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General Relativity Gedanken

RVM45

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I'm no Physicist, and my understanding of the Calculus is shaky in the extreme.

However I did read that Albert Einstein justified General Relativity(in part) by the Gedanken experiment of a scientist in a closed windowless room. Supposedly there is no experiment that could distinguish whether he was in a gravity field of X gees; or if his room was being towed by a very smoothly accelerating rocket accelerating at the rate of X gees.

Well, I don't expect this to make a big splash in the scientific community; but I found a cook in the gedanken(I think.)

Since this is a gedanken, our room can be arbitraily large; or our instruments arbitraily accurate--Nicht Wahr?

A gravity field weakens with distance from the center of mass. If our hypothetical scientist measures "G" at one foot from the floor; and at four foot from the floor with his very precise scale; in a gravity field his reading will be marginally less at four feet than at one--but in the rocket-towed ship, they will be the same.

If it makes you feel better, build a REALLY high tower in your gargantuan room; and mesure gravity at "Sea Level" and ten miles high.

Am I missing something?--quite possible--and has anyone ever noticed this cook before?{And if it's not a cook, why not?}

.....RVM45 :cool:
 
I'd imagine the solution is something as simple as "specify the precision of your measuring system, then build something approximating an infinite plane to provide the gravitational attraction, as big as necessary to make the differences smaller than the precision".

(the gravity due to an actually infinite plane would be constant no matter where you are)
 
RVM45 said:
I'm no Physicist, and my understanding of the Calculus is shaky in the extreme.

However I did read that Albert Einstein justified General Relativity(in part) by the Gedanken experiment of a scientist in a closed windowless room. Supposedly there is no experiment that could distinguish whether he was in a gravity field of X gees; or if his room was being towed by a very smoothly accelerating rocket accelerating at the rate of X gees.

Well, I don't expect this to make a big splash in the scientific community; but I found a cook in the gedanken(I think.)

Since this is a gedanken, our room can be arbitraily large; or our instruments arbitraily accurate--Nicht Wahr?

A gravity field weakens with distance from the center of mass. If our hypothetical scientist measures "G" at one foot from the floor; and at four foot from the floor with his very precise scale; in a gravity field his reading will be marginally less at four feet than at one--but in the rocket-towed ship, they will be the same.

If it makes you feel better, build a REALLY high tower in your gargantuan room; and mesure gravity at "Sea Level" and ten miles high.

Am I missing something?--quite possible--and has anyone ever noticed this cook before?{And if it's not a cook, why not?}

.....RVM45 :cool:
Click to expand...
From my understanding that's all right and Einstein was well aware of it. The equivalence is only true locally (not sure if I'm using terms correctly here) - basically, if you move around in your room, you can tell if it's a gravitational field or not, but that fits just fine in the theory.
 
A "Cook" is a newly discovered flaw in an old accepted Chess variation; that is prepared and sprung at a major match or tournament.

I thought I'd seen it used in the same fashion in reference to freshly discovered problems in a Gedanken.

.....RVM45 :cool:
 
RVM45 said:
I'm no Physicist, and my understanding of the Calculus is shaky in the extreme.

However I did read that Albert Einstein justified General Relativity(in part) by the Gedanken experiment of a scientist in a closed windowless room. Supposedly there is no experiment that could distinguish whether he was in a gravity field of X gees; or if his room was being towed by a very smoothly accelerating rocket accelerating at the rate of X gees.

Well, I don't expect this to make a big splash in the scientific community; but I found a cook in the gedanken(I think.)

Since this is a gedanken, our room can be arbitraily large; or our instruments arbitraily accurate--Nicht Wahr?

A gravity field weakens with distance from the center of mass. If our hypothetical scientist measures "G" at one foot from the floor; and at four foot from the floor with his very precise scale; in a gravity field his reading will be marginally less at four feet than at one--but in the rocket-towed ship, they will be the same.

If it makes you feel better, build a REALLY high tower in your gargantuan room; and mesure gravity at "Sea Level" and ten miles high.

Am I missing something?--quite possible--and has anyone ever noticed this cook before?{And if it's not a cook, why not?}

.....RVM45 :cool:
Click to expand...

The experiment is just an analogy. The gedankenexperiment literally needs a windowless room. This is to stop the scientist getting any extra information about the outside world - the only source of information is supposed to be the force acting on the scientist (or on her desk, or whatever).

If you feel there's a "way around" it then the analogy is not an accurate description of reality ;)

Anyway. Let's imagine that our scientist finds that the force near the ceiling was slightly less than the force at the floor. Could our scientist be sure that it's all caused by gravitation? Or perhaps the variation in force could be explained by the pull from the spaceship, plus perhaps a bit of rotation or whatever, plus three smaller planets dancing in a little circle beneath?

The forces are indistinguishable. Of course, if you build up many different measurements of the forces, then in the real world these measurements will sometimes give you some useful extra information. However, in principle, at each each measurement the apparent force could be due to either acceleration or gravity.
 
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Your "cook" (cook?) is a standard part of GR: all inertial frames are said to be "locally indistinguishable"---you can't tell them apart by doing experiments at a single point.

This is a standard thing in curved geometries; any sufficiently small patch of a curved surface can be approximated as a flat surface; if you're sitting blindfolded on an unknown surface, the only way to measure its curvature is to reach out and feel a larger patch of the surface around you. (How small is "sufficiently small"? Well, keep moving to smaller and smaller patches until you can't discern any curvature. Now it's small enough.)

This is not a tautology; there are lots of quantities which are equally easy to measure no matter how small your instrument is. Magnetic fields, for example: you can sit somewhere in space and say, "The magnetic field right here is X", and you'll get the same answer (to first order) no matter how big your measurement-area is. Acceleration force; a small pendulum, a large pendulum, or a micron-scale superconducting gravimeter will all give the same answer for a local acceleration.
 
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