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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 speculatio

by cb321 18d 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. ;-)

lh712 18d ago
Thank you for your reply! Yes, I fully agree that meaning of "derive" and other related concepts are non-trivial. (And I actually changed my own "working definition" between my two posts; while in the first one I was leaning more towards theories anchored by observation, even if indirectly, in the second one I slipped into more mathematical/philosophical perspective. The second part of my first reply makes sense only from the first kind of perspective, because in that part I imagine that the observed reality, even at the medieval level of knowledge, might perhaps necessitate a particular kind of underlying theory, from which the relativity principle would then "fall out". That was the only way I could think of at that moment how SR could have been "derived" without further observations.) Your points about Leibniz are very interesting, and while I find that line of thought fascinating I must admit my own lack of knowledge of the historical context. In any case, thank you for pointing out that idea!
- cb321 17d ago
  You're welcome. Another lesser known wrinkle along these lines is that if more of Aristarchus of Samos' work on heliocentricity had been developed into a "calculational framework" for planetary motion by a contemporaneous Ptolemy competitor (a la Copernicus in 1543), various relativity ideas might well have started in 270BC instead of 1600 AD. Aristarchus was already WAY ahead of a few games - making a guess that "absolute rest" was illusory and tiny stars were similar to giant Sol. If not for Archimedes' serious star power, we might not even know of Aristarchus' heliocentric ideas! Relativity ideas of various kinds are short intellectual hops from "the absolute rest of your intuition is illusory". Aristarchus and his supporters just had to assert The Stars were very distant -- far enough for there to be NO PARALLAX! Various "coincidences" all conspired to suppress Aristarchus' plausibility, like: A) Just HOW DISTANT stars are/local galactic stellar density &| B) poor human VISUAL ACUITY relative to C) Earth ORBIT vs. Sun LUMINOSITY (parallax baseline) & maybe existence of Moon to vent atmo &| D) VERY SLOW (3 millennium) development from near prehistoric glass (1500BC) to grinding lenses for human eyes in the 1300s AD leading to Galileo's telescopes & etc. If ANY of (A)..(D) were about ~10x better (ALL of which are imaginably so), the day that universe changed could've been much earlier. Heck, even if Aristarchus just had a really good spin doctor like a major religion pushing the plausibility of "Sun=A close Star", that might've been enough. Archimedes almost invented the underlying ideas of integration and limits and all that, too. Close but no cigar, but (had that been in hand) analytic geometry and differential equations are short steps away. I mean, Newton surely noted the equivalence of gravitational and inertial "mass" (charge vs. kinematics) which is the weak principle of equivalence of GR, after all. Like I said - "littered". ;-) There are probably whole books written on the topic (or adjacent topics) of "All the Things Humanity Nearly Figured Out Earlier" that have a more historical bent than the usual "sci-fi tilt".

by cb321 18d ago

lh712 18d ago

Thank you for your reply! Yes, I fully agree that meaning of "derive" and other related concepts are non-trivial. (And I actually changed my own "working definition" between my two posts; while in the first one I was leaning more towards theories anchored by observation, even if indirectly, in the second one I slipped into more mathematical/philosophical perspective. The second part of my first reply makes sense only from the first kind of perspective, because in that part I imagine that the observed reality, even at the medieval level of knowledge, might perhaps necessitate a particular kind of underlying theory, from which the relativity principle would then "fall out". That was the only way I could think of at that moment how SR could have been "derived" without further observations.) Your points about Leibniz are very interesting, and while I find that line of thought fascinating I must admit my own lack of knowledge of the historical context. In any case, thank you for pointing out that idea!

cb321 17d ago
You're welcome. Another lesser known wrinkle along these lines is that if more of Aristarchus of Samos' work on heliocentricity had been developed into a "calculational framework" for planetary motion by a contemporaneous Ptolemy competitor (a la Copernicus in 1543), various relativity ideas might well have started in 270BC instead of 1600 AD. Aristarchus was already WAY ahead of a few games - making a guess that "absolute rest" was illusory and tiny stars were similar to giant Sol. If not for Archimedes' serious star power, we might not even know of Aristarchus' heliocentric ideas! Relativity ideas of various kinds are short intellectual hops from "the absolute rest of your intuition is illusory". Aristarchus and his supporters just had to assert The Stars were very distant -- far enough for there to be NO PARALLAX! Various "coincidences" all conspired to suppress Aristarchus' plausibility, like: A) Just HOW DISTANT stars are/local galactic stellar density &| B) poor human VISUAL ACUITY relative to C) Earth ORBIT vs. Sun LUMINOSITY (parallax baseline) & maybe existence of Moon to vent atmo &| D) VERY SLOW (3 millennium) development from near prehistoric glass (1500BC) to grinding lenses for human eyes in the 1300s AD leading to Galileo's telescopes & etc. If ANY of (A)..(D) were about ~10x better (ALL of which are imaginably so), the day that universe changed could've been much earlier. Heck, even if Aristarchus just had a really good spin doctor like a major religion pushing the plausibility of "Sun=A close Star", that might've been enough. Archimedes almost invented the underlying ideas of integration and limits and all that, too. Close but no cigar, but (had that been in hand) analytic geometry and differential equations are short steps away. I mean, Newton surely noted the equivalence of gravitational and inertial "mass" (charge vs. kinematics) which is the weak principle of equivalence of GR, after all. Like I said - "littered". ;-) There are probably whole books written on the topic (or adjacent topics) of "All the Things Humanity Nearly Figured Out Earlier" that have a more historical bent than the usual "sci-fi tilt".