty history-of-science literature than in the Technical Comments section of Science .
Discussion--and even controversy--are at the heart of progress in science and scholarship more generally. We certainly do not consider any of our conclusions sacrosanct, and we had no objection at the time to the publication of Prof. Winterberg's paper and even prepared a reply; nor do we have any objections now (although we shall make some critical comments about inclusion of one feature of the new version). We do agree, however, with the Science editor's suggestion that further discussion would be more appropriate in a journal devoted to the history of science. Evidently, Prof. Winterberg disagrees: he wishes to continue the discussion of a topic in the history of science in a physics journal, and the editors of this journal have accepted his paper. So be it.
But it is less than candid for Prof. Winterberg to submit a paper that has been greatly altered--evidently, as we shall see, in at least some measure in response to our critical comments- as if it were his original paper, and without even mentioning that he is in possession of our comments. It is especially ironical that he should present the current version of his paper without mentioning that it is a substantially altered version of the paper he submitted "on Nov. 21, 2002," since it is just such an unacknowledged change of Hilbert's paper between the dates of its original submission and of its final publication that constitutes a major issue in the discussion.
While we have no objection to continued discussion of these matters, we must object to the introduction of what we can only characterize as "the paranoid style"1 in the current version of Prof. Winterberg's paper, starting with the Abstract . It originally closed with the word "untenable." He has now added:
and has no probative value. I will rather show that the cut off part[s] of the proofs suggests a crude attempt by some unknown individual to falsify the historical record.2
This raises the suspicion that it was not done with scissors, but with a razor blade or pocket knife, possibly in the special collection reading room of the Göttingen library, with the intent to erase the long held view that Hilbert had the correct final form of the field equation before Einstein.
This is followed by a brief excursus into scholarly forgeries, the relevance of which, on even the most charitable interpretation, is dubious since none of the cited forgeries involved the excision of anything.
Let us be clear. If Prof. Winterberg has a specific accusation to make against some person or persons, let him make it; vague, unsupported charges of a conspiracy in favor of Einstein and against Hilbert have no place in a scholarly article. All members of the scholarly community must be presumed to be seekers of the truth, however wrong or misguided we may feel that they are in the course of the search, unless and until some proof to the contrary is offered. If the paranoid style that has pervaded much politics for decades- and neither Germany, Israel nor the United States (to cite only the home countries of those involved in the controversy) has been immune to it--if this style is now to be allowed in scholarly discussion we are lost! Or rather, we are back to the days of "Jewish physics" in Germany, "bourgeois genetics" in the Soviet Union and "Godless evolutionism" in the U.S.A.
But now let us turn to the content of Prof. Winterberg's paper. In the attempt to return the discussion to its proper level, we have decided to reproduce our comments on his original article as prepared in 2002, and add additional comments on the new version in footnotes3 and at the end of our paper. We shall leave it to the reader to decide how much has been changed in response to our comments. Of course, we have no objection to changing views in the course of a discussion- that is what discussions are for. But we do think that the source of such changes should be acknowledged.
Prof. Winterberg does not mention our first claim, discussion of which takes up most of our three-page paper; so we shall assume that he does not wish to contest this claim. He confines himself to a discussion of the second claim, which is addressed in about one quarter of a page of our paper. He reformulates the issue as the following question:
Did Hilbert "anticipate Einstein in arriving prior to Einstein at the correct form of the gravitational field equations?" (his Abstract , our emphasis).4
But the claim made in our paper, both as cited above and repeated anew, is that "Hilbert, however, does not give the explicit form of this gravitational part of the field equations". (3) There is a clear difference between "correct" (as opposed to "wrong," Winterberg's distinction as in his statement that on "November 4, 1915, Einstein submits the still wrong equations to the Prussian Academy"5, his original paper, p. 3), and "explicit" (as opposed to "implicit," which is our implicit distinction. No claim is made in our paper that eq. (26) on p. 11 of the proofs (see the illustration of this page in Prof. Winterberg's article) is "wrong"; indeed it is "correct" but not "explicit," since it merely indicates the need to take the variational derivative of the gravitational term in the Lagrangian with respect to the metric tensor, without evaluating that derivative.
Prof. Winterberg states that "the variational derivative automatically leads to the trace term" (his original paper, p. 4, our emphasis), and indeed it does--but only if one evaluates it. The value of pi "automatically" leads to the one-billionth digit in its decimal expansion. Perhaps Prof. Winterberg could tell us what that digit is without evaluating it, but we cannot.
Of course, Prof. Winterberg believes that this variational derivative was explicitly evaluated in the small part of p. 8 of the proofs that is missing from the copy preserved in Göttingen. (By the way, in our follow-up paper, (4) it is not "admitted," as Winterberg puts is, but just noted that "the upper part of page 8 of the proofs has been cut off."). Now in the final, published version of his paper, (5) Hilbert did present his evaluation of this variational derivative (based on a fallacious argument, as we demonstrated in our paper) immediately after the sentence in which he writes down the gravitational field equations (Eq. (26) in Hilbert's paper). Except for the numbering of the equation, this sentence read almost word-for-word the same as the corresponding sentence on p. 11 of the proofs (reproduced in Prof. Winterberg's article). If such an evaluation had appeared on p. 8 of the proofs, as Prof. Winterberg suggests, he offers no reason why Hilbert should have then moved it from its earlier place to its final resting place in the published version. We can think of no reason, and until Prof. Winterberg supplies one, we must consider his suggestion to be entirely unsubstantiated.
On the other hand, in both, (1) (4) we have given reasons for believing that Hilbert had not yet evaluated the variational derivative in the proofs. Our reasoning is based on the study of Hilbert's treatment of the question of evaluation of the left hand side of the field equations in four successive versions of his paper. Rather than repeat this discussion, we shall now present an additional argument in favor of our claim.
Prof. Winterberg fails to note that "the trace term" introduced by Hilbert is quite different from that introduced by Einstein. Indeed, there is no one single "correct form of the gravitational field equations," as Winterberg writes (his Abstract). As one of us noted (6) in discussing the published version of Hilbert's paper,
"the trace term 1/2 g μν R, where R is the trace of the Ricci tensor, is subtracted from the Ricci tensor, giving what we now call the Einstein tensor as the left-hand side of the field equations ," and "he was the first to give the field equations in this form. ...Einstein, in his paper of 25 November had the Ricci tensor on the left hand side, with the trace of the stress-energy tensor subtracted on the right hand side . The two forms are completely equivalent, of course; but whether Hilbert or Einstein immediately recognized this is not clear; nor is it clear, if Hilbert did recognize it, whether it influenced him in any way. What is clear is that the argument he offers for the form of the left-hand side of the field equations is fallacious" (Reference (6) , 2002 reprint, pp. 360-361, emphasis added).
Since Prof. Winterberg does not contest our claim about the fallacious nature of Hilbert's original argument for the trace term, we shall not repeat the argument for it here. But let us cite the evidence suggesting mutual incomprehension in November 1915. After reading Einstein's first communication of November 4, 1915, Hilbert wrote Einstein, "Insofar as I understand your new paper, the solution given by you is completely different from mine..." (David Hilbert to Albert Einstein, 14 November, 1915, cited from Reference (1) , p. 1272). After "Hilbert ...sent the requested copy or summary of his paper" ( ibid ., p. 1272; in spite of Prof. Winterberg's statement that "Einstein acknowledges having received in advance a copy of Hilbert's paper to be delivered by Hilbert to the Göttingen Academy on November 20, 1915," it is not clear precisely what Hilbert sent Einstein), Einstein replied: "The system given by you agrees-as far as I can see-exactly with that which I found in recent weeks and submitted to the Academy" (Albert Einstein to David Hilbert, November 15, 1915, again cited from ibid ., p. 1272).
Prof. Winterberg does not cite Hilbert's letter, and omits an important clause in his citation of Einstein's letter--"as far as I can see," a phrase which counterpoints Hilbert's "Insofar as I understand your new paper". It is clear from this exchange that, at this point, at least one of the two--and probably each--is misunderstanding the other's work.
Prof. Winterberg evidently wants to say that Einstein is wrong--indeed he has a penchant for using the words "right" and "wrong" in a context in which the protagonists use "the same" and "different" when comparing their equations. But how does he propose to interpret Hilbert's statement that "the solution given by you is completely different from mine"? If, as Prof. Winterberg contends, by then Hilbert had already written down the explicit form of his field equations with the trace term on the left-hand side, this would be a curious statement indeed for him to make: A great mathematician like Hilbert could hardly regard equations differing only by a trace term as "completely different."
It seems much more natural to assume (as we did for other reasons) that Hilbert had not yet written down the explicit form of his field equations, and so did not yet realize that, as far as the left-hand side goes, his field equations differed from Einstein's only by a trace term in the Ricci tensor. Hilbert's mathematical approach led him to propose the variational derivative of the Ricci scalar as the left-hand side of the field equations. But nothing in the proofs nor the final, published version of Hilbert's paper depends on the explicit form of this variational derivative, so he was under no obligation to evaluate it in the draft.
Einstein, for his part, had good and sufficient reasons for introducing a trace term involving the stress-energy tensor on the right-hand side of his field equations, based on his physical arguments for the form of the gravitational field equations. Indeed, if he knew about the need for a trace term by 15 November 1915 because of Hilbert's work, as Prof. Winterberg assumes, it would have been odd indeed for him to then submit his paper of 18 November 1915, which is still based on the field equations without a trace term and with restricted covariance.
Be it further noted that the final, published version of Hilbert's paper did not appear in print until March 1916, long after Einstein's paper of November 15, 1915, which appeared on December 2, 1915. There can be no question about whether Hilbert was aware of this paper by Einstein when he revised his first draft for publication (remember, the proofs are dated "December 6"). Indeed, in the final, published version of his paper he cites it, along with Einstein's three earlier papers in the 1915 Academy Proceedings sequence,.
Hilbert certainly changed many things in his first draft in response to Einstein's final paper, as discussed briefly in (1) and in detail in (4). Rather than making any flat assertion about the influence of Einstein's paper on Hilbert's explicit evaluation of the trace term in the final version, all we say about this question in (1) is: "... knowledge of Einstein's result may have been crucial to Hilbert's introduction of the trace term into his field equations" (p. 1272, emphasis added).
(4) J. Renn and J. Stachel, "Hilbert's Foundation of Physics: From a Theory of Everything to a Constituent of General Relativity," Max-Planck-Institut für Wissenschaftsgeschichte, Preprint 118 , 1999. Download PDF file at (http://www.mpiwg-berlin.mpg.de/PREPRINT.HTM).
(6) John Stachel, "New Light on the Einstein-Hilbert Priority Question," Journal of Astrophysics and Astronomy 20 (1999): 91-101, reprinted in ibid., Einstein from `B' to `Z' (Boston: Birkhauser 2002), pp. 353-364.
Now we shall make some additional comments on the new version of Prof. Winterberg's paper. Prof. Winterberg has evidently seen the force of our distinction between "implicit" and explicit: We never challenged the obvious fact that the exact form of the left-hand side of Einstein field equations is implicit in Hilbert's variational Lagrangian (on the right-hand side he could only get the Mie stress-energy tensor, of course, as Prof. Winterberg notes in his new version). What we do challenge is the assertion that the explicit form of these field equations is to be found in the proofs of Hilbert's paper, even if we take into account the missing portion of pp. 7-8.
First let us turn to the question of the size of cut-off top portion of pp. 7-8.6 In the current version, he has interpolated the phrase: "approximately one third" in his description of the extent of the missing portions of p. 7 and of p. 8. We are grateful to him for raising the question of just how much is missing. It leads to a simple comparison of pp. 7-8 with (any of) the complete pages in the proofs, which shows that less than one fifth of each page is missing (6 3/4 inches compared to 8 1/4 inches in the photocopy in our possession). So any candidates for the missing material would have to fit into 1 1/2 inches on pages 7 and 8. The crucial page by common agreement is p. 8, so we shall concentrate on it.
If one examines the layout of any page of the proofs, it is seen that, if a one-line equation is included in 1 1/2 inches of a page, there is room for only five additional lines of type, or (taking into account the blank spacing above and below and equation) two lines plus an additional one-line equation.
If the missing eq. (17) in the proofs is the equation H = K + L as Renn and Stachel believe, the equation for the variational derivative [equation omitted] would come after eq. (17) on the missing part of p. 8, as in the published version where it comes after eq. (21), and where it has been given no number.
Several comments are in order. Eq. (21) in the published paper is indeed H = K + L . But Prof. Winterberg neglects to inform the reader that this is the second time that this equation appears in the paper. It was introduced first two pages earlier, without numbering, but followed by the definitions of K and L . Since this would be the first time that K and L are introduced in the proofs, it seems most likely that the five remaining lines would be used for their definition.
Secondly, if the equation for the variational derivative that Prof. Winterberg suggests- or any other equation, for that matter--were included in the missing 1 1/2 inches, there would remain room for only a couple of lines of text-hardly enough to explain why the field equations are suddenly introduced into a discussion of energy expressions that starts on p. 7 before and continues on p. 8 after the missing portion. So it is clear why Prof. Winterberg wants "approximately one third" of a page to be missing- but it is equally clear that it is not.
Now let us turn to possible explanations of why this portion is missing. Prof. Winterberg's paranoid style explanation has been discussed earlier. But there are other possible explanations, one offered by Dr. Tilman Sauer, that Prof. Winterberg evidently does not like. We shall leave to Dr. Sauer the defense of his position.7
But, since Prof. Winterberg seems fond of speculation, we shall suggest another possible, non-paranoid explanation of the missing portion. It is well known that Hilbert sent Felix Klein three sheets from the proofs in 1918, with the request that they be returned to him as he had no other copy.8 Dr. Sauer has noted that:9
But this suggestion does not seem quite right to us, since Hilbert's letter to Klein makes explicit mention of p. 6 of the proofs. So let us assume that it was pp. 1-2, 3-4 and 5-6 that were the "three sheets" ["drei Blätter'], to which Hilbert refers in the letter.
Now page 6 ends in the middle of a sentence, and the remaining portion of p. 7 starts with a new paragraph. So we suggest it is possible that Hilbert himself cropped off the top of p. 7 to include it with the three sheets he sent Klein, in order that they not end in mid-sentence. This would also explain why the cropping on p. 7 cuts into the first sentence on the remaining portion of this page: Hilbert was only concerned with including the completion of the paragraph which started at the bottom of p. 6, and didn't care if he cropped part of the next paragraph on p. 7. The missing small slip of paper could have been lost any time in the course of the pages of proofs being sent to Felix Klein, Klein's returning them to Hilbert, or the intervening years until they ended up in the Göttingen Library.
Since Einstein still believed his erroneous equations were correct as late as Nov. 18, 1915, it is clear that Hilbert, who had the correct equations before Nov. 18, 1915, arrived at them before Einstein.
and with his assertion that the proofs contain the explicit form of the gravitational field equations If Einstein had received a paper from Hilbert by November 18 that contained the explicit form of the gravitational field equations,10 how could he write Hilbert that he (Einstein) had obtained "the same equations in the last weeks" (Winterberg's words, not Einstein's) and at the same time "still [have] believed his erroneous equations were correct as late as Nov. 18" (again Winterberg's words)? Clearly, something has to give in Prof. Winterberg's set of incompatible assertions. We believe that none of just-cited assertions of Prof. Winterberg's are accurate; but we leave it up to him how he wishes to modify them to at least make them consistent.
Prof. Winterberg has introduced substantial modifications of the last part of his paper in order to highlight the part played by Marcel Grossmann in the development of general relativity. While we cannot agree with many of Prof. Winterberg's assertions, there is no need for us here to enter further into this question for two reasons:
1. See Richard Hofstadter, "The Paranoid Style in American Politics," Harper's Magazine , November 1964, pp. 77-86; reprinted in his book The Paranoid Style in American Politics and Other Essays (paperback reprint, Harvard University Press 1996): "I call it the paranoid style simply because no other word adequately evokes the sense of heated exaggeration, suspiciousness, and conspiratorial fantasy that I have in mind. In using the expression `paranoid style' I am not speaking in a clinical sense, but borrowing a clinical term for other purposes. I have neither the competence nor the desire to classify any figures of the past or present as certifiable lunatics., In fact, the idea of the paranoid style as a force in politics would have little contemporary relevance or historical value if it were applied only to men with profoundly disturbed minds. It is the use of paranoid modes of expression by more or less normal people that makes the phenomenon significant."
10. Dr. Tilman Sauer has established that Hilbert submitted his manuscript to the printers on November 19 (see Sauer 1999 [Winterberg's reference], p. 543), which makes it unlikely he had completed it much earlier. As noted above, it is still quite unclear just what Hilbert sent Einstein.