Gravity/acceleration equivalent?

JesseM
pervect said:
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?

JesseM said:
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 therfore 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.

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JesseM
ubavontuba said:
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).
ubavontuba said:
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.
ubavontuba said:
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.
ubavontuba said:
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.
JesseM said:
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.
ubavontuba said:
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 acheive 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.
ubavontuba said:
I think Einstein knew his theory better than he was able to describe it in this context and therfore it's valid on its own merits in spite of his inability to describe it well (in this context).
Fair enough, although I disagree.
JesseM said:
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.
ubavontuba said:
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).

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pervect
Staff Emeritus
JesseM said:
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.

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ubavontuba said:
... 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.:tongue2:

Creator

Creator said:
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!)

JesseM said:
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 therfore 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 aparent 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 accross 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
ubavontuba said:
Sure. This is possible, but the mass of the accelerating framework (AF) would have to be pretty large and therfore 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.
JesseM said:
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).
ubovontuba said:
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 [Broken] would be around 1.3 * 10^8 kg), then for a plausible maximum velocity the amount the battleship would move would probably be microscopic.
JesseM said:
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.
ubavontuba said:
Actually, even in this scenario I could still hypothetically tell. This would simply be a matter of measuring how much I could tilt the aparent 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 accross 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.
ubavontuba said:
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?
JesseM said:
...if the framework's mass is much larger than the pendulum's mass, this sliding wouldn't be noticeable anyway).
ubavontuba said:
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.

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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...

pervect said:
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
ubavontuba said:
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"?
ubavontuba said:
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 travelling 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.

JesseM said:
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 relevent 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 travelling 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.

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Thought Experiment

Principle of equivalence

http://www.oxfordreference.com/pages/Sample_Entries__sample_01.html [Broken]

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??

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jtbell
Mentor
LightStorm said:
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
LightStorm said:
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.

this guy completely misses the point.

LightStorm said:
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.

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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?

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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.

rbj said:
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! :rofl:

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).

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JesseM said:
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 cant 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 doesnt exist. You cant make a measurement or perform an experiment in a point reference frame. The principle is about performing experiments.

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 dont 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 lemme me join the debate.

JesseM
LightStorm said:
Why dimensions greater than zero? Because a point reference frame doesnt exist. You cant 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?

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.

LS:The principle was designed for "reference frames". Not to individual points in a reference frame. My thought experiment deals with a reference frame too. Read the definition of the principle...

http://hyperphysics.phy-astr.gsu.edu/HBASE/relativ/grel.html

"Experiments performed in a uniformly accelerating reference frame with acceleration a are indistinguishable from the same experiments performed in a non-accelerating reference frame which is situated in a gravitational field where the acceleration of gravity = g = -a = intensity of gravity field. "

See the principle talks about "experiments". Measuring the weight of an object at different locations in a given reference frame is an "experiment", correct? You agree that, measuring the weight of an object at different locations in any given reference frame is an experiment?

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?

LS: I am not a mathematician. But as the limit approaches zero, you are getting into the realms of QM. We already know QM invalidates GR in quantum scales.

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JesseM
LightStorm said:
LS:The principle was designed for "reference frames". Not to individual points in a reference frame. My thought experiment deals with a reference frame too. Read the definition of the principle...
You're wrong. The definition of the principle states that general relativity reduces to special relativity locally, ie in an arbitrarily small region of spacetime. Most statements of the principle will say something to this effect. From this page:
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
And from http://scholar.uwinnipeg.ca/courses/38/4500.6-001/Cosmology/Principle%20of%20Equivalence%20in%20Mathematical%20Form.htm [Broken]:
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.
LightStorm said:
http://hyperphysics.phy-astr.gsu.edu/HBASE/relativ/grel.html

"Experiments performed in a uniformly accelerating reference frame with acceleration a are indistinguishable from the same experiments performed in a non-accelerating reference frame which is situated in a gravitational field where the acceleration of gravity = g = -a = intensity of gravity field. "
In this case, they specify that the frame is in a uniform gravitational field where the intensity of the gravity field is the same at every point. This is physically unrealistic, but in this case I suppose you can dispense with the requirement that you only look at a small region.
LightStorm said:
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?

LS: I am not a mathematician. But as the limit approaches zero, you are getting into the realms of QM. We already know QM invalidates GR in quantum scales.
Yes, but the equivalence principle is solely about the fact that the mathematical theory of GR reduces to SR locally--the question of whether it does is independent of whether you believe this mathematical theory is a completely accurate description of the real world or not (as you say, it almost certainly isn't, although it's quite possible the equivalence principle would hold for a theory of quantum gravity as well).

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Mike2 said:
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 [Broken]

Creator
Has the Unruh effect been confirmed? I think this is the same as confirming the existence of the zero point energy, right?

OK... If the gravitational acceleration has an Unruh temperature, then... what reference frame is the gravitational field being compared to? If there is a temperature associated by the mere fact that some point is in a deeper well then other points, then aren't there an infinite number of frames that are accelerating differently from the point in question so that it depend what you are comparing that point to when calculating the Unruh temperature? Thanks.

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LightStorm said:
rbj sez: 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 your proof of invalidation deal with that?

LS: I dont underestand your scenario. Mayeb you could restate it in a different manner?

do you know what would be the nature of the gravitational field created by a hypothetical infinite plane of mass?

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.

it's only because of the geometry, a specific geometry that creates an inverse-square field (coming from a nice spherically symmetrical mass) and you are citing the different strengths of the gravitational field in such a geometry as your "proof" that the EP is wrong. so i changed the geometry to one where the strength of the graviational field does not change with distance. then, no matter how sensitive your instruments, you would not be able to tell the difference, because there would be no difference. EP lives.

Hello, Mike.

Mike2 said:
Has the Unruh effect been confirmed? I think this is the same as confirming the existence of the zero point energy, right?

Not really.
First, what do you mean by confirmed? Unruh-Davies radiation is a prediction of QED and is generally accepted as valid. Experimental confirmation hasn't yet arrived (to my knowledge) due to the extremely high accelerations required; however, several interesting exp. tests have been proposed.

On the other hand, zero point energy was first predicted by Max Planck around 1911. Einstein and Otto Stern (not related to a screwball named Howard :yuck:) also recognized zero point energy and took account of it in their calculations.
Unbeknownst to many is the fact that it was first experimentally detected in the vibrational spectra of diatomic molecules by a physical chemist named Robert Mullikan; (I think it was in mid or late 1920's). [This is not the same as the Robert Millikan who measured the electron charge to mass ratio - notice the difference in spelling).

Later (1947) Willis Lamb (and Rutherford) discovered the 'Lamb shift' in the Hydrogen spectrum, which can also be considered direct exp. confirmation of zero point vacuum fluctuations.
There are other exper. validations also, Casimir, etc.

OK... If the gravitational acceleration has an Unruh temperature, then... what reference frame is the gravitational field being compared to?

I guess the usual,.... the Minkowski (flat space time) frame.
Maybe I missed the point of the question.