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In trying to support this contention, he imagined a large closed chest which was first at rest on the surface of a large body like the Earth, and then later removed to a great distance from other matter where it was pulled by a rope until its acceleration was g . No experiment made inside could, he claimed, detect the difference in the two cases.
The equivalence principle is only an approximation. It's well known that sufficiently precise equipment (or a sufficiently large elevator) can reveal whether you are at rest on a planet or in an accelerating elevator.
Quote from: mad aetherist on 11/12/2018 23:13:25In trying to support this contention, he imagined a large closed chest which was first at rest on the surface of a large body like the Earth, and then later removed to a great distance from other matter where it was pulled by a rope until its acceleration was g . No experiment made inside could, he claimed, detect the difference in the two cases. Einstein imagined a small chest, not a large one. He asserted that no local experiment could detect the difference. Putting two plumb lines a foot apart with instruments sufficiently sensitive to detect the angle constitutes a non-local test.
I thought the idea was you do not know you are accelerating unless there is an external gravity field acting on you ? Whether you hit and feel the source of the field is not relevant really.
An elevator shaft through the centre of the earth higher than the atmosphere, if you pass the earth over an elevator, the elevator would be attracted to the central gravitational point, chasing the centre until escaping from the gravitational attraction. It would not feel any resistance.
But in this he was mistaken, as I have shown (Brown 1960). In the first case, if two simple pendulums were suspended with their threads a foot apart, the threads would not be parallel but point towards the centre of mass of the Earth (or a point somewhat nearer allowing for their mutual attraction). The angle between them would, in principle, be detectable by the Mount Palomar telescope.
So, u are not allowed to have an experiment that has width.
And, if u come up with an experiment that involves height
Local, so no significant depth either. If your experiment relies on a field difference over a distance, it is not a local test. The restriction is lifted for a uniform gravitational field. A uniform gravitational field is indistinguishable from acceleration at any size box.
General relativity is a local theory, as is it derived from special relativity, which says that nothing can move faster than c inside a box. Things can move faster outside it.
Like detection of tides. There are no tidal forces in a uniform gravitational field.
Are you sure about this? Gravity would be stronger at the bottom of the pendulum (~ space more curved and time slowed down). So whether you used a ruler or a light to measure the separation the threads may still appear parallel.
Quote from: set fair on 12/12/2018 11:24:38Are you sure about this? Gravity would be stronger at the bottom of the pendulum (~ space more curved and time slowed down). So whether you used a ruler or a light to measure the separation the threads may still appear parallel.You would also be hard pushed to find a place (or two) where the plumb lines definitely point towards the centre of the earth. As @Halc said, we can only rely on local measurements.
PS @Halc you say “but uniform gravitation is impossible”. It can be done, look up spherical cavity in a solid uniform sphere. I agree that it is tricky to achieve
Ok SR is trumped by GR, but uniform gravitation is impossible, which opens up another avenue for non-equivalence
How about if we shine a light across the elevator. The light beam bends down. In a gravitational field the photons hitting the far wall will be aiming-progressing on a downward angle. In an inertial field the photons will at all times be aiming horizontally, but progressing on a downward angle.
The only height issue that i can think of is that in a gravity field a clock near the ceiling might tick faster than a clock near the floor, whilst in the inertial case the ticking would be the same.
Quote from: mad aetherist on 11/12/2018 23:13:25But in this he was mistaken, as I have shown (Brown 1960). In the first case, if two simple pendulums were suspended with their threads a foot apart, the threads would not be parallel but point towards the centre of mass of the Earth (or a point somewhat nearer allowing for their mutual attraction). The angle between them would, in principle, be detectable by the Mount Palomar telescope. Are you sure about this? Gravity would be stronger at the bottom of the pendulum (~ space more curved and time slowed down). So whether you used a ruler or a light to measure the separation the threads may still appear parallel.
Quote from: mad aetherist on 12/12/2018 12:57:22Ok SR is trumped by GR, but uniform gravitation is impossible, which opens up another avenue for non-equivalenceYea, well continuous acceleration is similarly impossible, so we could violate locality by a test that extends the temporal size of our box. Wait to see if the acceleration stops. That's a non-local test to distinguish between the two.
But no difference in an accelerating box. Both beams bend down. Using the equivalence principle is how they made the prediction that gravity would bend light.
But an accelerating box is not inertial. So the clock at the top of the box ticks faster than the one at the bottom.
If gravity were not stronger at the bottom of the line then the thread would not point, it would just float around.
But a solid rod would not be affected as much as is light. It would show that the threads are not parallel. According to GR the length of rods is only affected in the radial direction,
Quote from: Halc on 12/12/2018 13:48:20Quote from: mad aetherist on 12/12/2018 12:57:22 but uniform gravitation is impossibleYea, well continuous acceleration is similarly impossible, so we could violate locality by a test that extends the temporal size of our box. Wait to see if the acceleration stops. That's a non-local test to distinguish between the two.No, a thort-X allows all sorts of non-practical assumptions.
Quote from: mad aetherist on 12/12/2018 12:57:22 but uniform gravitation is impossibleYea, well continuous acceleration is similarly impossible, so we could violate locality by a test that extends the temporal size of our box. Wait to see if the acceleration stops. That's a non-local test to distinguish between the two.
but uniform gravitation is impossible
No. Think it throo. In the inertial case the photon retains its heading at all times.
dont understand. All clocks anywhere in the accelerating elevator must tick the same.
The only possible problem being how to measure all of their tickings.
Quote from: mad aetherist on 12/12/2018 13:52:52If gravity were not stronger at the bottom of the line then the thread would not point, it would just float around.Nonsense. Any gravity/acceleration will make a plumb-line point a certain way. It need not be stronger at the bottom for this to be true.
Example is a plumb line in a coal mine, where gravity is weaker near the bottom of the line, and strongest at the top. Plumb lines still work in mines.
Yes, I agree that widely separated plumb lines will point different ways if they're near the gravity source. Geometry demands that. It is a non-local test after all.
Does gravity have any effect on the radial length of something? Speed does of course, but all objects in question here are stationary in their respective frames (the frame of the box).
You're looking for relativistic details in a straightforward Newtonian example. Make the box 10000 km wide and notice that the plumb lines are perpendicular. Length contraction from trivial gravity of Earth (if there is such a thing at all) isn't going to hide that. If you're going to break the rules, do it right.