![]() ![]() ![]() In my opinion though, the great insight of Einstein (which is sort of captured in the above posts, but not quite) is to elevate space and time from passive backdrops upon which physics takes place to actual actors themselves in the game. So the good formulas are the ones where you can follow the notation. If you don't succeed, then it relies on the coordinates in question. If you succeed in writing something in Einstein notation, then chances are big that it's coordinate invariant. The great part is that Einstein notation actually tells you something about geometry. Vectors are written with a lower index and covectors with an upper index. Basically, you have vectors and covectors. The genius in the Einstein notation is knowing which indices come above and which below. The genius in Einstein notation is not that we can leave out the signs, of course. In that case, we leave out the summation sign and write We see that one index i is above and one index i is below. The notation convention just says that you can leave out summation signs. The summation convention? Please do explain, someone! If Wannabe is liking it, I'd love to understand it! Hints of mass-energy equivalence date from the 1800s too īut Einstein put all the ideas together, lined up all the ducks in a row, and had to invent new math too.Īlso back in those days they didnt have email & arxiv. In 1899 Lorentz assumed that the electrons undergo length contraction. There were many "almost made it" moments - Lorentz come up with his transformation in 1895. There may be said to several collateral or secondary paradigm shifts in physics created by Einstein, but the fundamental ones in relation to relativity was a shift from Newtonian conception of gravity as an "attractive force" to one of gravity as "curved spacetime," and the shift from the conception of "time" as the universal constant of spacetime to "lightspeed" as the universal constant.Įveryone had been thinking the same way as Newton for 200 years & Maxwell for 40 years. This reversal of the roles of the physics and the coordinates seems to me to be worthy of the term 'paradigm shift'. He thus took the light as the fixed quantity and ascribed the results to the coordinates and clocks. He said things like ' the moving clock runs slow', and 'the moving rod is shorter than the stationary one'. He didn't say things like 'the light takes more time to reach A than to reach B'. In his analysis of light he also used coordinates and time, but he did not describe his results as properties of light. The coordinates remained fixed by some condition outside the projectile analysis.īut Einstein turned the relation around. The results were considered to be properties of the projectile. For example, the position of a projectile could be given as a function of time. īut there is another idea, perhaps related to the two mentioned, that lurks in his writing that I haven't seen mentioned.īefore Einstein the custom was to form the coordinates and time and use them as fixed quantities to describe a given physics problem. ![]() I agree that these two principles were inspired ideas that made major changes in how people thought about things. The equivalence principle that led to general relativity: The effects of gravitational force are indistinguishable from the effects of acceleration in the absence of gravity, so we don't need to treat gravity as a force if we don't want to. The second postulate of special relativity, which could be informally (but with, in my opinion, historical accuracy) paraphrased as "We don't need no steenkin' ether!" ![]()
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