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How Einstein Lost His Bearings, and With Them, General Relativity (quantamagazine.org)
Kevin Hartnett, writing for Quanta magazine: Albert Einstein released his general theory of relativity at the end of 1915. He should have finished it two years earlier. When scholars look at his notebooks from the period, they see the completed equations, minus just a detail or two. "That really should have been the final theory," said John Norton, an Einstein expert and a historian of science at the University of Pittsburgh. But Einstein made a critical last-second error that set him on an odyssey of doubt and discovery -- one that nearly cost him his greatest scientific achievement. The consequences of his decision continue to reverberate in math and physics today.
Here's the error. General relativity was meant to supplant Newtonian gravity. This meant it had to explain all the same physical phenomena Newton's equations could, plus other phenomena that Newton's equations couldn't. Yet in mid-1913, Einstein convinced himself, incorrectly, that his new theory couldn't account for scenarios where the force of gravity was weak -- scenarios that Newtonian gravity handled well. "In retrospect, this is just a bizarre mistake," said Norton. To correct this perceived flaw, Einstein thought he had to abandon what had been one of the central features of his emerging theory. Einstein's field equations -- the equations of general relativity -- describe how the shape of space-time evolves in response to the presence of matter and energy. To describe that evolution, you need to impose on space-time a coordinate system -- like lines of latitude and longitude -- that tells you which points are where. Another interesting read on Quanta: Why Stephen Hawking's Black Hole Puzzle Keeps Puzzling.
Here's the error. General relativity was meant to supplant Newtonian gravity. This meant it had to explain all the same physical phenomena Newton's equations could, plus other phenomena that Newton's equations couldn't. Yet in mid-1913, Einstein convinced himself, incorrectly, that his new theory couldn't account for scenarios where the force of gravity was weak -- scenarios that Newtonian gravity handled well. "In retrospect, this is just a bizarre mistake," said Norton. To correct this perceived flaw, Einstein thought he had to abandon what had been one of the central features of his emerging theory. Einstein's field equations -- the equations of general relativity -- describe how the shape of space-time evolves in response to the presence of matter and energy. To describe that evolution, you need to impose on space-time a coordinate system -- like lines of latitude and longitude -- that tells you which points are where. Another interesting read on Quanta: Why Stephen Hawking's Black Hole Puzzle Keeps Puzzling.
In this era of computers and CPU's and constant distraction, he wouldn't have managed to get to even first realization. The Theory of Relativity was a triumph of abstract thought; this is something that doesn't really happen anymore.
... back.
WTF is this?
Hawking passes and we get Slashdot Esquire magazine?
It little behooves the best of us to comment on the rest of us.
Classical physics does not depend on a reference frame as long as the limitspeed is infinite and until 1880 or so that was the assumption. I mean it was known that the lightspeed was finite but there was no reason to believe it was the limitspeed. You can turn newtonian mechanics into a covariant system for general coordinate systems but why would you do that? If you want to describe a merry go round , don't get all that overhead and use a shortcut.
Then with special relativity you could again decide to do the same: support general coordinate systems, make it work for accelerated observers. You could still classify it as special relativity.
It was Einstein who decided we couldn't avoid to formulate things in a covariant manner, and the example was that inside an elevator it was strictly impossible to distinguish between floating in space or plummetting towards the earth in free fall and and likewise there was no distinction between standing on the surface of the earth and being pulled in space.
Therefore the math had to be the same too.