Dear physicists!
In many physics textbooks the authors say that it was concluded on the basis of experimental tests that the euclidean geometry is valid in the huge range, from 10^(-15) to 10^26 meters. But they only describe Gauss experiment on the triangle angles sum measurement between 3 mountains. (see russian books, e.g. Sivukhin General physics course. Mechanics, M, 1979; Matveev Mechanics and relativity theory, M., 2003).
I have interested in it and I tried to find the articles on the experimental tests of euclidean geometry. I searched the following: elibrary.ru, sciencedirect, google academia, onlinewiley, iop.org, google, yandex. I have found NOTHING!
How do physicists work? How do they discover new physical laws?? Is the physical experiment correct if the physicist did not test whether the space in his experiment euclidean or not? Maybe he even does not carry on it.
I would be grateful if you direct me in the right way or send some references! Thank you for an advance!
Уважаемый Анатолий Анатольевич,
К сожалению, не могу Вам помочь. Не являюсь экспертом в этой области.
Ю.Ионих
Maybe I'm misunderstanding, but isn't what you're describing either just Newtonian physics, or maybe special relativity? Both assume a flat manifold; Euclidean for Newton and Minkowski for SR. Newtonian physics wouldn't be correct if space wasn't Euclidean - this is what's responsible for the 2nd and 3rd laws of motion. (The geodesics wouldn't be straight lines, so objects would not "continue in uniform motion", for instance. This is essentially definitive.) Ditto SR. Since both theories are extremely well-justified experimentally, that would imply that so is the assumption of Euclidean space in the absence of gravity. The mountains experiment is not the only one that implies flat space - any experiment that proves the validity of Newton or SR does too, and there are hundreds of both!
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