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The earliest you could reasonably derive special relativity is probably 1881 with the first version of the Michelson–Morley experiment, which showed that speed

The earliest you could reasonably derive special relativity is probably 1881 with the first version of the Michelson–Morley experiment, which showed that speed of light is the same no matter how you move through space. Which, on the scale of discoveries, is a pretty short timeline to the 1905 publication of special relativity. Which doesn't really stop you from training an LLM on 1904 knowledge and having it derive special relativity. LLMs trained with knowledge cutoffs that far back is a fun exercise, and one I've also dabbled in in the past. But you don't have anywhere near enough training data to reach SotA levels of intelligence, even if you had the money for those training runs. And lobotomizing all modern information out of LLMs doesn't seem viable either. So I don't see how you could ever turn that into a viable benchmark

cb321 12d ago
This is something of an aside on your first paragraph and lh712's. The theory of special relativity (and field theory in general) can be "derived" (as done in e.g., Landau, Lifshitz _Classical Theory Of Fields_) without empirical observation using concepts known to Galileo/Newton (if they count as "Medieval") - just with different assumptions/ideas about inertial frames. If you assume there is any phenomenon with a fixed observed speed in all "inertial frames" then you get special relativity with Einstein's gestalt-switch. After that it is, like so much in physics, a matter of thinking of an experiment to distinguish what matches capital-N Nature best. Thinking otherwise mistakes a fundamental error that the only way for something to happen is how it historically happened. Reconciling observations forced relativity historically, but it could have been sussed out without those. That there were very fast but finite speed phenomena (which could motivate relativity reducing to Newtonian models) was seen in 1676 by Rømer with the speed of light and eclipses of Io, a Galilean moon of Jupiter. It probably could have been done with Galileo's telescopes in 1610. (That is just one example of a phenomenon with a very fast yet finite speed to suggest other experiments to test that "hypothetical relativity".) TBH, this all relates to teaching "physics without calculus" and that sort of thing. Is the most clear presentation/derivation that which mirrors the history of our muddled yet ever demuddling ideas or that which starts from our most thoroughly demuddled ideas, best notations, etc.? The momentum is certainly the historical approach, yet there are notable exceptions.
- lh712 12d ago
  Well, exactly, and I think that that is in line with what I originally wrote, and which is that you need the general relativity principle (by general I don't mean the general relativity but the concept of the equivalence of inertial frames) and the theory electromagnetism. (By the way, I am familiar with the Landau--Lifshitz textbook.) (1) The relativity principle is exactly what you refer to yourself. You can't apply "Landau--Lifshitz"-like arguments without it. (And I don't think these principles count as medieval knowledge.) (2) I mentioned electromagnetism, because you need some clue for the concept of an absolute speed that is same for all inertial observers. This is very counterintuitive from our everyday experience, and counterintuitive from the point of view of somebody living in the time of "Galilean" or Newtonian mechanics. Theory of electromagnetism is the only thing that I am aware of, that is nearly (by a stretch) accessible at the level of "medieval" knowledge, from which the concept of constant speed follows. (Historically: Maxwell's completion of previously inconsistent equations of electromagnetism yielded a wave solution propagating with the constant speed of light. This was interpreted in terms of the ether originally, but it is a strong hint in itself for Einsteinian principle of relativity; and a reasoning along the lines you alluded to can them be applied, at least in principle.)
  - cb321 12d ago
    Yeah. My point was mostly to expand upon your original post - sorry if it sounded like I disagreed. You say the same in your original "iteration of speculation and observation". Everything else is about what "derive" and "knowledge" might mean (I agree "medieval" usually means pre-Renaissance and Galileo is modern-era), how much empirical "proof" is in "derive", etc. However, all you need for "possible" is "the idea", some "consequences", and ways to test. So, to push back a tad on your more recent "only thing that I am aware of" and to maybe explain my above point better, I do think there was enough information/ideas in the abstract in Galileo/Newton/Leibniz' times to suggest the idea. Leibniz himself pushed back hard on Newton's absolute space/time (long before Mach). For Leibniz, it would have been counterintuitive space/time vs. counterintuitive fixed speed. So, that pushback itself could have been enough of a "clue" in your terms -- in some alternate timeline -- to drive a speculation-observation cycle starting from different inertial concepts - with Galilean moon eclipses then enough a clue that fast speeds existed to fool our slow-speed intuitions. (And all this in the "modern era".) So, I continue to think it "not impossible" that the relativity principle could have arisen before any EM theory at all -- it just didn't. That matters for these kinds of speculative questions about what information horizons support what developments. A single "fast enough" fixed speed is is not that wild & crazy. The modern world has a zillion obscure physics theories like that (mostly just because so many more people work on that stuff, but that's a probability thing, not a possibility thing, and I suppose also partly inspired by how physics turned out - so not truly independent). History is littered with things that could have happened, but didn't. P.S.: and apologies for "mistakes a fundamental error". I of course meant "makes a", if you wanted any evidence that I was not an LLM. ;-)

cb321 12d ago

This is something of an aside on your first paragraph and lh712's. The theory of special relativity (and field theory in general) can be "derived" (as done in e.g., Landau, Lifshitz _Classical Theory Of Fields_) without empirical observation using concepts known to Galileo/Newton (if they count as "Medieval") - just with different assumptions/ideas about inertial frames. If you assume there is any phenomenon with a fixed observed speed in all "inertial frames" then you get special relativity with Einstein's gestalt-switch. After that it is, like so much in physics, a matter of thinking of an experiment to distinguish what matches capital-N Nature best. Thinking otherwise mistakes a fundamental error that the only way for something to happen is how it historically happened. Reconciling observations forced relativity historically, but it could have been sussed out without those. That there were very fast but finite speed phenomena (which could motivate relativity reducing to Newtonian models) was seen in 1676 by Rømer with the speed of light and eclipses of Io, a Galilean moon of Jupiter. It probably could have been done with Galileo's telescopes in 1610. (That is just one example of a phenomenon with a very fast yet finite speed to suggest other experiments to test that "hypothetical relativity".) TBH, this all relates to teaching "physics without calculus" and that sort of thing. Is the most clear presentation/derivation that which mirrors the history of our muddled yet ever demuddling ideas or that which starts from our most thoroughly demuddled ideas, best notations, etc.? The momentum is certainly the historical approach, yet there are notable exceptions.

lh712 12d ago
Well, exactly, and I think that that is in line with what I originally wrote, and which is that you need the general relativity principle (by general I don't mean the general relativity but the concept of the equivalence of inertial frames) and the theory electromagnetism. (By the way, I am familiar with the Landau--Lifshitz textbook.) (1) The relativity principle is exactly what you refer to yourself. You can't apply "Landau--Lifshitz"-like arguments without it. (And I don't think these principles count as medieval knowledge.) (2) I mentioned electromagnetism, because you need some clue for the concept of an absolute speed that is same for all inertial observers. This is very counterintuitive from our everyday experience, and counterintuitive from the point of view of somebody living in the time of "Galilean" or Newtonian mechanics. Theory of electromagnetism is the only thing that I am aware of, that is nearly (by a stretch) accessible at the level of "medieval" knowledge, from which the concept of constant speed follows. (Historically: Maxwell's completion of previously inconsistent equations of electromagnetism yielded a wave solution propagating with the constant speed of light. This was interpreted in terms of the ether originally, but it is a strong hint in itself for Einsteinian principle of relativity; and a reasoning along the lines you alluded to can them be applied, at least in principle.)
- cb321 12d ago
  Yeah. My point was mostly to expand upon your original post - sorry if it sounded like I disagreed. You say the same in your original "iteration of speculation and observation". Everything else is about what "derive" and "knowledge" might mean (I agree "medieval" usually means pre-Renaissance and Galileo is modern-era), how much empirical "proof" is in "derive", etc. However, all you need for "possible" is "the idea", some "consequences", and ways to test. So, to push back a tad on your more recent "only thing that I am aware of" and to maybe explain my above point better, I do think there was enough information/ideas in the abstract in Galileo/Newton/Leibniz' times to suggest the idea. Leibniz himself pushed back hard on Newton's absolute space/time (long before Mach). For Leibniz, it would have been counterintuitive space/time vs. counterintuitive fixed speed. So, that pushback itself could have been enough of a "clue" in your terms -- in some alternate timeline -- to drive a speculation-observation cycle starting from different inertial concepts - with Galilean moon eclipses then enough a clue that fast speeds existed to fool our slow-speed intuitions. (And all this in the "modern era".) So, I continue to think it "not impossible" that the relativity principle could have arisen before any EM theory at all -- it just didn't. That matters for these kinds of speculative questions about what information horizons support what developments. A single "fast enough" fixed speed is is not that wild & crazy. The modern world has a zillion obscure physics theories like that (mostly just because so many more people work on that stuff, but that's a probability thing, not a possibility thing, and I suppose also partly inspired by how physics turned out - so not truly independent). History is littered with things that could have happened, but didn't. P.S.: and apologies for "mistakes a fundamental error". I of course meant "makes a", if you wanted any evidence that I was not an LLM. ;-)