Gravity/acceleration equivalent? [Archive]

JesseM

Feb1-06, 02:11 AM

So if I can really do this, it would really be important? Yes. As this page (http://aether.lbl.gov/www/science/equiv.html) says: 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. Or as this page (http://scholar.uwinnipeg.ca/courses/38/4500.6-001/Cosmology/Principle%20of%20Equivalence%20in%20Mathematical%2 0Form.htm) puts it: General relativity yields the special theory of relativity as an approximation consistent with the Principle of Equivalence. If we focus our attention on a small enough region of spacetime, that region of spacetime can be considered to have no curvature and hence no gravity. Although we cannot transform away the gravitational field globally, we can get closer and closer to an ideal inertial reference frame if we make the laboratory become smaller and smaller in spacetime volume. In a freely falling (non-rotating) laboratory occupying a small region of spacetime, the laws of physics are the laws of special relativity. Hence all special relativity equations can be expected to work in this small segment of spacetime. So, a violation of this would certainly be important, although the fact that thousands of smart physicists have studied the issue and found no reason to doubt the equivalence principle should lead you to suspect there is very likely a flaw in your idea.

JesseM

Feb1-06, 02:13 AM

Even if your room was very small if you let enough time go by there would be a tidal effect which you could observe. Although I think this would only apply in the freefalling (or extremely low acceleration) case, since if you were accelerating at any decent rate your test particles would hit the floor of your box before you noticed any tidal effects. How would these tidal effects manifest in the freefalling case, for a very small room falling for an extended period of time?

ubavontuba

Feb1-06, 02:56 AM

JesseM et al,

I need to make it clear that I'm referring to the hanging room case as per this paper (http://www.bartleby.com/173/20.html) written by Albert Einstein. I'm not saying I can make this determination in a free-falling room in space versus a free-falling room in a gravity field ("Except for the splat at the end... they're practically similar" -Tigger). Would this still be important?

I feel I should forewarn you that this concept really works, but it's also a bit mischevious. That is; I have found a loophole to the conundrum, but I don't think it has a lot of practical considerations.

Edit: I wish to add that I will start out with a simple and rather silly version of the test. You will then likely wish to qualify the experiment, so I strongly recommend you satisfy your qualifications now to the best of your abilities. I will accept later qualifications, but only if it is conceded that my first experiment works under the current treatise.

Any qualifications you make will be examined for merit and depending on their limiting factors I will refine the experimental concept to compensate. If the restrictions get severe, I may need to ascertain that the measurements are purely hypothetical (as they may be very small) and have this still be accepted as valid. Of course, this will only be in response to restrictions that are not specified in the Einstein paper.

Is everyone in accordance? Are you ready for the silliness to begin?

dicerandom

Feb1-06, 03:08 AM

How would these tidal effects manifest in the freefalling case, for a very small room falling for an extended period of time?

The test particles would slowly seperate from one another due to the extremely minute difference in the gravitational force (or geodesics, if you prefer) due to their differing heights above the planet. Even with a very small room this effect would become evident given enough time, provided you don't hit the ground first. This seperation would not occur in the flat space room.

JesseM et al,

I need to make it clear that I'm referring to the hanging room case as per this paper (http://www.bartleby.com/173/20.html) written by Albert Einstein. I'm not saying I can make this determination in a free-falling room in space versus a room free-falling in a gravity field ("Except for the splat at the end... they're practically similar" -Tigger). Would this still be important?

I feel I should forewarn you that this concept really works, but it's also a bit mischevious. That is; I have found a loophole to the conundrum, but I don't think it has a lot of practical considerations.

Well don't keep us in suspense, let's hear it :wink:

JesseM

Feb1-06, 10:46 AM

JesseM et al,

I need to make it clear that I'm referring to the hanging room case as per this paper (http://www.bartleby.com/173/20.html) written by Albert Einstein. I'm not saying I can make this determination in a free-falling room in space versus a free-falling room in a gravity field ("Except for the splat at the end... they're practically similar" -Tigger). Would this still be important? I don't think it should matter--after all, a hanging room as seen by a freefalling observer passing it should look just like an accelerating room as seen by an inertial observer passing it. You could even imagine a small room in a box inside a freefalling lab, with the box using rockets to maintain a constant distance from the earth even as the lab falls so the box approaches the lab's ceiling--this should appear just like a small room-in-a-box inside an inertial lab in deep space using rockets to accelerate in the direction of the lab's ceiling. I feel I should forewarn you that this concept really works, but it's also a bit mischevious. That is; I have found a loophole to the conundrum, but I don't think it has a lot of practical considerations. Again, the fact that this would violate such a basic principle should lead you to have some doubts about whether you have actually found such a loophole, I think. But anyway, let's hear it! Edit: I wish to add that I will start out with a simple and rather silly version of the test. You will then likely wish to qualify the experiment, so I strongly recommend you satisfy your qualifications now to the best of your abilities. I will accept later qualifications, but only if it is conceded that my first experiment works under the current treatise. OK, the best way I can put it is that if you compare the hanging room and the accelerating room, for any small but finite room over a finite time there will be some slight differences, but in the limit as the volume and time approach zero, the magnitude of these differences should also approach zero. I'd be very surprised if you could find something that violates this.

pervect

Feb1-06, 01:45 PM

Forum,

Okay, so Einstein says that to an internal observer a room being pulled under a constant 1g acceleration is indistinguishable (by experiment) from a room hanging from a tree by a rope.

Putting gravitational divergence aside, do you think this is true?

If I (as an inside observer) can demonstrate by internal experiment that the room is either accelerating or is at rest in a gravitational field, would this be important?

The tidal forces (aka Riemann curvature tensor) are different for the observer in the room and the observer standing on a spherical planet.

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

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

Even with a finite disk rather than an infinite one, the supression of tidal forces should be good (but not perfect).

rbj

Feb1-06, 02:47 PM

You could even imagine a small room in a box inside a freefalling lab, with the box using rockets to maintain a constant distance from the earth even as the lab falls so the box approaches the lab's ceiling--this should appear just like a small room-in-a-box inside an inertial lab in deep space using rockets to accelerate in the direction of the lab's ceiling.

:cool: I had never heard that version of the EP thought experiment. (only the two basic ones, accelerating room in space vs. one sitting on the planet and free-falling room vs. one drifting freely in outer space, and in both comparisons what light or other free objects would be observed to do.) thanks for bringing it up.

JesseM

Feb1-06, 04:49 PM

:cool: I had never heard that version of the EP thought experiment. (only the two basic ones, accelerating room in space vs. one sitting on the planet and free-falling room vs. one drifting freely in outer space, and in both comparisons what light or other free objects would be observed to do.) thanks for bringing it up. I just made that thought-experiment up, to illustrate why it seems to me that the equivalence of free-falling frames and inertial frames would automatically imply the equivalence of an accelerating frame and a frame at rest relative to a gravitational field.

yogi

Feb1-06, 06:47 PM

OK ubavontuba - Lets hear the revelation

rbj

Feb1-06, 07:54 PM

I just made that thought-experiment up, to illustrate why it seems to me that the equivalence of free-falling frames and inertial frames would automatically imply the equivalence of an accelerating frame and a frame at rest relative to a gravitational field.

well, it's a good one. i'll have to remember to credit "JesseM" if i ever use it.

ubavontuba

Feb1-06, 08:02 PM

Forum,

Okay. Beginning with the treatise that the room is either hanging from an earthbound structure or an accelerating vehicle, I'd like to clarify one important aspect. That being that other than the fact that constant acceleration at the stated rate is currently impossible, all structures and systems obey all currently known laws of physics and that the structures are of reasonable parameters for either condition. Is this agreeable?

The occupant begins by being completely unaware of the conditions of the room and he must perform all tests within the room. He cannot look outside (through a window or some such). Nor may he use devices that can perceive exterior conditions directly through the walls (like an X-ray observatory).

Also, all effects of divergence are disallowed. That meaning that I will not fall on the effects of divergence as being a method to test for gravity (including tidal effects).

Lastly, I will reitterate that this is not meant to be a serious examinination of equivalence. Rather this is simply an exercise in creative thinking. Enjoy!

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.

The equivalence principal basically states that it is impossible in a sealed room to conduct an experiment that could distinguish the difference between gravity and constant acceleration.

Of course there is spherical divergence to consider (immeasureably small), but let's place that aside for now and look at this in a more fundamental way.

Let's say I am in a sealed, hanging room (you'd like that, wouldn't you?) and that I want to find out if my room is part of an accelerating rocketship, or is situated comfortably on Earth. How might I easily determine this? Let's make this even harder by stipulating that initially, I don't even know that the room is hanging, or floating, or stable, or whatever.

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.

If the brandy sloshes, I am in a relatively low mass room and therefore must be accelerating, or at least be separated from the Earth (suspended). If sloshes, go to the next step. If not, then you are in a fixed room on a heavy mass. You are feeling gravity (end of experiment).

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.

Even so, you could still tell because a shock absorbed room must take time to settle (it's just quicker) Whereas an accelerating room and frame in free space is ALWAYS settled on it's center of mass (laterally) regardless of where you go in the room. The system will always stop moving laterally when you do. A massive room would just require more sensitive equipment.

Therefore, you can determine the difference between acceleration and gravity in a sealed room, right?

DaveC426913

Feb1-06, 08:32 PM

JesseM

Feb1-06, 09:31 PM

dicerandom

Feb1-06, 09:46 PM

I can jump up and down in my apartment and get a half-full snifter of brandy to slosh, it isn't built so well :wink:

Cute though.

ubavontuba

Feb1-06, 10:10 PM

You are trying to move the room. While technically not actually peeking out the window, you are still gleaning information about what is outside the room from within. You are not using the sensations of gravity or acceleration to do so. That's effectively cheating.

There are umpteen ways in practice to determine the difference, especially if you allow the sort of real-world engineering effects (such as the fact that the room can swing).

The effect holds in principle, if not in practice.

Too late! You didn't prequalify this.

Besides, the dichotomy of the experiment clearly states that no test conducted within the room might distinguish the difference. It is not qualified as in; no experiment except___ (fill in the blank) can tell.

It's a fundamental statement. It's not an; "He found a solution, so his solution can't count!" That's like kids saying, "Not it!" after they've been tagged already.

ubavontuba

Feb1-06, 10:18 PM

Actually, I disagree that your methods would even produce any different results depending on whether the box was being accelerated or held still in a gravitational field. It is crucial, though, that we assume the force on the box is coming from the same point in both cases--for example, if the box in earth gravity is being held up by a cable which is attached to a crane sitting on the surface of the earth, then we should assume the box in deep space is being pulled from a cable attached to its top which is attached to a crane which is being accelerated by a rocket whose inertia is just as great as the earth's (but assume in this case we are dealing only with the laws of SR so this rocket doesn't distort spacetime). Likewise, if the box is sitting on the top of the earth, then in the accelerating case it should be pushed from below by a rocket whose inertia is as great as the earth's. And if the box is being kept at a constant height from the earth by rockets attached to its bottom, then the box in space should be accelerating by means of identical rockets attached to its bottom. As long as we keep things analogous in this way, I don't think you would detect any difference in your brandy experiment.

Wait a minute! "whose inertia is just as great as the earth's... so this rocket doesn't distort spacetime!?" If we must fantasize away the fundamentals of physics to get the result we want, then I want to fantasize away the limitations of conservation so that we can have unlimited energy and while we're at it, let's imagine there is no cosmic speed limit either (warp drive!).

The experiment becomes invalid on a fundamental level... if it has no basis in physics to begin with. Einstein didn't prequalify it thusly (he merely dismissed the importance of the accelerating device).

ubavontuba

Feb1-06, 10:21 PM

I can jump up and down in my apartment and get a half-full snifter of brandy to slosh, it isn't built so well :wink:

Cute though.

Aha! A person of good cheer! That's the spirit!

yogi

Feb1-06, 10:36 PM

Shucks - thought we were going to get some new insight - we skeptics always look for wierd stuff - all you are doing is evaluating the structure - I want my money back

JesseM

Feb1-06, 10:52 PM

Wait a minute! "whose inertia is just as great as the earth's... so this rocket doesn't distort spacetime!?" If we must fantasize away the fundamentals of physics to get the result we want 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.

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.

ubavontuba

Feb1-06, 10:54 PM

Shucks - thought we were going to get some new insight - we skeptics always look for wierd stuff - all you are doing is evaluating the structure - I want my money back

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.

JesseM

Feb1-06, 11:58 PM

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.

TheAntiRelative

Feb2-06, 11:04 AM

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).

Mike2

Feb2-06, 11:06 AM

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.

leandros_p

Feb2-06, 11:28 AM

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. :biggrin:.

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

Leandros

pervect

Feb2-06, 01:18 PM

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.

TheAntiRelative

Feb2-06, 02:11 PM

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

Feb2-06, 02:24 PM

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

Feb2-06, 02:32 PM

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? (http://math.ucr.edu/home/baez/physics/Relativity/SR/clock.html)

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.

TheAntiRelative

Feb2-06, 05:09 PM

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.

ubavontuba

Feb2-06, 06:28 PM

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

Feb2-06, 08:47 PM

Sure, but This isn't how Einstein wrote it in that paper I referenced. Well, as you say, I think he was just talking about what an observer would detect in a steadily accelerating box in that paper. And I think a mathematical statement of the equivalence principle would probably just be in terms of the equivalence between freefalling and inertial frames (though I'm not sure of this), but physicists writing for a popular audience will often treat this and the sitting still in a gravitational field/accelerating in empty space thought-experiment as interchangeable. This is probably because, as I said earlier, the second one does follow directly from the first one if you impose the appropriate restrictions. However, if the accelerating framework was thusly fixed and it had less mass than the Earth, I can still think of an experiment that would determine acceleration versus gravity. You're saying that even if the box's motion cannot be affected from the inside, you think you could tell? How? Even with lateral thrusters, I could still tell. I'm pretty sure you couldn't, not if the lateral thrusters were programmed to make sure the parts of the structure on the boundary of the inertial observer's imaginary box responded in exactly the same way to motions of the physical box as the same structures would respond as they would on earth.

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

pervect

Feb2-06, 10:25 PM

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.

Creator

Feb2-06, 11:14 PM

ubavontuba

Feb3-06, 01:20 AM

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

Feb3-06, 02:07 AM

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. If you want the room to be still too, then let's compare it to a room that is fixed on the earth. In this case, I could tell (comparing apples with apples, you know). But if the room is fixed, how could you tell? Just to be clear, by "fixed" I mean it's impossible to move the room at all relative to the earth (including swinging it back and forth), and it's impossible to change the rate of acceleration of the room in space. I'm pretty sure you couldn't, not if the lateral thrusters were programmed to make sure the parts of the structure on the boundary of the inertial observer's imaginary box responded in exactly the same way to motions of the physical box as the same structures would respond as they would on earth. I'm not clear on what you mean here. Do you mean the room swings freely on earth and in the accelerating frame, but the accelerating framework's motion is fixed (self-compensates to maintain constant and straight acceleration)? Yes, in both cases I'm assuming the physical framework that the cable holding the room is attached to cannot be moved, but the room/cable can still swing around. In this case, I could still tell. I'm pretty confident that you couldn't. If you think you could, how would you do it? As you've suggested, the popular version that Albert Einstein wrote versus the theory, aren't necessarily quite the same. It appears to me that equivalence is still a perfectly valid concept in free-fall reference frames. It also seems valid in conditions that properly isolate the room in accelerating frames. He just failed to properly isolate the imaginary room.

I just find it very interesting that the master's own work in his own hand can be challenged succesfully (especially by a goof like me). Am I the first to realize this? Can anyone find any prior references? I wouldn't really regard this as a mistake on Einstein's part because the description seems to assume that the rate of acceleration of the room in space is constant (ie no swinging, which would involve changing sideways acceleration). From the paper (http://www.bartleby.com/173/20.html) you referenced: To the middle of the lid of the chest is fixed externally a hook with rope attached, and now a “being” (what kind of a being is immaterial to us) begins pulling at this with a constant force. The chest together with the observer then begin to move “upwards” with a uniformly accelerated motion. And likewise, it is assumed that the chest would be at rest in the gravitational field: Just then, however, he discovers the hook in the middle of the lid of the chest and the rope which is attached to it, and he consequently comes to the conclusion that the chest is suspended at rest in the gravitational field. He's saying that with these conditions, all experiments in the room will give the same results in the two situations; his description doesn't really say anything one way or another about experiments which change the basic conditions of his thought-experiment (and nowhere does he make any blanket statement like 'there is no experiment the man can do to determine whether he is really being pulled at an accelerating rate in empty space or hanging from a rope in a gravitational field').

ubavontuba

Feb3-06, 04:32 AM

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Mike2

Feb3-06, 07:59 AM

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

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

TheAntiRelative

Feb3-06, 10:12 AM

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

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

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

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

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

Ich

Feb3-06, 10:28 AM

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

TheAntiRelative

Feb3-06, 01:12 PM

That´s not true.

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

TheAntiRelative

Feb3-06, 01:47 PM

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

Feb3-06, 02:32 PM

JesseM

Feb3-06, 03:54 PM

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

Please note the term "constant force," not "steady rate." But you're ignoring the next sentence, which I highlighted: 'The chest together with the observer then begin to move “upwards” with a uniformly accelerated motion.' I would say this is part of the conditions of the thought-experiment he is describing, if you do something to cause the motion to no longer be 'uniformly accelerated' then you're describing a different thought-experiment. I'm pretty confident that you couldn't. If you think you could, how would you do it?Oh ye of little faith! Do you not remember how you thought I couldn't tell in the first place? Why do you doubt me now? (with apologies to my fellow Christians).o:)

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

Anyway, if you think I'm wrong, don't be coy--what's your experiment? He's saying that with these conditions, all experiments in the room will give the same results in the two situations; his description doesn't really say anything one way or another about experiments which change the basic conditions of his thought-experiment (and nowhere does he make any blanket statement like 'there is no experiment the man can do to determine whether he is really being pulled at an accelerating rate in empty space or hanging from a rope in a gravitational field') Yeah, but this statement kind of implies it:
"Relying on his knowledge of the gravitational field (as it was discussed in the preceding section), the man in the chest will thus come to the conclusion that he and the chest are in a gravitational field which is constant with regard to time." I don't think it implies it too strongly, in any case--he's still talking about what the man will include in the experiment as he describes it, which includes the idea that the chest is moving with a "uniformly accelerated motion". Also, you had earlier made this statement yourself and even referenced some papers in regards to it. The papers I referenced in post #6 only defined the equivalence principle in terms of the freefalling/inertial equivalence, though. Also, in your initial post you also suggested it was part of the conditions of the experiment that the room was 'being pulled under a constant 1g acceleration'--so if you allow experiments which cause the room to no longer accelerate at 1g, you're changing the conditions of the experiment. Finally, when you asked for qualifications I did say that I was justifying the at-rest-in-a-gravitational-field/accelerating-in-space equivalence in terms of the freefalling/inertial equivalence, using the "box-inside-a-larger-box" argument that I've been using frequently, in post #10. If you have a structure holding up the smaller box which cannot fit inside the freefalling/inertial observer's small imaginary box, and this structure would behave differently on earth vs. when accelerating in space, this argument breaks down.

I'm not saying you haven't hit on an interesting point though, what you show is that one needs to be careful about exactly how one states the equivalence between the observer at rest in a gravitational field and the observer accelerating in empty space. I'm sure you could find some authors who have not been careful enough, but I don't think Einstein is really guilty of this sort of mistake here. As the man in the box must obviously move about to perform the observations Einstein mentions, wouldn't the box tend to sway? Well, you can always make the idealization that the man's mass is very small compared to the mass of the chest. Anyway, it's a thought-experiment, so I think you're allowed to ignore practical complications like this. "Relying on his knowledge of the gravitational field," wouldn't a lack of normal swaying tell the observer that he shouldn't be too quick to jump to Einstein's conclusion? Aside from the fact that Einstein specified the box should be accelerating at a "uniform" rate, there would be swaying in space if you performed the same experiment that led to swaying on earth. What makes you think there wouldn't be? Conservation of sideways momentum should hold just as well in space as on earth (in both cases there is no external force being applied in the sideways direction), so if I jump sideways inside the chest, the chest itself will have to temporarily move a bit in the opposite direction to conserve total sideways momentum. Of course, as soon as I land on the floor again the swaying should stop, but this would be true on earth too if you were in a vacuum and the structure holding the cable was fixed and not able to move on its own.

TheAntiRelative

Feb3-06, 05:07 PM

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

Feb3-06, 05:34 PM

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

You're still missing the point :-(.

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

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

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

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

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

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

JesseM

Feb3-06, 06:21 PM

Because the Earth frame is effectively an inertial frame for the muon experiment, there is no gravitational time dilation in that frame. Why would the earth frame be considered effectively inertial? In the presence of gravity, isn't it only a freefall frame that can be considered equivalent to an inertial frame, while a frame at rest in the gravitational field is equivalent to an accelerating frame? Or are you just saying it's effectively inertial because earth's gravity is weak enough that gravitational time dilation effects would be negligible compared to velocity-based time dilation effects in this experiment?

ubavontuba

Feb3-06, 08:25 PM

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... :wink:

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.

JesseM

Feb3-06, 09:22 PM

Actually, I feel that you're taking this out of context. It seems to clearly imply to me that the total mass of the chest and the occupant are accelerating at a unifrom rate as a result of the constant force. Not that the uniform acceleration is constant regardless of the force. And I think they are both part of the conditions that he's describing, that the external force is constant and that the acceleration is constant (implying internal forces are considered negligible). However, the parameters of this experiment must be clearly understood by both of us, so that I don't accidently claim success (or failure) for the wrong experiment, applied to the wrong conditions. Please specify your conditions, but keep it relevent. That is, the conditions of the box on earth should match the conditions of the box under acceleration, save for the fact of acceleration. Also, the accelerating framework's physics must be described to a reasonable degree. I.e. does it keep it's uniform rate and latteral conditions with retro rockets? Is it a sort of elevator accelerating in a fixed framework/shaft? If the accelerating framework's properties are ignored (or made to be arbitrarily equivalent to gravity without defined rules), then we can state anything we want and therefore we might as well call it "magic." Well, the condition we were discussing was that the box and the cable can move around but the acceleration of the framework the cable is attached to can be considered negligible. You don't really need to introduce retro rockets to achieve this, just consider the limit as the mass of the box and cable becomes negligible compared to the mass of the framework (but keep the mass of the framework constant so you don't have to worry about its increasing mass curving spacetime enought to have a noticeable effect on the experiment).

One other simple solution that occurs to me is to assume the framework itself is capable of sliding without friction on the surface of the earth, so you don't have to worry about any of its sideways momentum being transferred to the earth and thus the inertia of the earth isn't relevant to the problem. In this case the acceleration of the framework doesn't need to be negligible, but it will be the same in both the at rest on earth case and the accelerating in space case.As I've said above, I disagree with this interpretation. However, I (by ""Relying on (my) knowledge of the gravitational field") would know that I'm not in gravity, even if Einstein's occupant is unable to make this determination. I'm not saying his occupant is stupid, but... But Einstein doesn't ever say that there is nothing the occupant could do to determine which is really the case (he could blow a hole in the side of the chest and look outside, for example). Given the conditions he sets, which includes uniform acceleration, any experiment the guy does in the accelerating box could just as easily be explained in terms of a gravitational field, that's the only point he's making. You are right about having to be careful in regards to modelling the principle. But I disagree with you in your assertion that Einstein was so careful. In my view, his theory has become widely accepted on its own merits in spite of his explanation (in this context). There is nothing in the quoted text that dignifies being called a "theory", it is simply an illustration of the equivalence of uniform acceleration and uniform gravity, which is part of his theory of general relativity. Well, you can always make the idealization that the man's mass is very small compared to the mass of the chest. Anyway, it's a thought-experiment, so I think you're allowed to ignore practical complications like this. I disagree. By ignoring the laws of physics while examining the laws of physics you endanger the outcome as being irrelevant. There is a big difference between "ignoring the laws of physics" and presenting idealized cases which would be valid approximations in certain limits. For example, it is common in illustrations of mechanics to assume zero friction even though this is impossible to 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. 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. Aside from the fact that Einstein specified the box should be accelerating at a "uniform" rate, there would be swaying in space if you performed the same experiment that led to swaying on earth. What makes you think there wouldn't be? Conservation of sideways momentum should hold just as well in space as on earth (in both cases there is no external force being applied in the sideways direction), so if I jump sideways inside the chest, the chest itself will have to temporarily move a bit in the opposite direction to conserve total sideways momentum. Of course, as soon as I land on the floor again the swaying should stop, but this would be true on earth too if you were in a vacuum and the structure holding the cable was fixed and not able to move on its own. My point here is that you coudn't swing it like a pendulum since this would disturb the center of mass for the system and would require a reactionary oscillation that isn't available in the accelerating system without unusual consequences. Well, in the ideal case you can't swing it like a pendulum on earth either, because without any external sideways force (assume the experiment is done in a vacuum chamber so there's force from the air) the center of mass should not be able to move in a sideways direction. But I suppose even an ordinary pendulum varies in its sideways momentum from the bottom of its arc to the top, and we know we can even change the size of our arcs on a playground swing by pumping our legs, so I guess this isn't very realistic. I'm actually not quite sure what the best explanation for this is, but if you imagine the pendulum swinging on a string which is looped around a rod sticking out of a wall, I think what's probably going on is that some of the pendulum's sideways momentum is being transferred to the rod (through the contact point between the loop of string and the rod) which in turn transfers it to the wall, which doesn't visibly move because its mass is so much larger. But there's no reason this should work much differently for a pendulum attached to a rod and wall which are accelerating in space than for one attached to a rod and a wall which is sitting on earth (and the slight difference due to the wall being attached to the earth itself can be eliminated by assuming the framework can slide on the surface earth without friction, as I suggested earlier...if the framework's mass is much larger than the pendulum's mass, this sliding wouldn't be noticeable anyway).

pervect

Feb4-06, 04:44 AM

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

There is some gravitational time dilation with height on Earth.

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

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

Creator

Feb4-06, 05:38 PM

... 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:biggrin:

ubavontuba

Feb4-06, 09:30 PM

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

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

ubavontuba

Feb4-06, 09:58 PM

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

Feb4-06, 11:59 PM

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. Well, the condition we were discussing was that the box and the cable can move around but the acceleration of the framework the cable is attached to can be considered negligible. You don't really need to introduce retro rockets to achieve this, just consider the limit as the mass of the box and cable becomes negligible compared to the mass of the framework (but keep the mass of the framework constant so you don't have to worry about its increasing mass curving spacetime enought to have a noticeable effect on the experiment). Naw, that's a bit vague. Even if the AF were fairly massive (like a battleship) the resonance of a swinging mass that could comfortably hold a man would tend to skew its trajectory. First of all, this is just an idealized limit, and since I specified that the mass of the framework was being held constant, it was implied that we are taking the limit as the mass of the man and box are becoming smaller and smaller (imagine using a series of smaller and smaller gnomes in smaller and smaller boxes).

But even if we want to be more practical, the swinging box isn't going to be able to shift the trajectory of the framework in any cumulative way because of conservation of sideways momentum, all it can do is shift the framework back and forth at the same rate the room is swinging back and forth. And how fast do you think the guy in the room is going to be able to get it swinging using resonance? I don't think there'd be any theoretical upper limit, but eventually it'd be going fast enough that the person won't be able to time the motions of his body to match the resonant frequency. If we plug in a number for a plausible maximum velocity of the box at the bottom of its arc, we can figure out the maximum velocity of the framework using conservation of momentum; if we also know the period of the box's swing, we can use this to figure out an upper limit on how far the framework can move back and forth. I would guess that if the box is assumed to have a mass of 200 kg and the framework is assumed to have the mass of a battleship (which according to this page (http://chemistry.umeche.maine.edu/~amar/fall2004/SigFigs.html) would be around 1.3 * 10^8 kg), then for a plausible maximum velocity the amount the battleship would move would probably be microscopic. One other simple solution that occurs to me is to assume the framework itself is capable of sliding without friction on the surface of the earth, so you don't have to worry about any of its sideways momentum being transferred to the earth and thus the inertia of the earth isn't relevant to the problem. In this case the acceleration of the framework doesn't need to be negligible, but it will be the same in both the at rest on earth case and the accelerating in space case. Actually, even in this scenario I could still hypothetically tell. This would simply be a matter of measuring how much I could tilt the 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. If the AF were rigidly held in its path by some means, I can even think of a hypothetical experiment to detect that.OK, what measurement would you make in this case? ...if the framework's mass is much larger than the pendulum's mass, this sliding wouldn't be noticeable anyway). Ah but it is still there in a hypothetical context and unless the mass were as big as the earth, it would be different than normal gravity and would therefore be hypothetically detectable. But see the point I made in the last post about approximations used in all of physics, like the assumption that objects can slide without friction or the assumption that the sun is the only body whose gravitational field affects the orbit of the earth.

ubavontuba

Feb5-06, 03:29 AM

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... :smile:

TheAntiRelative

Feb6-06, 09:19 AM

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

Feb6-06, 09:53 AM

JesseM,

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

What happens in this case is we start chipping away at the fundamental differences in an attempt to make the experiment fit the theory. We do this by applying restrictions that make the variances smaller and smaller until they become negligble to the point of only being hypothetical on a very small scale. They remain, but they diminish to the point of ambiguity. Well, I agree there will always be tiny differences, but they will go to zero in well-defined limits. You didn't really address my point about how virtually all thought-experiments in physics involve such idealizations that would be true in the limit, like objects sliding without friction. Not to mention the fact that the equivalence principle itself, even when stated in terms of freefall/inertial equivalence, depends on taking the limit as the size of the region of spacetime you're looking at goes to zero--for any small but finite-sized room, you will be able to tell the difference by looking at tidal forces. So what's the difference between this and the kind of differences you're talking about, which also disappear in the limit (in this case, the limit as box becomes arbitrarily light compared to the framework)? Would you say it is a problem that tidal forces "remain, but they diminish to the point of ambiguity"? In the friction free consideration, I could tell by measuring the mass with a kinetic energy experiment. If the AF were sufficiently small, it couldn't absorb a lot of kinetic energy without ringing like a bell. Basically, I need but strike the floor with a sledgehammer. Well, my main response is the one above, but at the risk of getting sidetracked from the main issue again, you said you had an experiment that could determine even in the case where the framework had thrusters to compensate for its motions--what if the thrusters were hooked into sensors which could detect waves of movement 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.

ubavontuba

Feb6-06, 12:45 PM

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.

LightStorm

Feb14-06, 04:00 AM

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

Principle of equivalence

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

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

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

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

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

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

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

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

jtbell

Feb14-06, 10:30 AM

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 (http://www.physicsforums.com/showthread.php?t=17355). If you want to argue about the validity of relativity, there are other places where you can do that, e.g. sci.physics.relativity (http://groups.google.com/group/sci.physics.relativity).

JesseM

Feb14-06, 05:21 PM

Relativists then claim that the principle applies only to very small reference frames where gravity is more or less uniform. But if we have a very sensitive weight measure device (accelerometer) then one can still distinguish between acceleration and a gravity field. By "very small" they mean "in the limit as the size of the spacetime region approaches zero". In this limit, the difference in gravity between different heights inside the box would also approach zero.

rbj

Feb14-06, 10:42 PM

this guy completely misses the point.

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

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

...

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

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

.
.
.

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

ubavontuba

Feb15-06, 01:23 AM

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).

LightStorm

Feb15-06, 01:46 AM

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.

LightStorm

Feb15-06, 01:55 AM

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

Feb15-06, 02:07 AM

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?

LightStorm

Feb15-06, 02:19 AM

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.

JesseM

Feb15-06, 02:50 AM

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 (http://aether.lbl.gov/www/science/equiv.html): 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 this page (http://scholar.uwinnipeg.ca/courses/38/4500.6-001/Cosmology/Principle%20of%20Equivalence%20in%20Mathematical%2 0Form.htm): 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. 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. 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).

Mike2

Feb15-06, 11:01 AM

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

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

Creator:biggrin:
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.

rbj

Feb15-06, 11:32 AM

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.

Creator

Feb16-06, 12:54 AM

Hello, Mike.

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.

Let me be a bit more explicit about my previous answer which apparently escaped your attention.
The differences between Unruh radiation and Hawking radiation near a BH in effect may be considered an EP violation; i.e., the Unruh radiation from acceleration will appear different from that of Hawking rad. due to a gravitational field. So you were on the right track if you were trying to look for an apparent EP violation here.

This link gives the type of conundrum that can arise by trying to apply Equivalence Principle here.
http://www.lns.cornell.edu/spr/2000-05/msg0024778.html

Creator:biggrin:

pervect

Feb16-06, 03:04 AM

LightStorm

Feb16-06, 04:44 AM

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.

LS: What is wrong with the definition that I posted?

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,

LS: My point exactly. There are no uniform gravitational fields in this universe. To claim gravity and acceleration are equivalent is unrealistic. Any observer in any given reference frame can distinguish between the effects of real gravity and uniform acceleration.

I dont deny that gravitational and inertial mass are equivalent. All I'm sayng is an observer can observe/tell/measure/distinguish between the effects of gravity and uniform acceleration. If you ask me how, all it takes is a sensitive weight measuring device. The more precise the device the more easy it is to tell the difference between an accelerating frame and a frame in a real gravity field.

LightStorm

Feb16-06, 05:15 AM

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

LS: Infinite plane of mass? Hehehe I dont know. I am not sure how to deal with an infinite quantity. Everything is infinity is guess. I dont know what the nature of the field would be.

But it is an observed fact that at least in this universe gravity is a gradient and is never uniform in any given reference frame.

you are citing the different strengths of the gravitational field in such a geometry as your "proof" that the EP is wrong.

LS: I am citing something that is true. The field is not uniform in this universe.

so i changed the geometry to one where the strength of the graviational field does not change with distance.

LS: In this universe it has been observed that gravitational field does 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.

LS: In this universe gravity is a gradient. Maybe your argument would hold in a different universe where infinite quantities rule. Not in this universe.

jtbell

Feb16-06, 09:15 AM

It seems to me that you are merely arguing against the imprecise statements of the equivalence principle that appear in pop-sci books and even some introductory physics textbooks. Nobody here disputes that gravitation has effects (e.g. tidal effects) that cannot be mimicked by accelerated reference frames. A precise statement of the equivalence principle such as the ones JesseM quoted, allows for those effects.

rbj

Feb16-06, 10:59 AM

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

You'd better tell him, I doubt he realizes that the gravitational field at the axis of a large disk does not vary with height until the height is >> radius.

i'm not going to bother. the guy certainly has not had 2 semesters of physics (or, if he has, he hasn't brought away from it what he should have been exposed to).

This makes the gravitational field of such a disk essentially constant. It also means that "real" gravitational fields from such a disk do mimic the gravitational fields of an accelerating rocket, including the fact that losely speaking, gravity doesn't change with height. (I'm cutting a few corners here, deliberately, considering my best guess of Lighstorm's level of physics understanding, but I'm not cutting any corners when I say that the gravitational field / metric of a large plane is identical to that of an accelerating spaceship).

but LS doesn't care. he has his instruments of infinite precision and can detect the difference in graviational field from a finite disk (or planet), no matter what the finite size. he has already convinced himself that he's smarter than Einstein and, say, the thousands of physicists that understand and affirm SR and GR.

It is simply physically difficult (though not impossible in principle) to build a large enough disk to mimic the field configuration (including invariance with height) of a rocket - not impossible as Lighstorm seems to think.

But the whole objection was really poorly motivated in the first place, it was basically missing the point.

that's what i was saying. he misses the point. he blames this discrepency of geometry on physical principle (thus giving him an excuse to reject the physical principle) and when i take that discrepency away (by introducing a hypothetical gravitational field one would get from an infinite plane of mass) he doesn't get it. we've seen kooks like that around other times and places.

In Newtonian physics, we have two sorts of mass - inertial and gravitational. There is no explanation for why they are the same.

The whole point of the equivalence principle is to assume that inertial mass and gravitational mass are fundamentally related, and that the equivalence between gravitational mass and inertial mass is not an accident.

That's the broad picture, the quibbling about the details is missing the point, rather like being unable to see the forest for the trees.

I've personally become somewhat jaundiced about arguing with people with an axe to grind against relativity. I've found it much more useful to talk to people who are actually interested in learning the theory.

i think i am there, too.

Mike2

Feb16-06, 11:27 AM

The differences between Unruh radiation and Hawking radiation near a BH in effect may be considered an EP violation; i.e., the Unruh radiation from acceleration will appear different from that of Hawking rad. due to a gravitational field. So you were on the right track if you were trying to look for an apparent EP violation here.
Creator:biggrin:
As I recall, you also confirmed my suspicion that the expansion of the universe was also an acceleration that had an Unruh particle creation effect to it. I wonder if this is the mechanism of particle creation during inflation, nevermind Higgs particles.

Anyway, if there is this Unruh radiation/ particle creation due to the expansion of the universe, then I have to wonder at that point how does one calculate the Unruh temperature? For every point of space is accelerating differently with respect to different distances. So do all the different accelerations/temperatures calculated from all the different reference points all add up? And would this temperature from expansion then result in a energy density equivalent to the cosmological constant? Thanks.

JesseM

Feb16-06, 12:29 PM

LS: What is wrong with the definition that I posted? It's not wrong, it's just too specific to qualify as a general definition of the equivalence principle--it only deals with the case of a uniform gravitational field. The two definitions I posted work for arbitrary gravitational fields--do you think anything is wrong with those definitions? 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,

LS: My point exactly. There are no uniform gravitational fields in this universe. To claim gravity and acceleration are equivalent is unrealistic. Not if you use the more general definitions I provided, which don't require the gravitational field to be uniform.

LightStorm

Feb17-06, 04:59 AM

the guy certainly has not had 2 semesters of physics (or, if he has, he hasn't brought away from it what he should have been exposed to).

LS: You are right. I am a student. Starting to learn a few things these days.

he has his instruments of infinite precision

LS: I have read sites that claim the principle has been verified to very high levels of accuracy and precision. Like this one here:

http://www.absoluteastronomy.com/reference/equivalence_principle

difference is less than 1 part in a trillion (trillion: The number that is represented as a one followed by 12 zeros) (most accurate to date)

If I use a weight measuring device that can be accurate enough to identify a difference of 1 part in a trillion, surely every observer can tell/observe/distinguish between the effects of a real field and uniform acceleration.

he has already convinced himself that he's smarter than Einstein and, say, the thousands of physicists that understand and affirm SR and GR.

LS: You are making stuff up.

he misses the point. he blames this discrepency of geometry on physical principle (thus giving him an excuse to reject the physical principle)

LS: I have a valid thought experiment as an excuse which can be verified experimentally. You are blaming the universe for having only non-uniform gravitational fields. You cant have everything your way. This universe has NO uniform gravitational fields. Period.

and when i take that discrepency away (by introducing a hypothetical gravitational field one would get from an infinite plane of mass) he doesn't get it.

LS: This universe has no uniform gravitational fields and you dont get it.

LightStorm

Feb17-06, 05:41 AM

It's not wrong, it's just too specific to qualify as a general definition of the equivalence principle--it only deals with the case of a uniform gravitational field.

LS: That is the correct definition because it doesnt use ciruclar logic.

The two definitions I posted work for arbitrary gravitational fields--do you think anything is wrong with those definitions?

LS: Yes they use circular logic.

http://en.wikipedia.org/wiki/Petitio_principii

In logic, begging the question is the term for a type of fallacy occurring in deductive reasoning in which the proposition to be proved is assumed implicitly or explicitly in one of the premises. For an example of this, consider the following argument: "Politicians cannot be trusted. Only an untrustworthy person would run for office; the fact that politicians are untrustworthy is proof of this. Therefore politicians cannot be trusted." Such an argument is fallacious, because it relies upon its own proposition, in this case, "politicians are untrustworthy", in order to support its central premise. Essentially, the argument assumes that its central point is already proven, and uses this in support of itself; the question remains, "begging" to be answered.

Begging the question is also known as petitio principii, and is related to the fallacy known as circular argument, circulus in probando, vicious circle or circular reasoning.

Not if you use the more general definitions I provided, which don't require the gravitational field to be uniform.

LS: See above.

I dont deny that gravitational mass and inertial mass are equivalent. This equivalence is the reason why all objects on this planet free fall at the same rate. (Newtonian Equivalence.)

All objects of differing masses fall at the same rate droppped from a given height and touch down simultaneously regardless of the size of the reference frame on this earth. And this has been verified. This is Newtonian Equivalence.

Newtonain equivalence works for all sized reference frames, from the really small to the reall really big. It works for a small tower or a really really big tower. The objects always touch down simultaneously. There are no reference frames on this earth where Newtonain equivalence becomes invalid.

But Einstein's equivalence is unrealistic. It not only claims the entire reference frames are equivalent but also includes the various experiments performed in it. And this is not true as seen in my thought experiment.

HallsofIvy

Feb17-06, 06:29 AM

We're still waiting!

rbj

Feb17-06, 09:49 AM

the guy certainly has not had 2 semesters of physics (or, if he has, he hasn't brought away from it what he should have been exposed to).

LS: You are right. I am a student. Starting to learn a few things these days.

well 35 years ago when i was taking my first Drivers Ed. class, about the first thing the teacher said to the class was that "the first mistake of a bad driver is thinking he's a good driver."

if you're a student, you need to position yourself to learn or it's all for naught.

LS: I have a valid thought experiment as an excuse which can be verified experimentally. You are blaming the universe for having only non-uniform gravitational fields. You cant have everything your way. This universe has NO uniform gravitational fields. Period.

"Period." is indicative of an unwillingness to learn anything. you have all of the answers and no need to open your mind.

i am not blaming the universe for anything. the premise of the Einsteinian ER thought experiment is that of comparing a stationary room in a uniform graviational field to an identical room, in free space, constantly accelerated by the same amount as the (uniform) acceleration of gravity. it also compares the room free falling with gravity to one that is unaccelerated in free space unaffected by any gravity. (gasp! LS says that no such place exists!)

you think that some instruments with 12 significant digits (as an engineer, i have my doubts that any such instrument exists - there is no A/D converter with 40 meaningful bits of data) can measure the difference in pull between the floor of a room and the ceiling 3 meters above it here on this planet Earth? have you done the math to check it out? can you do the math? (show us that you can do the math.) is the gravitational field ostensibly non-uniform or ostensibly uniform in this room on the Earth with 3 meters between the floor and the ceiling?

LS: This universe has no uniform gravitational fields ...

how do you know? the universe is a pretty big place, have you been to or looked everywhere in the universe to confirm your blanket assertion? can there be no place in the universe with such a geometry of mass so that in a finite volume the gravitational field is uniform? the onus is on you to prove that.

... and you dont get it.

so said Pharoah to Moses (or was it the other way around)?

LightStorm

Feb18-06, 05:14 AM

"the first mistake of a bad driver is thinking he's a good driver."

LS: I am not a bad driver. Therefore the first mistake I make cannot be the one that you stated. Hence my first statement: "I am not a bad driver" stands. You see circular logic there? That is exactly how you're defending EP. Your first assumption is: EP is right. Therefore one should not perform any experiments that invalidate EP. If someone tried to perform such an expeirment, limit the size of the reference frame to 3 meters and then question the accuracy of the instruments involved in the reference frame as if the inaccuracy of the instruments is proof that EP is right. LOL!!

You dont find that funny? I do!

Keep in mind, Newtonian equivalence works for all towers. From 3 meters to 100 meters. The problem is Einstein's equivalence doesnt work for all towers. Whose fault is it, mine?

if you're a student, you need to position yourself to learn or it's all for naught.

LS: Every student has the right to question dubious principles, particularly the ones that involve circular logic.

"Period." is indicative of an unwillingness to learn anything.

LS: Gee you jump to conclusions or what. I meant to indicate that gravitational fields in this universe are NOT uniform.

you have all of the answers and no need to open your mind.

LS: You're good at making stuff up.

i am not blaming the universe for anything.

Your first assumption is "EP cannot be wrong". Therefore if an experiment finds it wrong, you can either modify EP or modify the universe. Because your first assumption cannot be wrong, the only option you're left with is to modify the universe by introducing infinite quantities. You think the universe is at fault and not the principle for having uniform graivity fields.

there is no A/D converter with 40 meaningful bits of data) can measure the difference in pull between the floor of a room and the ceiling 3 meters above it here on this planet Earth?

A 3 meter tower is all I get to work with huh? Why cant I get the tallest building in the world? Why, relativity is afraid of tall buildings or something? Afraid of heights, maybe?

Or maybe you think that EP works only for a reference frame that has a height of 3 meters? Is that the standard operating reference frame? A 3 meter tower and boast the accuracy to 1 part in a trillion?

When I ask for a 20 meter tower (or taller, like the one that Galileo used) I wont get it because I may invalidate the principle, right? Dont you think a principle that works for a 3 meter tower must also work for all kinds of towers. You know this one clearly doesnt. Why doesnt this work? Maybe there is a chance it could be wrong?

how do you know? the universe is a pretty big place, have you been to or looked everywhere in the universe to confirm your blanket assertion?

LS: How do you know that the speed of light is only 300000 km/sec? Did Einstein look everywhere in the universe to confirm this blanket assertion?

can there be no place in the universe with such a geometry of mass so that in a finite volume the gravitational field is uniform?

LS: Can there be no place in the universe where the speed of light is only 10000 km/sec?

the onus is on you to prove that.

LS: Yea right. Whose onus is to prove that the speed of light is c in every corner of the universe? Did Einstein travel at 0.8c when he wrote relativity? How did you believe him when he never traveled at 0.8c? Oh wait, space-time curves right? Why does it curve and what is it made of? If you know it curves, you must know what it is made of too right? Onus? LOL! Forget Onus.