# Gravity/acceleration equivalent?

by ubavontuba
Tags: equivalent
 P: 167 Forum, Okay, so Einstein says that to an internal observer a room being pulled under a constant 1g acceleration is indistinguishable (by experiment) from a room hanging from a tree by a rope. Putting gravitational divergence aside, do you think this is true? If I (as an inside observer) can demonstrate by internal experiment that the room is either accelerating or is at rest in a gravitational field, would this be important?
P: 8,470
 Quote by ubavontuba Forum, Okay, so Einstein says that to an internal observer a room being pulled under a constant 1g acceleration is indistinguishable (by experiment) from a room hanging from a tree by a rope. Putting gravitational divergence aside, do you think this is true? If I (as an inside observer) can demonstrate by internal experiment that the room is either accelerating or is at rest in a gravitational field, would this be important?
Yes, that would contradict the equivalence principle, provided the room is arbitarily small so that differences in gravity from one internal region to another (tidal forces, for example) become negligible. Also, I think you'd have to assume the time period you're looking at becomes arbitrarily brief--the equivalence principle only applies to arbitrarily small regions of spacetime, although offhand I don't know how gravity could be distinguished from acceleration even given an extended period of time to make your observations.
P: 997
 Quote by ubavontuba Forum, Okay, so Einstein says that to an internal observer a room being pulled under a constant 1g acceleration is indistinguishable (by experiment) from a room hanging from a tree by a rope. Putting gravitational divergence aside, do you think this is true? If I (as an inside observer) can demonstrate by internal experiment that the room is either accelerating or is at rest in a gravitational field, would this be important?

A look at
Ling Tsai
The relation between gravitational mass, inertial mass and velocity
am.J.Phys. 54 340 (1986)
could be illuminating

P: 167
Gravity/acceleration equivalent?

 Quote by JesseM Yes, that would contradict the equivalence principle, provided the room is arbitarily small so that differences in gravity from one internal region to another (tidal forces, for example) become negligible. Also, I think you'd have to assume the time period you're looking at becomes arbitrarily brief--the equivalence principle only applies to arbitrarily small regions of spacetime, although offhand I don't know how gravity could be distinguished from acceleration even given an extended period of time to make your observations.
So if I can really do this, it would really be important? Does anyone disagree or wish to add qualifications?

 Quote by bernhard.rothenstein A look at Ling Tsai The relation between gravitational mass, inertial mass and velocity am.J.Phys. 54 340 (1986) could be illuminating
I'll Google this since it sounds like something in the same vein as I'm thinking from the title, but do you have a link?

Edit: Okay, I found it on my own. I'll do a little reading and let you know if it's applicable to my feat of derring-do...
P: 308
 Quote by JesseM Yes, that would contradict the equivalence principle, provided the room is arbitarily small so that differences in gravity from one internal region to another (tidal forces, for example) become negligible. Also, I think you'd have to assume the time period you're looking at becomes arbitrarily brief--the equivalence principle only applies to arbitrarily small regions of spacetime, although offhand I don't know how gravity could be distinguished from acceleration even given an extended period of time to make your observations.
Even if your room was very small if you let enough time go by there would be a tidal effect which you could observe. Although I think this would only apply in the freefalling (or extremely low acceleration) case, since if you were accelerating at any decent rate your test particles would hit the floor of your box before you noticed any tidal effects.
P: 8,470
 Quote by ubavontuba So if I can really do this, it would really be important?
 The equivalence principle can be stated as "At every spacetime point in an arbitrary gravitational field, it is possible to chose a locally inertial coordinate system such that, within a sufficiently small region of the point in question, the laws of nature take the same form as in unaccelerated Cartesian coordinate systems.
 General relativity yields the special theory of relativity as an approximation consistent with the Principle of Equivalence. If we focus our attention on a small enough region of spacetime, that region of spacetime can be considered to have no curvature and hence no gravity. Although we cannot transform away the gravitational field globally, we can get closer and closer to an ideal inertial reference frame if we make the laboratory become smaller and smaller in spacetime volume. In a freely falling (non-rotating) laboratory occupying a small region of spacetime, the laws of physics are the laws of special relativity. Hence all special relativity equations can be expected to work in this small segment of spacetime.
So, a violation of this would certainly be important, although the fact that thousands of smart physicists have studied the issue and found no reason to doubt the equivalence principle should lead you to suspect there is very likely a flaw in your idea.
P: 8,470
 Quote by dicerandom Even if your room was very small if you let enough time go by there would be a tidal effect which you could observe. Although I think this would only apply in the freefalling (or extremely low acceleration) case, since if you were accelerating at any decent rate your test particles would hit the floor of your box before you noticed any tidal effects.
How would these tidal effects manifest in the freefalling case, for a very small room falling for an extended period of time?
 P: 167 JesseM et al, I need to make it clear that I'm referring to the hanging room case as per this paper written by Albert Einstein. I'm not saying I can make this determination in a free-falling room in space versus a free-falling room in a gravity field ("Except for the splat at the end... they're practically similar" -Tigger). Would this still be important? I feel I should forewarn you that this concept really works, but it's also a bit mischevious. That is; I have found a loophole to the conundrum, but I don't think it has a lot of practical considerations. Edit: I wish to add that I will start out with a simple and rather silly version of the test. You will then likely wish to qualify the experiment, so I strongly recommend you satisfy your qualifications now to the best of your abilities. I will accept later qualifications, but only if it is conceded that my first experiment works under the current treatise. Any qualifications you make will be examined for merit and depending on their limiting factors I will refine the experimental concept to compensate. If the restrictions get severe, I may need to ascertain that the measurements are purely hypothetical (as they may be very small) and have this still be accepted as valid. Of course, this will only be in response to restrictions that are not specified in the Einstein paper. Is everyone in accordance? Are you ready for the silliness to begin?
P: 308
 Quote by JesseM How would these tidal effects manifest in the freefalling case, for a very small room falling for an extended period of time?
The test particles would slowly seperate from one another due to the extremely minute difference in the gravitational force (or geodesics, if you prefer) due to their differing heights above the planet. Even with a very small room this effect would become evident given enough time, provided you don't hit the ground first. This seperation would not occur in the flat space room.

 Quote by ubavontuba JesseM et al, I need to make it clear that I'm referring to the hanging room case as per this paper written by Albert Einstein. I'm not saying I can make this determination in a free-falling room in space versus a room free-falling in a gravity field ("Except for the splat at the end... they're practically similar" -Tigger). Would this still be important? I feel I should forewarn you that this concept really works, but it's also a bit mischevious. That is; I have found a loophole to the conundrum, but I don't think it has a lot of practical considerations.
Well don't keep us in suspense, let's hear it
P: 8,470
 Quote by ubavontuba JesseM et al, I need to make it clear that I'm referring to the hanging room case as per this paper written by Albert Einstein. I'm not saying I can make this determination in a free-falling room in space versus a free-falling room in a gravity field ("Except for the splat at the end... they're practically similar" -Tigger). Would this still be important?
I don't think it should matter--after all, a hanging room as seen by a freefalling observer passing it should look just like an accelerating room as seen by an inertial observer passing it. You could even imagine a small room in a box inside a freefalling lab, with the box using rockets to maintain a constant distance from the earth even as the lab falls so the box approaches the lab's ceiling--this should appear just like a small room-in-a-box inside an inertial lab in deep space using rockets to accelerate in the direction of the lab's ceiling.
 Quote by ubavontuba I feel I should forewarn you that this concept really works, but it's also a bit mischevious. That is; I have found a loophole to the conundrum, but I don't think it has a lot of practical considerations.
Again, the fact that this would violate such a basic principle should lead you to have some doubts about whether you have actually found such a loophole, I think. But anyway, let's hear it!
 Quote by ubavontuba Edit: I wish to add that I will start out with a simple and rather silly version of the test. You will then likely wish to qualify the experiment, so I strongly recommend you satisfy your qualifications now to the best of your abilities. I will accept later qualifications, but only if it is conceded that my first experiment works under the current treatise.
OK, the best way I can put it is that if you compare the hanging room and the accelerating room, for any small but finite room over a finite time there will be some slight differences, but in the limit as the volume and time approach zero, the magnitude of these differences should also approach zero. I'd be very surprised if you could find something that violates this.
Emeritus
P: 7,634
 Quote by ubavontuba Forum, Okay, so Einstein says that to an internal observer a room being pulled under a constant 1g acceleration is indistinguishable (by experiment) from a room hanging from a tree by a rope. Putting gravitational divergence aside, do you think this is true? If I (as an inside observer) can demonstrate by internal experiment that the room is either accelerating or is at rest in a gravitational field, would this be important?
The tidal forces (aka Riemann curvature tensor) are different for the observer in the room and the observer standing on a spherical planet.

This is essentially, however, a consequence of the gravitational divergence, so I'm not sure if you'd include it as a separate phenomenon or not.

One should be able to suppress the tidal forces in theory by making the planet a huge disk rather than a huge sphere. The metric for an infinite flat plane should be equivalent to two Rindler metrics (the metric of an accelerating spaceship) "glued together" at the z=0 plane, as I've mentioned in another thread.

Even with a finite disk rather than an infinite one, the supression of tidal forces should be good (but not perfect).
P: 2,251
 Quote by JesseM You could even imagine a small room in a box inside a freefalling lab, with the box using rockets to maintain a constant distance from the earth even as the lab falls so the box approaches the lab's ceiling--this should appear just like a small room-in-a-box inside an inertial lab in deep space using rockets to accelerate in the direction of the lab's ceiling.
I had never heard that version of the EP thought experiment. (only the two basic ones, accelerating room in space vs. one sitting on the planet and free-falling room vs. one drifting freely in outer space, and in both comparisons what light or other free objects would be observed to do.) thanks for bringing it up.