On Sunday, December 10, 2017 at 11:41:21 PM UTC, John Clark wrote: > > > > On Sun, Dec 10, 2017 at 4:42 PM, <[email protected] <javascript:>> > wrote: > > > >> What is the connection between the Equivalence Principle and Einstein's >> Field Equations? How did the former lead to the latter? Why was the man >> falling from the ladder so decisive in leading to the Theory of General >> Relativity? >> > > > The Equivalence Principle says if > you > ignore tidal effects and you're in a windowless elevator cab there is no > way to know if you're sitting on the Earth in a gravitational field or in > deep intergalactic space being accelerated by a rocket upward at 1G. If you > feel zero G and fire a Laser pointer from one wall > to the other > it will go in a straight line and hit the exact opposite side on the other > wall. But if you were being accelerated upward the elevator cab will move > slightly > upward in the time it takes for the light to go from one wall to the other > so the spot the laser makes on the other wall will be slightly lower than > it was when you were in zero G, you see the laser beam follow a curve. > > A curved line from one wall to the other is longer than a straight line > , > and yet when you measure the time it takes for light to do this with your > very accurate clock you notice its exactly the same. You already know the > measured speed of light never changes so > if something is moving at the same speed and moves a greater distance in > the same number of clock ticks then > you'd have to conclude that being accelerated makes your clock run slow. > And because of the Equivalence Principle you'd have to > also > conclude that a gravitational field bends light and makes time run slow > just as acceleration does. > > John K Clark > > Excellent summary. TY. But why would Einstein think there could be a covariant theory for accelerating frames when an observer inside such a frame can do measurements to confirm acceleration and differences with other such frames, unlike the case for inertial frames which are clearly equivalent? AG
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