Gravity/acceleration equivalent?

[JesseM]

Sure, but This isn't how Einstein wrote it in that paper I referenced.

Well, as you say, I think he was just talking about what an observer would detect in a steadily accelerating box in that paper. And I think a mathematical statement of the equivalence principle would probably just be in terms of the equivalence between freefalling and inertial frames (though I'm not sure of this), but physicists writing for a popular audience will often treat this and the sitting still in a gravitational field/accelerating in empty space thought-experiment as interchangeable. This is probably because, as I said earlier, the second one does follow directly from the first one if you impose the appropriate restrictions.

However, if the accelerating framework was thusly fixed and it had less mass than the Earth, I can still think of an experiment that would determine acceleration versus gravity.

You're saying that even if the box's motion cannot be affected from the inside, you think you could tell? How?

Even with lateral thrusters, I could still tell.

I'm pretty sure you couldn't, not if the lateral thrusters were programmed to make sure the parts of the structure on the boundary of the inertial observer's imaginary box responded in exactly the same way to motions of the physical box as the same structures would respond as they would on earth.

Besides this, if we assume any motions of the box only impart significant motion to the cable (swaying, for example), while the crane holding the cable is affected in a negligible way (perhaps the cable could be connected to the crane by a frictionless ball bearing), then we wouldn't even need thrusters to insure there was no difference between what is experienced when the crane is sitting on Earth vs. when it's being accelerated at 1G.

 

[pervect]

There is no gravity in an inertial frame, therefore there is no gravitational time dilation. All time dilation is due to velocity.

(I am ignoring, for the moment, the gravity of the Earth itself, which is a minor effect in this problem that's constant both for the muon in motion and the muon at rest, so not only is it small, it cancels itself out.)

If one works the problem in the coordinate system of the muon, one does have to take into account gravitational time dilation (or equivalently, a non-Minkowskian metric).

But in an inertial frame, the metric is always Minkowskian, and there is never any gravitational time dilation.

The sci.physics.faq entry that Jesse quoted earlier should also go into this.

 

[Creator]

What may be of interest is how the Unruh affect applied to accelerating frames of reference might be applied to small regions of space at a fixed distance from a gravitating body.

Good point; however, the effect is generally considered equivalent; and can be considered equivalent to Hawking radiation at the extreme, although there are some differences.
See:
http://www.emis.ams.org/journals/LRG/Articles/lrr-2001-6/node3.html

Creator

 

[ubavontuba]

You're saying that even if the box's motion cannot be affected from the inside, you think you could tell? How?

I was referring to the case where the room still hangs and swings freely, but the accelerating frame from which it hangs self-compensates. If you want the room to be still too, then let's compare it to a room that is fixed on the earth. In this case, I could tell (comparing apples with apples, you know).

I'm pretty sure you couldn't, not if the lateral thrusters were programmed to make sure the parts of the structure on the boundary of the inertial observer's imaginary box responded in exactly the same way to motions of the physical box as the same structures would respond as they would on earth.

This is basically as I've stated above. However you are missing a crucial difference here. I could tell.

Besides this, if we assume any motions of the box only impart significant motion to the cable (swaying, for example), while the crane holding the cable is affected in a negligible way (perhaps the cable could be connected to the crane by a frictionless ball bearing), then we wouldn't even need thrusters to insure there was no difference between what is experienced when the crane is sitting on Earth vs. when it's being accelerated at 1G.

I'm not clear on what you mean here. Do you mean the room swings freely on Earth and in the accelerating frame, but the accelerating framework's motion is fixed (self-compensates to maintain constant and straight acceleration)? In this case, I could still tell.

As you've suggested, the popular version that Albert Einstein wrote versus the theory, aren't necessarily quite the same. It appears to me that equivalence is still a perfectly valid concept in free-fall reference frames. It also seems valid in conditions that properly isolate the room in accelerating frames. He just failed to properly isolate the imaginary room.

I just find it very interesting that the master's own work in his own hand can be challenged succesfully (especially by a goof like me). Am I the first to realize this? Can anyone find any prior references?

 

[JesseM]

I was referring to the case where the room still hangs and swings freely, but the accelerating frame from which it hangs self-compensates.

By "accelerating frame", do you mean the actual physical structure it's hanging from, or do you mean the accelerating reference frame? I know what it would mean for the structure to self-compensate, but not for a reference frame to self-compensate.

If you want the room to be still too, then let's compare it to a room that is fixed on the earth. In this case, I could tell (comparing apples with apples, you know).

But if the room is fixed, how could you tell? Just to be clear, by "fixed" I mean it's impossible to move the room at all relative to the Earth (including swinging it back and forth), and it's impossible to change the rate of acceleration of the room in space.

I'm pretty sure you couldn't, not if the lateral thrusters were programmed to make sure the parts of the structure on the boundary of the inertial observer's imaginary box responded in exactly the same way to motions of the physical box as the same structures would respond as they would on earth.

I'm not clear on what you mean here. Do you mean the room swings freely on Earth and in the accelerating frame, but the accelerating framework's motion is fixed (self-compensates to maintain constant and straight acceleration)?

Yes, in both cases I'm assuming the physical framework that the cable holding the room is attached to cannot be moved, but the room/cable can still swing around.

In this case, I could still tell.

I'm pretty confident that you couldn't. If you think you could, how would you do it?

As you've suggested, the popular version that Albert Einstein wrote versus the theory, aren't necessarily quite the same. It appears to me that equivalence is still a perfectly valid concept in free-fall reference frames. It also seems valid in conditions that properly isolate the room in accelerating frames. He just failed to properly isolate the imaginary room.

I just find it very interesting that the master's own work in his own hand can be challenged succesfully (especially by a goof like me). Am I the first to realize this? Can anyone find any prior references?

I wouldn't really regard this as a mistake on Einstein's part because the description seems to assume that the rate of acceleration of the room in space is constant (ie no swinging, which would involve changing sideways acceleration). From the paper you referenced:

To the middle of the lid of the chest is fixed externally a hook with rope attached, and now a “being” (what kind of a being is immaterial to us) begins pulling at this with a constant force. The chest together with the observer then begin to move “upwards” with a uniformly accelerated motion.

And likewise, it is assumed that the chest would be at rest in the gravitational field:

Just then, however, he discovers the hook in the middle of the lid of the chest and the rope which is attached to it, and he consequently comes to the conclusion that the chest is suspended at rest in the gravitational field.

He's saying that with these conditions, all experiments in the room will give the same results in the two situations; his description doesn't really say anything one way or another about experiments which change the basic conditions of his thought-experiment (and nowhere does he make any blanket statement like 'there is no experiment the man can do to determine whether he is really being pulled at an accelerating rate in empty space or hanging from a rope in a gravitational field').

 

[ubavontuba]

First, I want to reitterate again that this is not meant to be a serious consideration in regards to equivalency, but rather this is meant to be a fun exercise in creative thinking.

By "accelerating frame", do you mean the actual physical structure it's hanging from, or do you mean the accelerating reference frame? I know what it would mean for the structure to self-compensate, but not for a reference frame to self-compensate.

Yes. I generally try to use "framework" to differentiate, but forgot in this case. Einstein's "being" seems to imply a thinking entity to me, so I prefer not to use it.

But if the room is fixed, how could you tell? Just to be clear, by "fixed" I mean it's impossible to move the room at all relative to the Earth (including swinging it back and forth), and it's impossible to change the rate of acceleration of the room in space.

Please note Einstein states: "and now a “being” (what kind of a being is immaterial to us) begins pulling at this with a constant force."

Please note the term "constant force," not "steady rate."

Therefore, in his ball dropping analogy, he analyzes the consequences incorrectly. If the dropped ball were of sufficient mass, the observer would notice a momentary "increase" in gravity (acceleration) as the ball is released (since it is momentarily dettached from the total mass and therefore the "constant force" will work just as hard to accelerate less mass), and there would be a subsequent decrease in gravity (deceleration) when the ball hits the floor.

In fact, the changes in kinetic energy might cause the ball to apparently bounce higher than it fell! (relative to the observer in the room)

So, it looks to me like Einstein played pretty loose with the rules. That is that he made statements that just aren't entirely true to demonstrate his points. Weird, isn't it? Maybe he just had trouble with English?

Again, am I the first person to notice this? I can't find any prior references. Has anyone else had any luck?

I'm pretty confident that you couldn't. If you think you could, how would you do it?

Oh ye of little faith! Do you not remember how you thought I couldn't tell in the first place? Why do you doubt me now? (with apologies to my fellow Christians).

Seriously, if we consider that the known laws of physics still apply to all structures (except for the impossible constant acceleration at a steady rate regardles of motion in the room)... I could tell.

He's saying that with these conditions, all experiments in the room will give the same results in the two situations; his description doesn't really say anything one way or another about experiments which change the basic conditions of his thought-experiment (and nowhere does he make any blanket statement like 'there is no experiment the man can do to determine whether he is really being pulled at an accelerating rate in empty space or hanging from a rope in a gravitational field').

Yeah, but this statement kind of implies it:
"Relying on his knowledge of the gravitational field (as it was discussed in the preceding section), the man in the chest will thus come to the conclusion that he and the chest are in a gravitational field which is constant with regard to time."

Also, you had earlier made this statement yourself and even referenced some papers in regards to it. And note how even the experiment he does explain is analyzed incorrectly (as I stated above).

As the man in the box must obviously move about to perform the observations Einstein mentions, wouldn't the box tend to sway? "Relying on his knowledge of the gravitational field," wouldn't a lack of normal swaying tell the observer that he shouldn't be too quick to jump to Einstein's conclusion?

 

[Mike2]

Good point; however, the effect is generally considered equivalent; and can be considered equivalent to Hawking radiation at the extreme, although there are some differences.
See:
http://www.emis.ams.org/journals/LRG/Articles/lrr-2001-6/node3.html

Creator

Has anyone studied what happens near gravitating bodies as the Unruh/Hawking effect adds an energy density to the surrounding space associated with the temperature - that since this added energy density adds an additional small equivalent mass density, then this would result in further gravitation, resulting in further Unruh/Hawking temperature, then energy density, then mass density, which would add further temperature, then energy, then mass, which would be iterated to infinity. How would such a process converge? Could this account for dark matter effects?

 

[TheAntiRelative]

"By the time the light from the bottom astronaut reaches me, I'll have picked up some speed, so that I'll be receding from the light at a higher rate than previously as I receive it. So it should be redshifted--and yes, so it is!"

Okay, so the point is here that he's actually receeding from the frame that the emitter was in at the moment of emission. No problem.

Where I'm having a problem is that the top astronaut should be experiencing time faster than the bottom one if they are truly in a gravitational field. If they are actually just accelerating in deep space he is not. That is proven by the muon test.

This means that if the bottom astronaut fires a pulse at the beginning of a muons life and one at the end, and the top astronaut measures a muon's life in his location. After factoring out SR considerations, it would be possible for the top astronaut to determine whether or not he is in a gravitational field or just accelerating.

Accelerating: Lifetime the Same.
Gravitational field: Bottom Muon lifetime > Top Muon Lifetime.

 

[Ich]

Where I'm having a problem is that the top astronaut should be experiencing time faster than the bottom one if they are truly in a gravitational field. If they are actually just accelerating in deep space he is not.

That´s not true.

 

[TheAntiRelative]

That´s not true.

Umm. Okay. Mind giving some detail/qualification? Which part?
Can you explain how your answer relates to the experiments I cited earlier?

 

[TheAntiRelative]

If one works the problem in the coordinate system of the muon, one does have to take into account gravitational time dilation (or equivalently, a non-Minkowskian metric).

But in an inertial frame, the metric is always Minkowskian, and there is never any gravitational time dilation.

The sci.physics.faq entry that Jesse quoted earlier should also go into this.

I read from the link Jesse posted and it was interesting but it didn't seem completely relevant to the context.

Unfortunately I don't entirely follow what you are saying about taking gravitational time dilation into account above. We factor out anything wrt the Earth's gravity because it is equal at rest and in the storage ring where it is accelerated.

The result of the experiment is that the muons decayed at the same rate under many thousand Gs of acceleration as they did in the lab frame. If acceleration and gravity are equivelent, the lifetime of the muons should have been greatly extended from the perspective of the lab frame. They were not.

Apposingly it is well known that Muons decay faster in outer space and clocks run faster in outer space when viewed from the same lab frame (assuming it is inertial for simplicity)

So, what exactly do you mean?



As an aside: The truth of the matter is that there is no such thing as a truly inertial frame because time would pass instantly (or not at all) without the presense of any gravitational field. Time contraction/dilation (crap! which word is right?) would be infinite. Time cannot exist without gravity so far as I understand it. (and have read Einstien's comments to the same)

 

[pervect]

The only gravity present in the Earth's frame is the Earth's gravity, which we both agree is irrelevant.

What is present in the Earth frame that makes the muons accelerate is not gravity, but a centripetal force. So the simple answer is that there is no gravitational time dilation in the Earth's frame, because there is no gravity there!

I.e. it is an electromagnetic force, NOT a gravitational force, that accelerates the muons radially. In order for there to be gravitational time dilation, there must be a gravitational force on the muon's. But there is no such force (except the negligible downwards force of Earth's gravity).

As an aside: The truth of the matter is that there is no such thing as a truly inertial frame because time would pass instantly (or not at all) without the presense of any gravitational field.

I don't know exactly where you got this idea, but it's totally wrong :-(. Clocks can exist just fine without gravity.

 

[JesseM]

Please note Einstein states: "and now a “being” (what kind of a being is immaterial to us) begins pulling at this with a constant force."

Please note the term "constant force," not "steady rate."

But you're ignoring the next sentence, which I highlighted: 'The chest together with the observer then begin to move “upwards” with a uniformly accelerated motion.' I would say this is part of the conditions of the thought-experiment he is describing, if you do something to cause the motion to no longer be 'uniformly accelerated' then you're describing a different thought-experiment.

I'm pretty confident that you couldn't. If you think you could, how would you do it?

Oh ye of little faith! Do you not remember how you thought I couldn't tell in the first place? Why do you doubt me now? (with apologies to my fellow Christians).

Seriously, if we consider that the known laws of physics still apply to all structures (except for the impossible constant acceleration at a steady rate regardles of motion in the room)... I could tell.

I'm actually pretty confident you couldn't, just by considering the point of view of a freefalling/inertial observer who draws an imaginary box around himself and observes the cable and smaller physical box as it passes through his imaginary box. If the structure the cable is attached to is not affected by the motions of the box/cable, then both the inertial and freefalling observer will see the point of attachment of the cable to the structure to be accelerating towards the ceiling at a constant rate. Therefore, the only thing which could vary between the inertial and freefalling observer is the cable and small box, which can be assumed to lie totally within his imaginary box for some small time-interval. So, it seems to me that the freefalling/inertial version of the equivalence principle, which you said before you don't dispute, would demand that there be no difference in how the box and cable behave in response to identical actions by the gnome in the box.

Anyway, if you think I'm wrong, don't be coy--what's your experiment?

He's saying that with these conditions, all experiments in the room will give the same results in the two situations; his description doesn't really say anything one way or another about experiments which change the basic conditions of his thought-experiment (and nowhere does he make any blanket statement like 'there is no experiment the man can do to determine whether he is really being pulled at an accelerating rate in empty space or hanging from a rope in a gravitational field')

Yeah, but this statement kind of implies it:
"Relying on his knowledge of the gravitational field (as it was discussed in the preceding section), the man in the chest will thus come to the conclusion that he and the chest are in a gravitational field which is constant with regard to time."

I don't think it implies it too strongly, in any case--he's still talking about what the man will include in the experiment as he describes it, which includes the idea that the chest is moving with a "uniformly accelerated motion".

Also, you had earlier made this statement yourself and even referenced some papers in regards to it.

The papers I referenced in post #6 only defined the equivalence principle in terms of the freefalling/inertial equivalence, though. Also, in your initial post you also suggested it was part of the conditions of the experiment that the room was 'being pulled under a constant 1g acceleration'--so if you allow experiments which cause the room to no longer accelerate at 1g, you're changing the conditions of the experiment. Finally, when you asked for qualifications I did say that I was justifying the at-rest-in-a-gravitational-field/accelerating-in-space equivalence in terms of the freefalling/inertial equivalence, using the "box-inside-a-larger-box" argument that I've been using frequently, in post #10. If you have a structure holding up the smaller box which cannot fit inside the freefalling/inertial observer's small imaginary box, and this structure would behave differently on Earth vs. when accelerating in space, this argument breaks down.

I'm not saying you haven't hit on an interesting point though, what you show is that one needs to be careful about exactly how one states the equivalence between the observer at rest in a gravitational field and the observer accelerating in empty space. I'm sure you could find some authors who have not been careful enough, but I don't think Einstein is really guilty of this sort of mistake here.

As the man in the box must obviously move about to perform the observations Einstein mentions, wouldn't the box tend to sway?

Well, you can always make the idealization that the man's mass is very small compared to the mass of the chest. Anyway, it's a thought-experiment, so I think you're allowed to ignore practical complications like this.

"Relying on his knowledge of the gravitational field," wouldn't a lack of normal swaying tell the observer that he shouldn't be too quick to jump to Einstein's conclusion?

Aside from the fact that Einstein specified the box should be accelerating at a "uniform" rate, there would be swaying in space if you performed the same experiment that led to swaying on earth. What makes you think there wouldn't be? Conservation of sideways momentum should hold just as well in space as on Earth (in both cases there is no external force being applied in the sideways direction), so if I jump sideways inside the chest, the chest itself will have to temporarily move a bit in the opposite direction to conserve total sideways momentum. Of course, as soon as I land on the floor again the swaying should stop, but this would be true on Earth too if you were in a vacuum and the structure holding the cable was fixed and not able to move on its own.

 

[TheAntiRelative]

The only gravity present in the Earth's frame is the Earth's gravity, which we both agree is irrelevant.

What is present in the Earth frame that makes the muons accelerate is not gravity, but a centripetal force. So the simple answer is that there is no gravitational time dilation in the Earth's frame, because there is no gravity there!

I.e. it is an electromagnetic force, NOT a gravitational force, that accelerates the muons radially. In order for there to be gravitational time dilation, there must be a gravitational force on the muon's. But there is no such force (except the negligible downwards force of Earth's gravity).

I don't know that I understand your point. "Its a chemical-reaction force that accelerates a rocket, not a gravitational one." In the end I really don't care what force accelerated something not under the influnce of gravity. But what I am saying may be obvious to your or something I guess. All I'm saying is that if you are in a rocketship in deep space being accelerated by rocket boosters as apposed to being in a rocketship sitting on the ground being accelerated by gravity. There is a testable difference and therefore gravity and accelleration are not equivelent.

I don't know exactly where you got this idea, but it's totally wrong :-(. Clocks can exist just fine without gravity.

Heh, well I got it from well known public Einstein quotes in which he states that time cannot exist without mass and gravity. So in effect, yes a physical clock would create a gravitational field but then it wouldn't be in a truly inertial frame anymore would it? I can go find the qoutes if you like...

 

[pervect]

I don't know that I understand your point. "Its a chemical-reaction force that accelerates a rocket, not a gravitational one." In the end I really don't care what force accelerated something not under the influnce of gravity. But what I am saying may be obvious to your or something I guess. All I'm saying is that if you are in a rocketship in deep space being accelerated by rocket boosters as apposed to being in a rocketship sitting on the ground being accelerated by gravity. There is a testable difference and therefore gravity and accelleration are not equivelent.

You're still missing the point :-(.

If you are in an accelerating rocketship
YOU ARE IN A NON-INERTIAL FRAME!

I'd make this blink if I could :-).

I.e when you are in a rocketship AND you adopt coordinates that accelerate along with the rocketship, you 'see' gravity, and you also 'see' gravitational time dilation.

If you are in an accelerating rocketship and you do NOT adopt accelerating coordinates (ie you use inertial coordinates), you do NOT 'see' any gravity, and you also do NOT 'see' any gravitational time dilation.

Because the Earth frame is effectively an inertial frame for the muon experiment, there is no gravitational time dilation in that frame. At least not in the sense you mean.

I have no additional comment to make on your other idea about time & gravity - I'll stand by my original comment, though.

 

[JesseM]

Because the Earth frame is effectively an inertial frame for the muon experiment, there is no gravitational time dilation in that frame.

Why would the Earth frame be considered effectively inertial? In the presence of gravity, isn't it only a freefall frame that can be considered equivalent to an inertial frame, while a frame at rest in the gravitational field is equivalent to an accelerating frame? Or are you just saying it's effectively inertial because Earth's gravity is weak enough that gravitational time dilation effects would be negligible compared to velocity-based time dilation effects in this experiment?

 

[ubavontuba]

But you're ignoring the next sentence, which I highlighted: 'The chest together with the observer then begin to move “upwards” with a uniformly accelerated motion.' I would say this is part of the conditions of the thought-experiment he is describing, if you do something to cause the motion to no longer be 'uniformly accelerated' then you're describing a different thought-experiment.

Actually, I feel that you're taking this out of context. It seems to clearly imply to me that the total mass of the chest and the occupant are accelerating at a unifrom rate as a result of the constant force. Not that the uniform acceleration is constant regardless of the force.

Anyway, if you think I'm wrong, don't be coy--what's your experiment?

I suppose it should be evident by now that I am anything but coy. I mean how coy could I be if I'm willing to scrutinize Einstein's own works so deliberately?

However, the parameters of this experiment must be clearly understood by both of us, so that I don't accidently claim success (or failure) for the wrong experiment, applied to the wrong conditions. Please specify your conditions, but keep it relevent. That is, the conditions of the box on Earth should match the conditions of the box under acceleration, save for the fact of acceleration. Also, the accelerating framework's physics must be described to a reasonable degree. I.e. does it keep it's uniform rate and latteral conditions with retro rockets? Is it a sort of elevator accelerating in a fixed framework/shaft? If the accelerating framework's properties are ignored (or made to be arbitrarily equivalent to gravity without defined rules), then we can state anything we want and therefore we might as well call it "magic."

I don't think it implies it too strongly, in any case--he's still talking about what the man will include in the experiment as he describes it, which includes the idea that the chest is moving with a "uniformly accelerated motion".

As I've said above, I disagree with this interpretation. However, I (by ""Relying on (my) knowledge of the gravitational field") would know that I'm not in gravity, even if Einstein's occupant is unable to make this determination. I'm not saying his occupant is stupid, but...

Also, in your initial post you also suggested it was part of the conditions of the experiment that the room was 'being pulled under a constant 1g acceleration'--so if you allow experiments which cause the room to no longer accelerate at 1g, you're changing the conditions of the experiment.

That was just my opening setup question to garner interest, but I'm willing to concede this as a parameter so long as it's described how it is achieved (rockets and brakes?). But note; I feel this exceeds Einstein's own given parameters.

I'm not saying you haven't hit on an interesting point though, what you show is that one needs to be careful about exactly how one states the equivalence between the observer at rest in a gravitational field and the observer accelerating in empty space. I'm sure you could find some authors who have not been careful enough, but I don't think Einstein is really guilty of this sort of mistake here.

You are right about having to be careful in regards to modelling the principle. But I disagree with you in your assertion that Einstein was so careful. In my view, his theory has become widely accepted on its own merits in spite of his explanation (in this context).

Well, you can always make the idealization that the man's mass is very small compared to the mass of the chest. Anyway, it's a thought-experiment, so I think you're allowed to ignore practical complications like this.

I disagree. By ignoring the laws of physics while examining the laws of physics you endanger the outcome as being irrelevant. I think Einstein knew his theory better than he was able to describe it in this context and therefore it's valid on its own merits in spite of his inability to describe it well (in this context).

Aside from the fact that Einstein specified the box should be accelerating at a "uniform" rate, there would be swaying in space if you performed the same experiment that led to swaying on earth. What makes you think there wouldn't be? Conservation of sideways momentum should hold just as well in space as on Earth (in both cases there is no external force being applied in the sideways direction), so if I jump sideways inside the chest, the chest itself will have to temporarily move a bit in the opposite direction to conserve total sideways momentum. Of course, as soon as I land on the floor again the swaying should stop, but this would be true on Earth too if you were in a vacuum and the structure holding the cable was fixed and not able to move on its own.

My point here is that you coudn't swing it like a pendulum since this would disturb the center of mass for the system and would require a reactionary oscillation that isn't available in the accelerating system without unusual consequences.

 

[JesseM]

Actually, I feel that you're taking this out of context. It seems to clearly imply to me that the total mass of the chest and the occupant are accelerating at a unifrom rate as a result of the constant force. Not that the uniform acceleration is constant regardless of the force.

And I think they are both part of the conditions that he's describing, that the external force is constant and that the acceleration is constant (implying internal forces are considered negligible).

However, the parameters of this experiment must be clearly understood by both of us, so that I don't accidently claim success (or failure) for the wrong experiment, applied to the wrong conditions. Please specify your conditions, but keep it relevent. That is, the conditions of the box on Earth should match the conditions of the box under acceleration, save for the fact of acceleration. Also, the accelerating framework's physics must be described to a reasonable degree. I.e. does it keep it's uniform rate and latteral conditions with retro rockets? Is it a sort of elevator accelerating in a fixed framework/shaft? If the accelerating framework's properties are ignored (or made to be arbitrarily equivalent to gravity without defined rules), then we can state anything we want and therefore we might as well call it "magic."

Well, the condition we were discussing was that the box and the cable can move around but the acceleration of the framework the cable is attached to can be considered negligible. You don't really need to introduce retro rockets to achieve this, just consider the limit as the mass of the box and cable becomes negligible compared to the mass of the framework (but keep the mass of the framework constant so you don't have to worry about its increasing mass curving spacetime enought to have a noticeable effect on the experiment).

One other simple solution that occurs to me is to assume the framework itself is capable of sliding without friction on the surface of the earth, so you don't have to worry about any of its sideways momentum being transferred to the Earth and thus the inertia of the Earth isn't relevant to the problem. In this case the acceleration of the framework doesn't need to be negligible, but it will be the same in both the at rest on Earth case and the accelerating in space case.

As I've said above, I disagree with this interpretation. However, I (by ""Relying on (my) knowledge of the gravitational field") would know that I'm not in gravity, even if Einstein's occupant is unable to make this determination. I'm not saying his occupant is stupid, but...

But Einstein doesn't ever say that there is nothing the occupant could do to determine which is really the case (he could blow a hole in the side of the chest and look outside, for example). Given the conditions he sets, which includes uniform acceleration, any experiment the guy does in the accelerating box could just as easily be explained in terms of a gravitational field, that's the only point he's making.

You are right about having to be careful in regards to modelling the principle. But I disagree with you in your assertion that Einstein was so careful. In my view, his theory has become widely accepted on its own merits in spite of his explanation (in this context).

There is nothing in the quoted text that dignifies being called a "theory", it is simply an illustration of the equivalence of uniform acceleration and uniform gravity, which is part of his theory of general relativity.

Well, you can always make the idealization that the man's mass is very small compared to the mass of the chest. Anyway, it's a thought-experiment, so I think you're allowed to ignore practical complications like this.

I disagree. By ignoring the laws of physics while examining the laws of physics you endanger the outcome as being irrelevant.

There is a big difference between "ignoring the laws of physics" and presenting idealized cases which would be valid approximations in certain limits. For example, it is common in illustrations of mechanics to assume zero friction even though this is impossible to achieve in practice. It is common to assume that gravitation is constant in the neighborhood of the surface of the Earth even though we know that the gravitational pull should be slightly less 2 meters above the surface as 1 meter above the surface. It is common to assume that the orbit of a planet is determined solely by the gravity of the sun, even though the gravity of other planets and distant stars and dust particles in space should have some small effect on a planet's orbit. Here we are dealing with a similar sort of approximation, where the mass of any moving parts in any experiments (such as the mass of a dropped ball) is assumed to be negligible compared to the mass of the chest. If you disagree with the whole practice of making true-in-the-limit approximations of this nature, then you would have to reject basically every illustration of every physics principle in every textbook.

I think Einstein knew his theory better than he was able to describe it in this context and therefore it's valid on its own merits in spite of his inability to describe it well (in this context).

Fair enough, although I disagree.

Aside from the fact that Einstein specified the box should be accelerating at a "uniform" rate, there would be swaying in space if you performed the same experiment that led to swaying on earth. What makes you think there wouldn't be? Conservation of sideways momentum should hold just as well in space as on Earth (in both cases there is no external force being applied in the sideways direction), so if I jump sideways inside the chest, the chest itself will have to temporarily move a bit in the opposite direction to conserve total sideways momentum. Of course, as soon as I land on the floor again the swaying should stop, but this would be true on Earth too if you were in a vacuum and the structure holding the cable was fixed and not able to move on its own.

My point here is that you coudn't swing it like a pendulum since this would disturb the center of mass for the system and would require a reactionary oscillation that isn't available in the accelerating system without unusual consequences.

Well, in the ideal case you can't swing it like a pendulum on Earth either, because without any external sideways force (assume the experiment is done in a vacuum chamber so there's force from the air) the center of mass should not be able to move in a sideways direction. But I suppose even an ordinary pendulum varies in its sideways momentum from the bottom of its arc to the top, and we know we can even change the size of our arcs on a playground swing by pumping our legs, so I guess this isn't very realistic. I'm actually not quite sure what the best explanation for this is, but if you imagine the pendulum swinging on a string which is looped around a rod sticking out of a wall, I think what's probably going on is that some of the pendulum's sideways momentum is being transferred to the rod (through the contact point between the loop of string and the rod) which in turn transfers it to the wall, which doesn't visibly move because its mass is so much larger. But there's no reason this should work much differently for a pendulum attached to a rod and wall which are accelerating in space than for one attached to a rod and a wall which is sitting on Earth (and the slight difference due to the wall being attached to the Earth itself can be eliminated by assuming the framework can slide on the surface Earth without friction, as I suggested earlier...if the framework's mass is much larger than the pendulum's mass, this sliding wouldn't be noticeable anyway).

 

[pervect]

Why would the Earth frame be considered effectively inertial? In the presence of gravity, isn't it only a freefall frame that can be considered equivalent to an inertial frame, while a frame at rest in the gravitational field is equivalent to an accelerating frame? Or are you just saying it's effectively inertial because Earth's gravity is weak enough that gravitational time dilation effects would be negligible compared to velocity-based time dilation effects in this experiment?

There is some gravitational time dilation with height on Earth.

This gravitational time dilation is due only to height. It's not important to the muon experiment because 1) the effect is small and 2) all the muons in the ring are at essentially the same height anyway.

If you performed this experiment out in empty space, without gravity, you would get no different results. If you performed it on a rocketship accelerating out in empty space at 1G, the resutls would be the same as well. The non-inertiality of the Earth's frame due to its height (or any of several other small effects) just doesn't matter.

 

[Creator]

... I (by ""Relying on (my) knowledge of the gravitational field") would know that I'm not in gravity, ...

.

That's only because your original experimental proceedure used a mere 1/2jigger of brandy.
Had you used the entire bottle of brandy for step #1 there is no way you would have been able to determine from which direction gravity is (or is not) operating.

Creator

 

[ubavontuba]

That's only because your original experimental proceedure used a mere 1/2jigger of brandy.
Had you used the entire bottle of brandy for step #1 there is no way you would have been able to determine from which direction gravity is (or is not) operating.

Ha, Ha! That's too funny! However, I'd note a certain amount of unusual angular momentum! (Since I'd be flat on my back with the room apparently spinning!)

 

[ubavontuba]

And I think they are both part of the conditions that he's describing, that the external force is constant and that the acceleration is constant (implying internal forces are considered negligible).

Sure. This is possible, but the mass of the accelerating framework (AF) would have to be pretty large and therefore it would have its own gravity (messing things up). It doesn't really matter though as the effects I noted would be the same, only smaller (requiring the more accurate, perhaps hypothetical measurements I wrote of earlier).

Well, the condition we were discussing was that the box and the cable can move around but the acceleration of the framework the cable is attached to can be considered negligible. You don't really need to introduce retro rockets to achieve this, just consider the limit as the mass of the box and cable becomes negligible compared to the mass of the framework (but keep the mass of the framework constant so you don't have to worry about its increasing mass curving spacetime enought to have a noticeable effect on the experiment).

Naw, that's a bit vague. Even if the AF were fairly massive (like a battleship) the resonance of a swinging mass that could comfortably hold a man would tend to skew its trajectory. Anyways like I said above, the amount of mass it has isn't important since hypothetically the same effects are still observable.

One other simple solution that occurs to me is to assume the framework itself is capable of sliding without friction on the surface of the earth, so you don't have to worry about any of its sideways momentum being transferred to the Earth and thus the inertia of the Earth isn't relevant to the problem. In this case the acceleration of the framework doesn't need to be negligible, but it will be the same in both the at rest on Earth case and the accelerating in space case.

Actually, even in this scenario I could still hypothetically tell. This would simply be a matter of measuring how much I could tilt the apparent gravity by bouncing off the walls, attempting to tip the room. On earth, it would always slide parallel with the the circumference. On a smaller mass, the uneven pressure resonating across the center of mass would cause the whole system to tilt back and forth.

If the AF were rigidly held in its path by some means, I can even think of a hypothetical experiment to detect that.

Well, in the ideal case you can't swing it like a pendulum on Earth either, because without any external sideways force (assume the experiment is done in a vacuum chamber so there's force from the air) the center of mass should not be able to move in a sideways direction. But I suppose even an ordinary pendulum varies in its sideways momentum from the bottom of its arc to the top, and we know we can even change the size of our arcs on a playground swing by pumping our legs, so I guess this isn't very realistic.

A swing works on resonance. The first upswing cannot exceed the boundaries of the box, but subsequent swings can get higher and higher. Hypothetically there is a reaction to this transmitted to the earth, but as you noted, the overwhelmingly large mass doesn't seem to care.

...if the framework's mass is much larger than the pendulum's mass, this sliding wouldn't be noticeable anyway).

Ah but it is still there in a hypothetical context and unless the mass were as big as the earth, it would be different than normal gravity and would therefore be hypothetically detectable. But note, if the mass were as great as the Earth and accelerating at the rate of 1g, our hapless man-in-the box being towed by the mass would be in free-fall!

 

[JesseM]

Sure. This is possible, but the mass of the accelerating framework (AF) would have to be pretty large and therefore it would have its own gravity (messing things up). It doesn't really matter though as the effects I noted would be the same, only smaller (requiring the more accurate, perhaps hypothetical measurements I wrote of earlier).

It wouldn't have to be that large, because as I've pointed out before, Einstein isn't saying that nothing the experimenter can do will reveal a difference between the chest in gravity and the accelerating chest, he just says that when he does typical experiments like dropping objects from his hand, the results will be just like if he were in a gravitational field. If you drop a 100 g ball inside a 1000 kg box, it's a reasonable approximation to treat the change in acceleration of the box as negligible.

Well, the condition we were discussing was that the box and the cable can move around but the acceleration of the framework the cable is attached to can be considered negligible. You don't really need to introduce retro rockets to achieve this, just consider the limit as the mass of the box and cable becomes negligible compared to the mass of the framework (but keep the mass of the framework constant so you don't have to worry about its increasing mass curving spacetime enought to have a noticeable effect on the experiment).

Naw, that's a bit vague. Even if the AF were fairly massive (like a battleship) the resonance of a swinging mass that could comfortably hold a man would tend to skew its trajectory.

First of all, this is just an idealized limit, and since I specified that the mass of the framework was being held constant, it was implied that we are taking the limit as the mass of the man and box are becoming smaller and smaller (imagine using a series of smaller and smaller gnomes in smaller and smaller boxes).

But even if we want to be more practical, the swinging box isn't going to be able to shift the trajectory of the framework in any cumulative way because of conservation of sideways momentum, all it can do is shift the framework back and forth at the same rate the room is swinging back and forth. And how fast do you think the guy in the room is going to be able to get it swinging using resonance? I don't think there'd be any theoretical upper limit, but eventually it'd be going fast enough that the person won't be able to time the motions of his body to match the resonant frequency. If we plug in a number for a plausible maximum velocity of the box at the bottom of its arc, we can figure out the maximum velocity of the framework using conservation of momentum; if we also know the period of the box's swing, we can use this to figure out an upper limit on how far the framework can move back and forth. I would guess that if the box is assumed to have a mass of 200 kg and the framework is assumed to have the mass of a battleship (which according to http://chemistry.umeche.maine.edu/~amar/fall2004/SigFigs.html would be around 1.3 * 10^8 kg), then for a plausible maximum velocity the amount the battleship would move would probably be microscopic.

One other simple solution that occurs to me is to assume the framework itself is capable of sliding without friction on the surface of the earth, so you don't have to worry about any of its sideways momentum being transferred to the Earth and thus the inertia of the Earth isn't relevant to the problem. In this case the acceleration of the framework doesn't need to be negligible, but it will be the same in both the at rest on Earth case and the accelerating in space case.

Actually, even in this scenario I could still hypothetically tell. This would simply be a matter of measuring how much I could tilt the apparent gravity by bouncing off the walls, attempting to tip the room. On earth, it would always slide parallel with the the circumference. On a smaller mass, the uneven pressure resonating across the center of mass would cause the whole system to tilt back and forth.

True, on Earth the framework could only move in a sideways direction, while in space it could also move up and down somewhat (but I'm not so sure if the movement of the pendulum could cause it to rotate at all--suppose the cable holding the pendulum was tied to a rod which was sticking out of the dead center of the framework, how could the pendulum's movements apply any torque to the framework?)...although again, I think this effect would be microscopic if the mass of the framework was large enough.

If the AF were rigidly held in its path by some means, I can even think of a hypothetical experiment to detect that.

OK, what measurement would you make in this case?

...if the framework's mass is much larger than the pendulum's mass, this sliding wouldn't be noticeable anyway).

Ah but it is still there in a hypothetical context and unless the mass were as big as the earth, it would be different than normal gravity and would therefore be hypothetically detectable.

But see the point I made in the last post about approximations used in all of physics, like the assumption that objects can slide without friction or the assumption that the sun is the only body whose gravitational field affects the orbit of the earth.

 

[ubavontuba]

JesseM,

As I'm sure you can see, and as I predicted, we are moving steadily away from the parameters of the thought experiment originally proposed by Einstein.

What happens in this case is we start chipping away at the fundamental differences in an attempt to make the experiment fit the theory. We do this by applying restrictions that make the variances smaller and smaller until they become negligble to the point of only being hypothetical on a very small scale. They remain, but they diminish to the point of ambiguity.

This is accomplished by either increasing the AF mass in order to make its inertial properties more earthlike, and/or by increasing the isolation of the room. (Note that I have said that properly isolated, I don't think I could tell.)

Your rocket powered floating room was a good example of proper isolation. However it ironically achieves this by being the same 1g acceleration device as a freely accelerating room, only it happens to be doing it in a 1g gravity field... for no net acceleration! (But it'd require loads of energy).

In the friction free consideration, I could tell by measuring the mass with a kinetic energy experiment. If the AF were sufficiently small, it couldn't absorb a lot of kinetic energy without ringing like a bell. Basically, I need but strike the floor with a sledgehammer. Of course increasing the mass will again diminish this effect, but it is still hypothetically different than gravity unless the mass becomes as large as the Earth (and then of course, you have normal gravity).

See? The fundamental difference between gravity and acceleration that I have been exploiting is that gravity is mass dependent and acceleration is not (acceleration is energy dependent).

This is of course not a profound consideration as I think it's rather obvious. It's just interesting that apparently no one (as far as I know) has put these facts together in the context of Einstein's thought experiment.

If I can think of a difference in the free-fall version I'll be sure to let everyone know, but I wouldn't hold my breath...

 

[TheAntiRelative]

You're still missing the point :-(.

If you are in an accelerating rocketship
YOU ARE IN A NON-INERTIAL FRAME!

I'd make this blink if I could :-).

I.e when you are in a rocketship AND you adopt coordinates that accelerate along with the rocketship, you 'see' gravity, and you also 'see' gravitational time dilation.

If you are in an accelerating rocketship and you do NOT adopt accelerating coordinates (ie you use inertial coordinates), you do NOT 'see' any gravity, and you also do NOT 'see' any gravitational time dilation.

Because the Earth frame is effectively an inertial frame for the muon experiment, there is no gravitational time dilation in that frame. At least not in the sense you mean.

I have no additional comment to make on your other idea about time & gravity - I'll stand by my original comment, though.

Oh, okay, so you are saying that you observe gravitational time dilation only if you share the same accelerated coordinate system?

How then can we on Earth observe gravitational red shift when observing stars and their light as they pass by massive objects etc. etc? We are not in their coordinate system by any means. All the effects of GR are tied together, how could one be observable from your separate frame without the rest?

 

[JesseM]

JesseM,

As I'm sure you can see, and as I predicted, we are moving steadily away from the parameters of the thought experiment originally proposed by Einstein.

What happens in this case is we start chipping away at the fundamental differences in an attempt to make the experiment fit the theory. We do this by applying restrictions that make the variances smaller and smaller until they become negligble to the point of only being hypothetical on a very small scale. They remain, but they diminish to the point of ambiguity.

Well, I agree there will always be tiny differences, but they will go to zero in well-defined limits. You didn't really address my point about how virtually all thought-experiments in physics involve such idealizations that would be true in the limit, like objects sliding without friction. Not to mention the fact that the equivalence principle itself, even when stated in terms of freefall/inertial equivalence, depends on taking the limit as the size of the region of spacetime you're looking at goes to zero--for any small but finite-sized room, you will be able to tell the difference by looking at tidal forces. So what's the difference between this and the kind of differences you're talking about, which also disappear in the limit (in this case, the limit as box becomes arbitrarily light compared to the framework)? Would you say it is a problem that tidal forces "remain, but they diminish to the point of ambiguity"?

In the friction free consideration, I could tell by measuring the mass with a kinetic energy experiment. If the AF were sufficiently small, it couldn't absorb a lot of kinetic energy without ringing like a bell. Basically, I need but strike the floor with a sledgehammer.

Well, my main response is the one above, but at the risk of getting sidetracked from the main issue again, you said you had an experiment that could determine even in the case where the framework had thrusters to compensate for its motions--what if the thrusters were hooked into sensors which could detect waves of movement traveling up the cable, and could anticipate exactly how they would cause the framework to accelerate when they reached the top, so that the firing of the rockets was timed to precisely compensate for this and insure that the framework never accelerates (or never changes its acceleration, in the accelerating-in-space case), not even briefly? In this case it would not ring like a bell or be affected in any other way by the motions of the box and cable.

 

[ubavontuba]

Well, I agree there will always be tiny differences, but they will go to zero in well-defined limits. You didn't really address my point about how virtually all thought-experiments in physics involve such idealizations that would be true in the limit, like objects sliding without friction. Not to mention the fact that the equivalence principle itself, even when stated in terms of freefall/inertial equivalence, depends on taking the limit as the size of the region of spacetime you're looking at goes to zero--for any small but finite-sized room, you will be able to tell the difference by looking at tidal forces. So what's the difference between this and the kind of differences you're talking about, which also disappear in the limit (in this case, the limit as box becomes arbitrarily light compared to the framework)? Would you say it is a problem that tidal forces "remain, but they diminish to the point of ambiguity"?

As far as idealized thought experiments are concerned, this is a good practice within limits. These limits should be used to consider the boundary potentials of the thought experiments. I.e. we can imagine a friction-free surface, as we can build low friction surfaces. We can't however create reduced inertia mass. Therefore the boundary potentials are rather fixed in this regard. We certainly can imagine inertialess mass, but I can imagine I'm a giant monster attacking Tokyo too (Godzilla!). For it to be relevant to reality, reasonable boundaries of thought must be considered.

You've been trying to consider the concept in a way that makes it reasonable to consider these effects to be negligible (and doing a pretty good job of it). I don't have a problem with this, so long as it's understood that this is the intent (as is the intent of considering a "finite region" of space is to limit divergency characteristics). But you must realistically understand that in order to accomplish this goal, you change the parameters of the experiment. I.e. if the AF mass gets too large, then it changes its own gravity/mass effects.

In the limit of a finite region of space thought experiment the tidal forces are negligible, but they hypothetically still exist. This is why finite region thought experiments will often state this as a given. The tidal forces remain (even to the point of ambiguity). This is a known difference between gravity and acceleration. This difference is widely understood and accepted. Therefore it requires no scrutiny or explanation from a goof like me. I was pointing out a difference that is not highly regarded (if at all).

There are several effects of divergence that are generally acknowledged besides tides. Obviously we have diminishing force with distance in gravity but not in acceleration, plumb angle differentials and whatnot. None of these are any more profound than my own consideration, as they simply relate to gravity's "radiating" from a single source quality.

So, since my concept can reasonably be imagined away to ambiguity, Einstein's theory withstands the test. However, it is still just as important a consideration as tides and divergence.

Well, my main response is the one above, but at the risk of getting sidetracked from the main issue again, you said you had an experiment that could determine even in the case where the framework had thrusters to compensate for its motions--what if the thrusters were hooked into sensors which could detect waves of movement traveling up the cable, and could anticipate exactly how they would cause the framework to accelerate when they reached the top, so that the firing of the rockets was timed to precisely compensate for this and insure that the framework never accelerates (or never changes its acceleration, in the accelerating-in-space case), not even briefly? In this case it would not ring like a bell or be affected in any other way by the motions of the box and cable.

In this case, you again have kinetic energy absorption differences that can be measured due to the law of opposite and equal reaction. You need simply to place a ball on the floor and jump up and down in the room. The compensating thrusters (while holding the AF constant) will send kinetic energy through the rope, to the room, and consequently to the ball. The ball will apparently start bouncing of its own accord.

 

[LightStorm]

Thought Experiment

http://forums.about.com/n/pfx/forum.aspx?msg=2109.782&nav=messages&webtag=ab-physics&sr=y

Principle of equivalence

http://www.oxfordreference.com/pages/Sample_Entries__sample_01.html

The point can be demonstrated with a thought experiment. Consider an observer in an enclosed box somewhere in space far removed from gravitational forces. Suppose that the box is suddenly accelerated upward, followed by the observer releasing two balls of different weights. Subject to an inertial force they will both fall to the floor at the same rate. But this is exactly how they would behave if the box was in a gravitational field and the observer could conclude that the balls fall under the influence of gravity. It was on the basis of this equivalence that Einstein made his dramatic prediction that rays of light in a gravitational field move in a curved path.​

LS: The above experiment can be modified to invalidate the principle of equivalence. Consider an observer in a large enclosed box somewhere in space far removed from gravitational forces. Suppose that the box is accelerated upward at 9.8m/s/s, then a ball's weight in the large enclosed box will not vary with the height. The ball's weight will be a constant in all locations in the very large enclosed box.

But in a real gravitational field (such as the earth), the ball's weight will vary according to the altitude because a real gravity field is a gradient. The higher up you go, the lesser your weight owing to the gradient nature of gravity.

But this behavior cannot be observed in an enclosed box that is accelerating at 9.8m/s/s. The weight of an object enclosed in a box that is accelerating at 9.8m/s/s will remain constant.

Relativists then claim that the principle applies only to very small reference frames where gravity is more or less uniform. But if we have a very sensitive weight measure device (accelerometer) then one can still distinguish between acceleration and a gravity field.

Relativists usually use circular logic to defend the principle by claiming it is not necessary to test the equivalence principle after having heard my thought experiment.

Is there any new any circular logic that I can get here in this forum in the defense of the principle??

 

[jtbell]

Relativists usually use circular logic to defend the principle by claiming it is not necessary to test the equivalence principle after having heard my thought experiment.

I see this is your first post here, so welcome to Physicsforums.com! I suspect that you haven't seen the sticky post at the top of this forum: IMPORTANT! Read before posting. If you want to argue about the validity of relativity, there are other places where you can do that, e.g. sci.physics.relativity.

 

[JesseM]

Relativists then claim that the principle applies only to very small reference frames where gravity is more or less uniform. But if we have a very sensitive weight measure device (accelerometer) then one can still distinguish between acceleration and a gravity field.

By "very small" they mean "in the limit as the size of the spacetime region approaches zero". In this limit, the difference in gravity between different heights inside the box would also approach zero.

 

[rbj]

this guy completely misses the point.

The above experiment can be modified to invalidate the principle of equivalence. Consider an observer in a large enclosed box somewhere in space far removed from gravitational forces. Suppose that the box is accelerated upward at 9.8m/s/s, then a ball's weight in the large enclosed box will not vary with the height. The ball's weight will be a constant in all locations in the very large enclosed box.

But in a real gravitational field (such as the earth), the ball's weight will vary according to the altitude because a real gravity field is a gradient. The higher up you go, the lesser your weight owing to the gradient nature of gravity.

...

Is there any new any circular logic that I can get here in this forum in the defense of the principle??

you see, it's a thought experiment so, being so i will restate it as one comparing the accelerating room to a stationary one in a gravitational field created by an infinite plane of mass with sufficient mass per unit area to result in an acceleration of gravity of 9.8 m/s². how does you proof of invalidation deal with that?

.
.
.

i just love it when we get smart-asses that esteem themselves as smarter than Einstein or the many, many physicists that affirm SR and GR.

 

[ubavontuba]

i just love it when we get smart-asses that esteem themselves as smarter than Einstein or the many, many physicists that affirm SR and GR.

Hey! I resemble that remark!

Of course I made certain to qualify my thought experiments as not being a challenge to relativity, but rather simply being an exercise in creative thinking.

There are known differences between gravity and acceleration that are often qualified in these thought experiments. However, since relativity includes, quantifies, assesses, addresses, qualifies and otherwise accurately describes these phenomena, they simply help to prove relativity is correct overall (if thought about in the correct context).

 

[LightStorm]

By "very small" they mean "in the limit as the size of the spacetime region approaches zero". In this limit, the difference in gravity between different heights inside the box would also approach zero.

You are using circular logic. You can't assume spacetime even before you prove the principle. You first need to identify two reference frames that have dimensions greater than zero. Then you perform experiment x,y,z in both the reference frames. The principle claims the results will be an exact match. My thought experiment shows they will never be equal in this universe.

Why dimensions greater than zero? Because a point reference frame doesn't exist. You can't make a measurement or perform an experiment in a point reference frame. The principle is about performing experiments.

 

[LightStorm]

you see, it's a thought experiment so, being so i will restate it as one comparing the accelerating room to a stationary one in a gravitational field created by an infinite plane of mass with sufficient mass per unit area to result in an acceleration of gravity of 9.8 m/s2. how does you proof of invalidation deal with that?

LS: I don't underestand your scenario. Mayeb you could restate it in a different manner? But it appears like you do understand my scenario and it clearly shows gravity and acceleration are distinguiable in all reference frames that have dimensions greater than zero. All it takes is a really sensitive weight measuring device. I read site claiming the equivalence principle has been verified to very high levels of accuracy. If it is that accurate then my thought experiment shows that it can invalidate to the same accuracy by way of a sensitive weight measuring device. It all depends on how accurate the weight measuring device can be.

By the way I was googling some sites on equivalence principle and I stumbled on this site. I found the debate interesting and I thought let me me join the debate.

 

[JesseM]

Why dimensions greater than zero? Because a point reference frame doesn't exist. You can't make a measurement or perform an experiment in a point reference frame.

No, but you can certainly figure out what the results would be in a series of small regions (which I assume is what you mean by 'reference frame', although this is incorrect terminology), each one of which is smaller than the last. Are you familiar with what a "limit" means in calculus? Would you understand what it means to say "the limit as x approaches zero", for example?