# Gravity/acceleration equivalent?

JesseM
ubavontuba said:
No refunds! :rofl:

Besides, technically the structure is important to the experiment. It is the key to the fundamental difference between gravity and acceleration, that I am exploiting.

Remember, I said it was a "loophole," not a "fundamental discovery."

This loophole is applicable on all sorts of scales though. Therefore it really is a fundamental difference (even if it's not a paradigm changing consideration).

Frankly, I'm surprised that Einstein didn't address it. Apparently it didn't occur to him (or anyone else?) in regards to his paper... or he didn't think it worthy of mention.
Well, the fundamental form of the equivalence principle is all about freefalling frames in GR being compared to inertial frames in SR, and in both cases no external structure is needed. But like I said, if you can imagine a smaller box inside your inertial/freefalling box, which accelerates/stays at rest in a gravitational field using some structure external to itself but internal to the larger box (say, using rockets on its bottom), then it's a trivial extension of the "everything must look the same inside an inertial/freefalling box" principle to show that everything must look the same inside these smaller boxes (since they are part of the inside of the larger boxes, both accelerating towards the ceiling at the same rate and in the same way). But the principle of equivalence is really fundamentally about comparing the freefalling frame to the inertial frame, it only says that the at-rest-in-a-gravitational field lab must be equivalent to the accelerating-in-space lab to the extent that you can show why this follows from the freefalling/inertial equivalence.

Of course, the larger freefalling box need not have actual physical walls, it's just supposed to be a local region moving along with freefalling objects, so you can imagine falling past something like a smaller box on a rope attached to a crane and drawing an imaginary box around you as you fall. But then you'd have to ignore everything outside the imaginary freefalling box, and fix the boundary conditions on the imaginary walls, and then reproduce those same boundary conditions on the imaginary walls of an imaginary inertial box moving past an accelerating box-on-a-crane in empty space. So however the shaking of the small box (due to a tiny gnome inside dancing around, perhaps) affects the parts of the crane on the boundary of the freefalling box, you have to make sure the parts of the accelerating crane on the boundary of the inertial box are moving in exactly the same way. One way to do this would might be to imagine attaching the crane to an object of equal inertial mass as the earth but ignore the gravitational effects of this mass as I suggested, another way would be to have thrusters on the sides of the crane on the portions outside the imaginary box which insure that the parts of the crane on the boundary move the same way as in the gravitational field. As long as you fix those boundary conditions, everything that happens inside the imaginary box should look the same whether the box is freefalling past a crane attached to the earth or whether it's moving inertially past a similar crane that's accelerating in empty space.

F. J. M. Farley, J. Bailey, R. C. A. Brown, M. Giesch, H. J¨ostlein, S. van der Meer, E. Picasso and M. Tannenbaum, Nuovo Cimento 45, 281-286 (1966), "The anomolous magnetic moment of the negative muon"

Above, they measured muon decay under many thousands of "G" from acceleration in a storage ring and there were no time effects unlike well-known decay rates of muons from the upper atmosphere. This, in my opinion, breaks equivelence. Below are more related studies I haven't been able to review yet though...

Bailey, J., Borer, K., Combley, F., Drumm, H., Eck, C., Farley, F.J.M., Field, J.H., Flegel, W., Hattersley, P.M., Krienen, F., Lange, F., Lebée, G., McMillan, E., Petrucci, G., Picasso, E., Rúnolfsson, O., von Rüden, W., Williams, R.W., and Wojcicki, S., “Final report on the CERN muon storage ring including the anomalous magnetic moment and the electric dipole moment of the muon, and a direct test of relativistic time dilation”, Nucl. Phys. B, 150, 1-75, (1979).

Carey, R.M. et al., “New Measurement of the Anomalous Magnetic Moment of the Positive Muon”, Phys. Rev. Lett., 82, 1632-1635, (1999).

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.

ubavontuba said:
Forum,

How to Test for Gravity in the Equivalence Thought Experiment

Let's examine one of the most basic tenants of relativity... that being the equivalence principal.

...
Remember, Einstein's equivalence principal states that I shouldn't be able to tell by using any experiment in the room. I'd have to look outside to tell. Here goes:
...
To accomplish my feat, I need some very specialized equipment.
....
I need a snifter of brandy (make it full to the brim) and myself.

Let's proceed:

Step 1. Drink half the brandy. "Ah... good stuff."

Step 2. Place brandy snifter on the floor, but to the side a bit.

Step 3. Begin leaping laterally (from side to side) in the room.

Step 4. Observe the brandy.

Step 5. Start leaping from side to side. Build up as much pendulum acceleration as you can (swing the room like a child on a swing). Stop. Does the room continue swaying normally? Then you are hanging over a heavy mass and are experiencing gravity. If it stops rather suddenly, or it has an unusual and increasing resonance, then you are accelerating (Oh no! It's gone out of control!). In the latter case, disaster is soon to follow.

You can qualify things by adding shock absorbers and whatnot to a suspended room or make the accelerating room's ship unusually massive, but this just defeats the spirit of the experiment and makes it so in that particular room it is hard to distinguish between gravity and acceleration. This wouldn't be applicable to a supposedly universal principal.

Hi ubavontuba,

Why don't you call a demolition unit to blow up the "damn" room, while keeping your eyes closed? Then, you should keep your promise not to look outside of the room and at the same time you would find out the status of the room. .

Now that's what I call "explosive" science, my friend. :rofl:

Leandros

pervect
Staff Emeritus
TheAntiRelative said:
F. J. M. Farley, J. Bailey, R. C. A. Brown, M. Giesch, H. J¨ostlein, S. van der Meer, E. Picasso and M. Tannenbaum, Nuovo Cimento 45, 281-286 (1966), "The anomolous magnetic moment of the negative muon"

Above, they measured muon decay under many thousands of "G" from acceleration in a storage ring and there were no time effects unlike well-known decay rates of muons from the upper atmosphere. This, in my opinion, breaks equivelence. Below are more related studies I haven't been able to review yet though...

Right now, I have no idea of what you believe the problem is.

The lifetime of a muon in its rest frame is 1.56 us
http://hyperphysics.phy-astr.gsu.edu/HBASE/relativ/muon.html

http://www.g-2.bnl.gov/hepex0401008.pdf
tells us that the lifetime of a muon is 64.4 us with a momentum of 3.09 Gev/c under the conditions when it's magnetic moment is measured.

So there is *significant* time dilation, as one would expect. However, this time dilation will be entirely due to the velocity of the muon, not the acceleration of the muon:

dtau^2 = dt^2 - dx^2, the flat space formula for the Lorentz interval, implies that

(dtau/dt)^2 = 1 - (dx/dt)^2

Thus in the laboratory frame, there is no time dilation effect from the acceleration of the muon, only from its velocity.

I probably just don't understand the context...

I was under the impression that there were time effects from gravitation alone and that there were well known in regards to muon decay. The SR effects are there and are exactly as predicted, but any GR time effects that one might incorrectly intuitively assume should be there are not.

Basically it comes down to that a gravitational field has depth whereas acceleration really only has intensity. This seems like a difference to me. Not a difference that changes anything fundamental, just simply a difference.

Because you can use something like this test to measure your depth in a gravitational field, it is distinguishable from acceleration. Hence my assertion that the whole elevator test fails and equivelency is approximate, not exact.

I'm trying my best to understand what you might have thought I was saying but I can't see any other way to interpret it. It's as simple as saying there are time effects that occur in gravitation that simply do not in acceleration. Is that not an inequivalence or am I missing something fundamental?

JesseM
TheAntiRelative said:
I'm trying my best to understand what you might have thought I was saying but I can't see any other way to interpret it. It's as simple as saying there are time effects that occur in gravitation that simply do not in acceleration. Is that not an inequivalence or am I missing something fundamental?
Unless these time effects from gravity would be observable in an arbitrarily small region of spacetime, this cannot count as a violation of the equivalence principle. For example, gravitational time dilation effects that depend on different clocks being at substantially different distances from the source of the gravitational field couldn't be reproduced in such a small neighborhood, so they wouldn't qualify.

JesseM
Also, you might find this answer from the Physics FAQ on John Baez's site helpful:

Does a clock's acceleration affect its timing rate?

And actually, I guess I was wrong that gravitational time dilation effects from being at different heights in the gravitational field can't be explained using the equivalence principle, because in one section of this answer they write:
But what about the Equivalence Principle?

Sometimes people say "But if a clock's rate isn't affected by its acceleration, doesn't that mean the Equivalence Principle comes out wrong? If the Equivalence Principle says that a gravitational field is akin to acceleration, shouldn't that imply that a clock isn't affected by a gravitational field, even though the textbooks say it is?"

No, the Equivalence Principle is fine. Again, the confusion here is the same sort of thing as above where we spoke about the wind chill factor. Let's try to see what is happening. Imagine we have a rocket with no fuel. It sits on the launch pad with two occupants, a couple of astronauts who can't see outside and who believe that they are accelerating at 1 g in deep space, far from any gravity.

One of the astronauts sits at the base of the rocket, with the other at its top, and they both send a light beam to each other. Now, general relativity tells us that light loses energy as it climbs up a gravitational field, so we know that the top astronaut will see a redshifted signal. Likewise, the bottom astronaut will see a blueshifted signal, because the light coming down has fallen down the gravitational field and gained some energy en route.

How do the astronauts describe what is going on? They believe they're accelerating in deep space. The top astronaut reasons "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!" The bottom astronaut reasons very similarly: "By the time the light from the top astronaut reaches me, I'll have picked up some speed, so that I'll be approaching the light at a higher rate than previously as I receive it. So it should be blueshifted--and yes, so it is!"

As you can see, they both got the right answer, care of the Equivalence Principle. But their analysis only used their speed, not their acceleration as such. So just like our wind chill factor above, applying the Equivalence Principle to the case of the rocket doesn't depend on acceleration per se, but it does depend on the result of acceleration: changing speeds!
edit: on second thought, is light redshifted because of a change in the strength of a gravitational field, or would it be redshifted even in a constant-gravity field? If the latter, then my comment about not worrying about effects that depend on different gravitational strengths at different distances from the source could still be right.

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JesseM said:
Unless these time effects from gravity would be observable in an arbitrarily small region of spacetime, this cannot count as a violation of the equivalence principle. For example, gravitational time dilation effects that depend on different clocks being at substantially different distances from the source of the gravitational field couldn't be reproduced in such a small neighborhood, so they wouldn't qualify.

Ok. Yeah, I see what you are saying.

Acceleration causes no time dilation is the point that the experiment proved. Gravity does. While that doesn't specifically fit with the thought experiment's criteria because of the need to communicate at a distance, there's still a difference between acceleration and gravity.

I guess the communication with a GPS satellite or some such was just kinda happening in my head without me noticing I glossed over that requirement.

JesseM said:
It's not fantasizing new laws of physics, it's simply subtracting out GR and imagining a universe where SR holds exactly. That's what the equivalence principle is all about, that locally a freefalling frame in GR is exactly like an inertial frame in SR.

Sure, but This isn't how Einstein wrote it in that paper I referenced. However, he dismissed the framework that is accelerating as being unimportant. I suspect he imagined it as being quite fixed in its trajectory in all dimensions. That is, it couldn't be steered, nor would it suffer acceleration differentials, like from jumping up and down (another test method I hadn't mentioned).

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.

In any case, you could always imagine the crane had thrusters or something so that it would be just as resistant to sideways acceleration as a crane sitting on the earth. And if you keep the box above the earth in a way that does not allow its movements to push or pull on the earth--say, by rockets attached to the bottom of the box--then you don't have to worry about the inertia of the earth. But if the box is attached to the earth in such a way that momentum applied to the box internally (by punching the wall, say) is dispersed into the earth, then it's no good to imagine a situation in space where the momentum is dispersed into a mass much less resistant to acceleration than the earth, these are non-equivalent physical situations just as much as if you imagine the box accelerated from the bottom through space but held up from the top on earth.

Even with lateral thrusters, I could still tell. However, if you isolate the room like in your free-floating rocket powered box, I don't think I could tell.

Truly isolating the room is the key. By "hanging" the room I'm sure he was attempting a form of isolation, but it still isn't true isolation.

Interestingly, Einstein's concept remains sound even though the thought experiment as he'd written it, fails under certain test conditions.

JesseM
ubavontuba said:
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.
ubavontuba said:
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?
ubavontuba said:
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.

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pervect
Staff Emeritus
There is no gravity in an inertial frame, therfore 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.

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

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JesseM said:
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 wich 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
ubavontuba said:
I was referring to the case where the room still hangs and swings freely, but the accelerating frame from wich 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.
ubavontuba said:
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.
JesseM said:
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.
ubavontuba said:
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.
ubavontuba said:
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?
ubavontuba said:
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').

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.

JesseM said:
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."

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?

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Creator said:
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 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?

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"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.

Ich
TheAntiRelative said:
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.

Ich said:
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?

pervect said:
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
Staff Emeritus
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
ubavontuba said:
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."

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.
JesseM said:
I'm pretty confident that you couldn't. If you think you could, how would you do it?
ubavontuba said:
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?
JesseM said:
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 said:
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".
ubavontuba said:
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.
ubavontuba said:
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.
ubavontuba said:
"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.

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pervect said:
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
Staff Emeritus
TheAntiRelative said:
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.

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