Always a pleasure to read an appreciation of this turning point in human thought. But, like most accounts, this book excerpt gives the impression that Einstein worked alone to develop his theory. In fact, it was more of a collaboration:
Everybody was working on it and it was much more of a race to an inevitable interpretation of the world, than most
credit historically. Certainly not a single man vision.
Though special relativity was coming no matter what, I don't think we would have had general relativity without Einstein for at least another couple decades, likely longer. We would have had it without Hilbert. Hilbert got the key insights from Einstein, but he did a lot of the necessary work on the math, important work but work other mathematicians could have done. That's the difference.
Everybody as in, the leading experts in theoretical physics of the time:
"It was noted by Sir Edmund Whittaker in his 1954 book that David Hilbert had derived the theory of general relativity from an elegant variational principle almost simultaneously with Einstein's discovery of the theory.[B 1] Hilbert's derivation of the theory predated that of Einstein by five days.[B 2]"
Be careful however, as unfortunately some, for other reasons, historically tried to appropriate this work, and use to try to diminish the contributions of Einstein. Something that of course, is very much incorrect.
That equation is associated with SR, not GR. I’m not aware of anyone, aside from Einstein and the small group at Göttingen who were working with him, and a couple of his friends, such as Grossmann, who were helping him with the math, even being aware of this work on gravity. But I’m willing to learn. Please provide some names. Who were the “experts of the domain at the time”? For that matter, what is this domain?
The equation is not more associated with SR or GR, more than its historical context where it was derived from. Its just a principle of physics SR, GR or any
other theory.
Who are the people? The Berlin Group, David Hilbert, Carl F. Gauss, Bernhard Riemann, Ernst Mach,Henri Poincaré, Hendrik Lorentz. The domain are the studies on the understanding the most basic fundamentals of physics derived from the analysis of electromagentism that most leading physicists of the time were busy with. Although Hilbert and Poincare are monsters of pure mathematics they were just doing physics by the side.
Looking at the biography of Hilbert, it starts to look like almost obvious what happened. In no way it diminishes the stature of Einstein to recognize it.
Hilbert was a monster:-) Hilbert did invariant theory, calculus of variations, commutative algebra, algebraic number theory, geometry, spectral theory of operators and its application to integral equations, mathematical physics.
Einstein by the contrary, always needed help with Mathematics, since
the times at University. That was how he met his first wife...
Hilbert was following the work of Einstein but this latest one was struggling to make any progress for years. In the summer 1915, Hilbert's was interested in general relativity, and he invited Einstein to Göttingen to deliver a week of lectures on the subject.
Suddenly within a few weeks, Einstein comes up with his Field equations while Hilbert follows with his foundations of physics. The fact that Hilbert fully credited Einstein as the originator of the theory, and did not engage in any public priority dispute is pretty clear was as a statement to the
previous work Einstein did for years. With the collaboration and common work that happened its pretty clear, Einstein did not have the mathematical prowess and skill, to come up with those sudden breakthroughs...
He had even better than mathematical prowess: an intuition and creativity. Einstein's thought experiments were what led him to the discovery. What's the difference between someone with superior raw mathematical talent and strong mathematical talent plus creative intuition? I would argue, in particular with regards to physics, it makes all the difference.
"...a paradox upon which I had already hit at the age of sixteen: If I pursue a beam of light with the velocity c (velocity of light in a vacuum), I should observe such a beam of light as an electromagnetic field at rest though spatially oscillating. There seems to be no such thing, however, neither on the basis of experience nor according to Maxwell's equations. From the very beginning it appeared to me intuitively clear that, judged from the standpoint of such an observer, everything would have to happen according to the same laws as for an observer who, relative to the earth, was at rest. For how should the first observer know or be able to determine, that he is in a state of fast uniform motion? One sees in this paradox the germ of the special relativity theory is already contained.[p 1]: 52–53 "
> Suddenly within a few weeks, Einstein comes up with his Field equations
It wasn't a few weeks, it was months. Einstein visited Hilbert in June/July 1915. He didn't publish his field equation until November 1915 (and even then it took him several tries before he got the final one).
This is sort of a myth. Einstein was a poor mathematician in comparison with Hilbert, but that goes for most of us. He was fairly strong by the standards of the era.
Even that article doesn't mention Minkowski. Journalists and writers have such huge egos that can never see past the man in Einstein no matter how hard he tried to explain he was also standing on the shoulders of giants.
Do you think that Minkowski was important in the development of GR? Why, specifically? (I mean in its creation, not in the evolution of its interpretation after 1915.)
EDIT: I don’t understand the relationship between the egos of writers and their estimation of Einstein’s role. “Shoulders of giants:” in fact, it was Einstein who jealously guarded his credit for GR and never seemed to mention, in public, the contributions of others, although he did in his private letters.
> Do you think that Minkowski was important in the development of GR? Why, specifically?
Minkowski came up with the concept of spacetime as a 4-dimensional geometric object. That was a crucial insight required for the development of GR: just take this geometric object, which was flat in SR, and allow it to be curved.
IIRC Einstein himself, who initially was dismissive of Minkowski's idea, later changed his mind and recognized its importance, and said so in a number of his writings about relativity. Unfortunately, Minkowski died the year after he came up with his idea, so he never got to see where it led.
Doesn't Minkowski's work with hyperbolic space predate GR? I thought it was like a stepping stone between Special and General Relativity. I don't understand GR, I'm not even close and I tried for years twice or thrice to teach myself GR and I find it pretty impenetrable. Maybe I see Minkowski's work as a stepping stone because that's one of the paths that I was put into to understand it.
In my article I talk about the people that Einstein collaborated with in his struggle to arrive at the field equations. Minkowski was not one of those people (although he was one of Einstein’s math teachers in school).
I don’t think this work of Minkowski’s that you mention is directly relevant, but, even if it’s part of the mathematical background, Minkowski is not part of that particular story. Now we talk about "four dimensional" spacetime, and that point of view is largely due to Minkowski. But it wasn’t Einstein’s point of view, and for years Einstein remarked that he didn’t see the point—it seemed needlessly formal and academic to him. But he sort of came around later.
> I don’t think this work of Minkowski’s that you mention is directly relevant, but, even if it’s part of the mathematical background, Minkowski is not part of that particular story.
Probably you are right, but... maybe its just me, but this coincidence seems too much of a coincidence. I can't resist hypothesizing, would it be possible to Minkowski somehow influence Einstein, maybe indirectly. For example, Minkowski was interested in curved spaces, it is possible that he somehow implanted his ideas into Einstein's mind, isn't it? Not consciously, but as it happens with teachers passionate with their subject by bringing his favorite topic in his lectures for any reason or even without any reason.
> But it wasn’t Einstein’s point of view, and for years Einstein remarked that he didn’t see the point—it seemed needlessly formal and academic to him. But he sort of came around later.
This fact also can be incorporated into my hypothesis, though with an additional assumption: teenager Einstein was exhausted by his teacher's constant remarks about curved spaces, and was conditioned to roll his eyes hearing about curved spaces. So he naturally continued to roll his eyes at curved space-time.
Yeah, it is just a hypothesis, a wild guess, and even if it was true, it wouldn't mean that Minkowski was a collaborator, but what a fun story it may be. A story about a passionate teacher shaping a mind of genius into a curved space despite all lack of mutual enthusiasm.
On a more serious note, I can remark, that this hypothesis consistent with all I know about a human mind. Einstein might have a mental model for a curved space, and his mind might have used this model to propose new thought experiments, but Einstein disliked the very idea to the point of not noticing how his mind relies on it, and he worked hard consciously to find another model to rely on. Moreover there are psychological theories stating that a mind must have at least two different models/representations of a problem domain to deal with it successfully, so this hypothetical inner conflict might benefited Einstein's genius by urging him to construct his second mental representation of gravity.
The way I understand it, out of all the fathers of general relativity, Einstein was one of the only ones who really did physics. That is, applying the formulas to real life observations, or thought experiments, something that Einstein was particularly famous for.
Einstein got a lot of help with the maths, but I think he deserves full credit for the physical application.
Accepted practice for listing authors on scientific papers is always changing. In older papers you often have people listed in an acknowledgement who, today, would absolutely be on the author list.
A collaboration.. and even the article says 8 years of hard work and missteps and still we stick to the "Einstein's genius" narrative. I think the genius narrative is disingenuous to the person and discounts all the effort and furthermore putting everyone else in the position of "are you a genius? No right? So don't hope to do Einstein level work."
Well, I think it could also be disingenuous to presume that anyone could do what he did if you just put in the hard work. If hard work was all you need, we would have a lot more Einstein level discoveries than we do.
We do have a lot more Einstein level discoveries than most people may realize. If anything, we have so many discoveries that it's hard to single one out for special consideration. The big difference between now and then I'd argue is that progress is much more incremental today so that it never seems like you just wake up and there's one major breakthrough that comes out of nowhere. Instead we're constantly being exposed to small improvements that add up to significant advances over a 15-20 year period.
What would you say are some examples where you look back what the state was 15 years ago vs the progress we made till the present and the jump would seem just as profound. Just curious.
I felt the same way - it seemed like the early 20th century made so much progress with those visionaries compared what what is being made now. Obviously I am not well informed because that is likely not the case.
https://arstechnica.com/science/2015/12/general-relativity-1...