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. >
At rest on Earth is not a situation of zero G; it's 1G. Or, say, if you want a straight beam, one can assume an inertial frame, and of course, in either frame one will observe the beam as straight. AG > > 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. > I think most of last paragraph incorrect. In experiments with GPS clocks, the ground clock, in the stronger gravity field, runs slower than an orbiting clock. Fewer ticks in ground clock, which is objectively behind the orbiting clock. In your elevator example, where zero G can be interpreted as being in an inertial frame, you claim the elapsed time duration using ticks, is identical for both beams. This contradicts GPS experiments if we assume for direct comparison that the orbiting clock is very far from Earth, effectively in the weaker (zero) gravity field. AG > 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 > > > > > -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
