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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.
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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. The reason that they will converge is that the gravitational attraction is from the equivalent of a point source. If you are on a sufficiently large planet the point will be far enough away that you can't detect the convergence. 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. The reason here is close to the same as for the first case. Since the force exerted on the marbles varies according to the inverse square law the force on the marbles is different based on the distance from the center of the planet. 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? If you were in free fall the marbles wouldn't move with respect to the box. They would be falling at the same speed you were. For the illustration of the equivalence principle we are assuming that the box is on the surface of the planet. The equivalence principle isn't an approximation, it is a simplification. It is the simplest statement of the principle. For real world situations you have to account for all the factors that aren't included in the statement, such as the fact that gravity generally comes from an approximately point source. It is the same as for F=Ma. There is no real case where only one force is acting on an object. So for the equivalence principle you have to do the sum of all the forces. For GR (you said SR, but I think you meant GR) you don't really talk about forces. You have to talk about perturbations in the gravitational field, but the idea is the same. Bill Gill
C is not the speed of light in a vacuum. C is the universal speed limit.
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If you are on a sufficiently large planet the point will be far enough away that you can't detect the convergence. Which is why I said “…if you have a sufficiently sensitive measuring instrument.” My understanding is that gravity operates as though the entire mass of the gravitating object were at its centre; so however large the planet, the marbles will still converge to as they near it. The reason here is close to the same as for the first case. Since the force exerted on the marbles varies according to the inverse square law the force on the marbles is different based on the distance from the center of the planet. Precisely: so you can still make the distinction. If you were in free fall the marbles wouldn't move with respect to the box They will not move vertically with respect to the box, but they will move horizontally with respect to the box. GR/SR. I’m mildly dyslexic, sometimes I don’t watch closely enough.
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If you were in free fall the marbles wouldn't move with respect to the box They will not move vertically with respect to the box, but they will move horizontally with respect to the box. Why would they move horizontally? GR/SR. I’m mildly dyslexic, sometimes I don’t watch closely enough.
It happens to all of us. It even happens to me even though we all know I am almost perfect Bill Gill
C is not the speed of light in a vacuum. C is the universal speed limit.
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Why would they move horizontally? In free fall towards a planet they would slowly move together, because they would be converging on the centre of the planet.
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That's true, if you include "towards a planet". However, the explanation of the equivalence principle with the elevator is really an analogy to help people picture what Einstein was trying to say. As is usual with analogies you can always find things that don't quite work right. The ideal conditions for that analogy would be for the gravity to be generated by an infinite flat plane. The essence is still the same. The equivalence principle is still quite safe.
Bill Gill
C is not the speed of light in a vacuum. C is the universal speed limit.
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You could actually replace your marbles with atoms and test the idea Bill S. Proposed last year: http://phys.org/news/2014-07-equivalence-principle-effects-spin-gravity-coupling.htmlInitial base results published last week: http://phys.org/news/2015-01-gravity-curvature.htmlWith the baseline now set the group will no doubt introduce the spins to test the initial idea. It is quite a nice simple experimental design. To do your explicit test you would need to accelerate it perhaps we ask them if they could put it in a truck and take it for a drive
Last edited by Orac; 01/12/15 02:38 PM.
I believe in "Evil, Bad, Ungodly fantasy science and maths", so I am undoubtedly wrong to you.
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In the new study, the researchers have for the first time tested the equivalence principle by comparing the gravitational interaction for a bosonic particle to that of a fermionic particle I must be missing something here; how does that test the equivalence principle?
Last edited by Bill S.; 01/12/15 11:12 PM.
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Is the earth moving or standing still Bill S? Now repeat the test in labs in different parts of the world what should happen? If you can't work it out ask Marosz what you should see (and he claims you can via various experiments). The experiments numbers and graph are only consistent with the equivalence principle something entirely different should happen if it were not true. Homework, see if you can work out what the graph and numbers should look like without equivalence?( Hint: The vertical section of the graph is no accident) For the more technical minded specifically what we are really looking at here is the weak equivalence principle which formally stated goes like this The outcome of any local non-gravitational experiment in a freely falling laboratory is independent of the velocity of the laboratory and its location in spacetime. To cover the strong equivalence principle which is formally stated as The gravitational motion of a small test body depends only on its initial position in spacetime and velocity, and not on its constitution. The constitution part is often left out by many in basic discussions but you can not exclude a fifth force without dealing with it because you could not exclude a composition dependent force. So what they are doing is extending the test to cover bosonic particle vs fermionic particles.
Last edited by Orac; 01/13/15 12:23 AM.
I believe in "Evil, Bad, Ungodly fantasy science and maths", so I am undoubtedly wrong to you.
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Marosz why address your response to me I have about as much interest in your garbage as getting infected from Ebola.
How many times do I have to tell you not remotely interested in your idea and spam because it is trivially wrong, so perhaps address your ideas to others.
Last edited by Orac; 01/19/15 01:15 AM.
I believe in "Evil, Bad, Ungodly fantasy science and maths", so I am undoubtedly wrong to you.
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