# Einstein's Discovery of General Relativity, 1905-1915

Busy day of meetings related to business of three separate committees. (The day started well, at about 6:00am, with writing and then giving a two hour class on string theory techniques….) But it’s all tiring and time-consuming. Sigh….

….But then the day ended wonderfully. We had Tilman Sauer of the Einstein papers Project give the final colloquium of the semeser, and it was entitled *“Einstein’s Discovery of General Relativity, 1905-1915”.* It was conceived as an event in celebration of the World Year of Physics or Einstein Year. The abstract:

Ninety years ago, on 25 November 1915, Einstein published the gravitational field equations of general relativity, the so-called Einstein equations. This event marks one of Einstein’s most significant achievements, even in comparison to his three most famous papers of his miracle year 1905. It also presents the end of a long and winding path that began soon after Einstein published his theory of special relativity as an unknown patent expert in 1905. At the end of this path he had risen through the ranks of academic hierarchy to being a member of the Prussian Academy of Sciences in Berlin. The experimental confirmation of his theory by a British eclipse expedition in 1919 then irreversibly catapulted Einstein to world fame, making him the first celebrity in the history of science. In the talk I will give an account of Einstein’s search for a theory of gravitation and a generalized theory of relativity in those years. I will show how an analysis of some of Einstein’s research notes helps us understand his heuristics, and will also comment on his competition with the mathematician David Hilbert in the final days of the discovery of general relativity.

(We can argue about whether he really was the first celebrity in the history of science -Galileo springs to mind- but I agree that the scale and scope was truly and unprecedentedly global in Einstein’s case, given modern communications, etc…. but we can discuss this maybe some other time…..)

Most of the focus of events for this year has been on Einstein’s “Miracle Year” of 1905, in which he wrote a series of five fantastic papers. But it so happens that November the 25th marks the 90th anniversary of his presentation of the field equations of General Relativity. So today, the 28th, was a good day to celebrate that event.

Let me point out the website for the Einstein papers project, and the associated online archive which is a collaboration with the Albert Einstein archives at the Hebrew University, which is here. It is a wonderful resource, and I should also mention the Einstein papers project’s books that the project releases containing the writings of Einstein, with historical commentary.

I thought it was an excellent colloquium, and the perfect end to the semester’s events. A good sign of how well-received it was by the audience (it was a full house again) is the fact that I had several hands up for questions -from students!- before the applause died down and before I could ask “are there any questions?”. Normally I have to beg, cry publicly, promise favours, or threaten violence (ok, I exaggerate…a bit), to get a student to ask a colloquium question, so that was just great.

One of the most valuable aspects of the talk for all to see and contemplate was the very process of theoretical physics research. The picture is of Einstein struggling along over the decade to try to construct the theory, trying what Sauer describes as a “physical approach” sometimes, and a “mathematical approach” at other times. It is excellent to see how he wrestled with the ideas, and how he made mistakes, wrong turns, missteps. How he turned away from the right answer in the wrong direction (he actually had the correct linearized field equations right there on his notebook pages in 1913…..two years earlier, and then turned away!), and how he learned from those around him, incorporating into his ideas what seemed good to him from wherever he could.

It was a good reminder of the truth of how this kind of process goes. We are often told (in our own recent struggles to construct a radical new theory of Nature), that we are wandering around blindly, and that we are not guided by a shining light along some elegant path to the answer like Einstein was. Well, it was not so elegant at times. He struggles along as best he could, and sometimes very inelegantly….he made guesses, and invented ad hoc “reasons” for his guesses that sometimes were just plain nonsense (in retrospect). He published paper after paper, (sometimes with collaborators) with half-baked and sometimes wrong-headed stabs at the answer. (For example, in an attempt to justify one guess (developed with Grossman in 1913), he spent a good couple of years on a quest to support the idea, in which he was willing to give up general covariance (that which we now believe to be at the core of gravitation) as simply incompatible with physics.)

It was not until the middle of 1915 (after taking his dog-and-pony show to Goettingen, the house of David Hilbert, Felix Klein, and Emmy Noether among others) did things begin to crystallize. The big climax was a series of four papers in November (each separated from the other by a week: the 4th, 11th, 18th, 25th!) that he -bit by bit- put things together, including getting the computation for the perihelion of Mercury’s orbit right (finally, after getting it wrong a number of times before). It is amusing to note that his computation of the latter was based on his penultimate version of the field equations -which was still incorrect- which were luckily correct just for that case (the terms that modify things to give the correct equations actually vanish for that particular computation…the equations in vacuum are much simpler than with sources).

(Yes, he did talk a bit about the so-called controversy over whether Hilbert published the correct field equations five days earlier. Well, he actually derived a variational principle which is equivalent to Einstein’s equations (actually, he was thinking only of the case of electromagnetic sources), and there is some question about the date. But his misses the point entirely…..Hilbert came into that game rather late, and was able to see more clearly the correct mathematics…..but we must not forget that he was able to build on all that Einstein had done over several years, putting all the right tools, principles and other pieces into place….nor must we forget Einstein’s great pains to compare what he was doing to Nature when he could, trying to derive observable consequences a several points. I digress. In addition to the books and other materials on the site already mentioned (see Princeton University Press for the collections of papers in several volumes) I recommend Pais’ wonderful Einstein biography “Subtle is the Lord” for discussion of this too, including the wonderful flurry of postcards they were exchanging in November as they kept dashing off papers to their respective academies to be rapidly published.)

This is an excellent lesson that these struggles can take a long time, and you cannot know how close you are to the end. Ten years could easily have been twenty…or more. This is what I meant in previous posts and comments when I say without embarrasment that it is too early to condemn the program of research into string theory. Nobody knows if it is right or wrong. Screaming loudly on blogs here, there, and elsewhere, and making spectacles in, and appeals to, the popular press won’t change that fact. I personally do not think that it is yet ready to compare to Nature. We don’t understand it at all well enough yet. Although, it would be nice if we were lucky, and we do need guidance from attempts to make comparisons, and so this is why it is important to have stringy and string-inspired phenomenological programs within the field. But we should not be surprised if those programs are not yet conclusive, since after all, we do not even understand the theory well enough to say what it is. Rather, we should be encouraged -given the tantalizing hints that the theory has given us so far- that we might be onto understanding something rather profound that arises in Nature when you combine gravity and the quantum. We shall see, but let’s not be hasty. One day, I hope, we will get it into the right shape to make a set of predictions that we can challenge with experimental and/or observational data. And then we will know, one way or another if it is right or wrong. (And in the meantime, the other benefits of this program of research in physics and mathematics have been numerous, and will no doubt continue to accumulate.)

This look over Einstein’s shoulder in his ten year struggle is also an excellent lesson that these battles are worth it in the end. I’ll close with the wonderful opening lines of his letter to his (dying) mother, in September 1919**:

Dear Mother,

Today some happy news. H. A. Lorentz telegraphed me that the English expeditions have recently verified the deflection of light by the sun.

-cvj

(**For those who don’t know, those expeditions went to South America (Brazil) and to Principe, an island off the Western coast of the African continent to witness a solar eclipse which allowed them to see that the distant stars that can be seen by looking near the edge of the sun, are slightly out of position because the gravity of the sun deflects the light from them. The deviation -and its actual amount- was predicted by Einstein’s 1915 theory.)

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