The Equivalence Principle - 01/03/15 09:03 PM
The Equivalence Principle seems to figure quite importantly in the development of general relativity. However, one has to ask how well the equivalence principle holds up under investigation. If, by the equivalence principle we mean that in a closed environment (e.g. a windowless box) an observer would be unable to tell the difference between acceleration and gravity, there are a few problems.
Suppose you have with you in your box two marbles. Can you use these in an experiment to discover if you are being mechanically accelerated, or stationary on the surface of the Earth? Surely you can, if you have a sufficiently sensitive measuring instrument.
Release your marbles simultaneously from the top of the box. They will fall to the bottom. If you are being accelerated, their trajectories will be parallel, but if you are on the surface of a planet their trajectories will converge on the centre of the planet, so they will converge as they fall.
Alternatively, if you release one from the top of the box and one from waist height, they will maintain that separation until the first one hits the floor, under acceleration. Under gravity, however, the lower marble will fall faster than the upper one, so the separation will increase.
Even in terms of SR it would be possible to distinguish between being in deep space and free falling towards a planet. If you released your marbles at the same elevation, with a horizontal separation, in deep space they would maintain that separation, but in free fall towards a planet they would slowly move together, thus warning you of a nasty crash in your future.
Have I got this wrong, or is the equivalence principle just a convenient approximation?
I hesitate to suspect that it is simply part of the “mushroom culture” which some scientists seem to think lay people deserve.
Suppose you have with you in your box two marbles. Can you use these in an experiment to discover if you are being mechanically accelerated, or stationary on the surface of the Earth? Surely you can, if you have a sufficiently sensitive measuring instrument.
Release your marbles simultaneously from the top of the box. They will fall to the bottom. If you are being accelerated, their trajectories will be parallel, but if you are on the surface of a planet their trajectories will converge on the centre of the planet, so they will converge as they fall.
Alternatively, if you release one from the top of the box and one from waist height, they will maintain that separation until the first one hits the floor, under acceleration. Under gravity, however, the lower marble will fall faster than the upper one, so the separation will increase.
Even in terms of SR it would be possible to distinguish between being in deep space and free falling towards a planet. If you released your marbles at the same elevation, with a horizontal separation, in deep space they would maintain that separation, but in free fall towards a planet they would slowly move together, thus warning you of a nasty crash in your future.
Have I got this wrong, or is the equivalence principle just a convenient approximation?
I hesitate to suspect that it is simply part of the “mushroom culture” which some scientists seem to think lay people deserve.