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Special relativity is pretty much math-free though (in Einstein's formulation, not in Minkowski's). I think Einstein himself wrote that to move to general rela

Special relativity is pretty much math-free though (in Einstein's formulation, not in Minkowski's). I think Einstein himself wrote that to move to general relativity he had to go to great lengths in studing fields of mathematics he didn't know - not least because the were just being discovered at the time. This lends credence to the idea that is genius was foremost guided by physical (I would say also philosophical) intuition, though of course you can' t discount the role of math in GE.

lutusp 11y ago
> Special relativity is pretty much math-free though (in Einstein's formulation, not in Minkowski's). True, but only because Einstein hadn't yet acquired the essential mathematical background. Instructive in this connection is a key equation from his first relativity paper (https://www.fourmilab.ch/etexts/einstein/specrel/www/ https://www.fourmilab.ch/etexts/einstein/specrel/www/): β = 1/sqrt(1-v^2/c^2)) (sorry -- the original paper doesn't number its equations) It should seem obvious that this equation describes a relation between orthogonal dimensions, something that Einstein didn't realize, but that Minkowski certainly did. Minkowski expanded and clarified Einstein's mathematics in order to express time as a separate dimension, then made his famous remark about spacetime: "Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality". Einstein then remarked, "Since the mathematicians have invaded the theory of relativity, I do not understand it myself anymore." But in subsequent years Einstein learned much more mathematics, and the general theory is much more dependent on mathematical ideas than the special theory was, indeed the general theory can't be meaningfully expressed without advanced mathematics.

lutusp 11y ago

> Special relativity is pretty much math-free though (in Einstein's formulation, not in Minkowski's). True, but only because Einstein hadn't yet acquired the essential mathematical background. Instructive in this connection is a key equation from his first relativity paper (https://www.fourmilab.ch/etexts/einstein/specrel/www/ https://www.fourmilab.ch/etexts/einstein/specrel/www/): β = 1/sqrt(1-v^2/c^2)) (sorry -- the original paper doesn't number its equations) It should seem obvious that this equation describes a relation between orthogonal dimensions, something that Einstein didn't realize, but that Minkowski certainly did. Minkowski expanded and clarified Einstein's mathematics in order to express time as a separate dimension, then made his famous remark about spacetime: "Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality". Einstein then remarked, "Since the mathematicians have invaded the theory of relativity, I do not understand it myself anymore." But in subsequent years Einstein learned much more mathematics, and the general theory is much more dependent on mathematical ideas than the special theory was, indeed the general theory can't be meaningfully expressed without advanced mathematics.