Free fall acceleration in SR

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stevendaryl

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For example, what does proper acceleration--path curvature of a worldline--mean in this "SR + gravity" theory? I know we've gone back and forth about what different types of accelerometers would read, but in standard SR and GR, a key element of the physical interpretation of the theory is that proper acceleration, path curvature of a worldline, is a direct physical observable; there is *some* device, call it an "ideal accelerometer", that measures it. A given worldline in the presence of gravity has *different* path curvature according to "SR + gravity" than it does according to GR, because "SR + gravity" still uses flat spacetime; so "SR + gravity" can't possibly get good agreement with the physical predictions of GR with regard to path curvature.
After thinking about it, I'm not convinced that you are right, but I am convinced that it's much more complicated than I was thinking it was. The problem is that, as you say, things like lengths and proper times and proper accelerations are assumed to be measurable in most SR type thought experiments, while they are no longer measurable if you assume a universal "gravitational force". The notion of proper time in the theory SR + gravity will not be the same as the GR notion of proper time, and similarly for length measurements and proper acceleration measurements. That makes the comparison of "SR + gravity" with experiment exceedingly difficult.
 
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I am convinced that it's much more complicated than I was thinking it was.
I agree. If it were straightforward then it would have been done more than a century ago and GR would probably never have been developed in the first place.

Personally, I stand by the assertion that all you can do with gravity in SR is neglect it. I may be wrong in that, but it will take someone smarter than Einstein to show it.
 
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The problem is that, as you say, things like lengths and proper times and proper accelerations are assumed to be measurable in most SR type thought experiments, while they are no longer measurable if you assume a universal "gravitational force". The notion of proper time in the theory SR + gravity will not be the same as the GR notion of proper time, and similarly for length measurements and proper acceleration measurements.
Yes, exactly, this is what I was getting at.
 
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As remarked earlier (post #82), it depends a lot on one's exact definitions of "special relativity", "accelerometer", etc.
In a quick search I found no other literature on this topic, so I just summarize with the few "authorative" literature references that I already had. For completeness I include again also Langevin, as apparently is necessary:
What is the "Langevin scenario"? Are you referring to a twin scenario where the turn-around is achieved by looping around a distant star under the effect of the star's gravitation? If so, Langevin never mentioned any such thing. (Granted, another poster claimed the gravitational turn-around scenario was in Langevin's 1911 paper, but when I asked him to point to where in that paper the gravitational turn-around was discussed, he admitted there was no such thing in that paper, so it was just a mis-attribution.)
- Einstein 1905:
Theory from two postulates.
http://www.fourmilab.ch/etexts/einstein/specrel/www/

- Langevin 1911
"it is sufficient that our traveler consents to be locked in a projectile that would be launched from Earth with a velocity sufficiently close to that of light but lower, which is physically possible, while arranging an encounter with, for example, a star that happens after one year of the traveler's life, and which sends him back to Earth with the same velocity. "
http://en.wikisource.org/wiki/The_Evolution_of_Space_and_Time

He thus gives the prediction of SR for a turnaround using a gravitational sling.

- Einstein 1916:
"The Special Relativity Theory does not differ from the classical mechanics through the assumption of [the first] postulate, but only through the postulate of the constancy of light-velocity in vacuum "
http://en.wikisource.org/wiki/The_Foundation_of_the_Generalised_Theory_of_Relativity#.C2.A7_1._Remarks_on_the_Special_Relativity_Theory.

- Einstein 1916:
"the special theory of relativity cannot claim an unlimited domain of validity; its results hold only so long as we are able to disregard the influences of gravitational fields on the phenomena".
http://en.wikisource.org/wiki/Relativity:_The_Special_and_General_Theory/Part_II#Section_22_-_A_Few_Inferences_from_the_General_Principle_of_Relativity

I note that Einstein similarly did not claim that SR has no results in the presence of gravitation; it can be used as long as the ignored effects are relatively small - as is always the case with theories. I think that most of us agree that this is the case in principle with Langevin's scenario which assumes a relatively short turn-around (see for example post #85).
And with "the phenomena" he obviously meant (or should have meant) the "relativistic" effects and not all phenomena of the experiment (just think of MMX which in full uses the orbit of the Earth with the Sun as gravitational sling!).

Taking, as he did himself, Einstein's postulates as basis and definition for SR, I see no reason for a change of the classical prediction that a perfect mechanical accelerometer will indicate null in free fall: neither postulate seems to impose a difference in gravitational acceleration between the different parts of a standard mechanical accelerometer.
To elaborate with the simple basic case of a silicon accelerometer in free fall (and in agreement with post #113): as gravitation cannot be shielded, the attractive force of a far away body on one Si atom of the accelerometer must be equal to the attractive force on another Si atom (any basic textbook suffices!).

In contrast, it follows directly from the second postulate that a non-mechanical (fully optical) accelerometer would indicate free-fall acceleration (contrary to GR and experience and explained in posts #50 and #72).
 
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Einstein 1916:
"the special theory of relativity cannot claim an unlimited domain of validity; its results hold only so long as we are able to disregard the influences of gravitational fields on the phenomena".
http://en.wikisource.org/wiki/Relativity:_The_Special_and_General_Theory/Part_II#Section_22_-_A_Few_Inferences_from_the_General_Principle_of_Relativity

I note that Einstein similarly did not claim that SR has no results in the presence of gravitation; it can be used as long as the ignored effects are relatively small - as is always the case with theories. I think that most of us agree that this is the case in principle with Langevin's scenario which assumes a relatively short turn-around
I don't agree. A large error for a small amount of time is not the same as a small error.

Einstein's quote is correct, but the Langevin scenario is one where we are not "able to disregard the influences of gravitational fields on the phenomena", IMO. Not only are the accelerometer readings erroneous during the turnaround if you disregard gravitational fields, but also if you disregard the gravitational fields then the path itself is erroneous since it is gravitational fields which cause the turnaround. By disregarding the influences of gravitational fields you get two large errors, one of which is a large error for a small amount of time, and the other is a large error for a large amount of time.
 
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Indeed, also the full MMX makes in its conception use of the gravitational field for measurements at different velocities*.

Thanks everyone for the comments, I think that this topic has been sufficiently discussed now.

* it is just possible that the resultant velocity at the time of the observations was small though the chances are much against it. The experiment will therefore be repeated at intervals of three months, and thus all uncertainty will be avoided - http://en.wikisource.org/wiki/On_the_Relative_Motion_of_the_Earth_and_the_Luminiferous_Ether
 
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I don't know what you think the relevance of that is. The analysis you quote was using the aether wind theory which was current at the time. It was not a SR analysis.

In any case, the errors in the MMX are small, not the Langevin scenario.
 
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In contrast, it follows directly from the second postulate that a non-mechanical (fully optical) accelerometer would indicate free-fall acceleration (contrary to GR and experience and explained in posts #50 and #72).
I thought I had already responded to the substance of this, but it doesn't look like I have. You appear to be claiming that light bending would make a freely falling optical accelerometer register a nonzero reading. But there is no light bending in a local inertial frame; there is only light bending in an accelerated frame. If I am in a freely falling elevator and watch light bounding back and forth between mirrors on the walls, I won't measure any bending; but someone standing on the ground watching the experiment will measure bending of the same light beams. So an optical accelerometer using light bending as a measure of acceleration should only measure actual proper acceleration; it should read zero in free fall.
 
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Still a few more clarifications then:
I don't know what you think the relevance of that is. The analysis you quote was using the aether wind theory which was current at the time. It was not a SR analysis. [..]
Most people and textbooks hold that SR can be used to analyse MMX, despite its reliance on the gravitational swing of the Sun to enable measurements at considerably different velocities. I agree with that.
[..] You appear to be claiming that light bending would make a freely falling optical accelerometer register a nonzero reading. [...]
Certainly not. Instead, and as Einstein elaborated in his 1916 papers, the second postulate of SR implies that light cannot bend in vacuum, as measured with a classical inertial frame. That was modified with GR.
 
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Most people and textbooks hold that SR can be used to analyse MMX, despite its reliance on the gravitational swing of the Sun to enable measurements at considerably different velocities. I agree with that.
I agree that the MMX can be analyzed using SR also, but the quote you used earlier (from the MMX paper itself) is irrelevant since it refers to an aether analysis, not an SR analysis. The reason that the MMX can be analyzed using SR is that the interference fringes are not sensitive to the gravitational effects in the experiment. It has nothing to do with changing velocities over the course of the year, there simply is no measurable effect at any velocity.

The same is not true of the Langevin version of the twins paradox. In the twins paradox the key to resolving the scenario is to identify that there is an asymmetry between the twins. This asymmetry is either proper acceleration measured by an accelerometer or spacetime curvature. The error produced by neglecting gravity is therefore important to Langevin where it was not important to MMX.
 
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"For this it is sufficient that our traveler consents to be locked in a projectile that would be launched from Earth with a velocity sufficiently close to that of light but lower, which is physically possible, while arranging an encounter with, for example, a star that happens after one year of the traveler's life, and which sends him back to Earth with the same velocity."

He thus gives the prediction of SR for a turnaround using a gravitational sling.
One might surmise that this is what Langevin had in mind, especially from this translation, but he doesn’t actually mention gravitation – and for good reason: No star (as Langevin knew them) would have been sufficient to accomplish such a turn-around. In order for a projectile moving at nearly the speed of light to be turned around gravitationally, it would need to pass within a distance where the escape velocity is comparable to the speed of light, which is not possible for any star that Langevin could have known about – unless you think he was assuming the existence of something like John Michell’s "black holes", from which even light could not escape, but this would have been (to his contemporaries) even more fantastical than the twins paradox that he was trying to illustrate, especially in the context of special relativity (with which Michell didn’t have to contend). A Newtonian slingshot would require the projectile to speed up to superluminal speed at the perigee, which Langevin knew was impossible, so he really wasn't in a position to reconcile a gravitational mechanism with special relativity. Also no Newtonian hyperbolic or parabolic trajectory could precisely turn the projectile around, although it could come close. (Ironically, in general relativity it actually is possible to send a particle back in exactly the same direction as its approach, but not in Newtonian gravity.)

I’d also be careful with the English translation, especially the words "and which sends him back", which don't seem to come from a simple literal translation of the French. In fact, looking back at the original version of the Wiki translation you cited, that specific phrase was translated differently. It originally said

“For this it is sufficient that our traveler consents to be locked in a projectile that would launched from Earth with a velocity sufficiently close to that of light, although lower so that it is physically possible, then arranging an encounter with, for example, a star that happens after one year of life, and then the traveler returns to Earth with the same velocity.”

This is even less suggestive of gravitational sling mechanism. However, the words were changed from this to the current version (the one phrased to suggest that the destination star somehow “sends” the projectile back) by a wikipedia editor named Harald88. I don’t know which version of the translation is more accurate.

But even accepting the revised translation of Harald88, which seems worded to promote the idea that Langevin was talking about a gravitational slingshot, the fact remains that Langevin didn't specify the mechanics of how the projectile is accelerated from Earth, nor how it is decelerated at the star. The same method (e.g., rockets) could have been used for both. If he really had in mind a gravitational slingshot (which is only circumstantially suggested by his mentioning of a star “for example” as the destination point), then at the very least he was being coy about the fantastical kind of “star” that would be required to accomplish a gravitational turn-around of an object traveling at near light speed.

It’s also strange that he says "meeting with a star for example...". Why does he say "for example"? If he was describing a gravitational slingshot, what else could it be other than a star (or rather, a black hole)? This suggests he was just using a star as an arbitrary destination and turn-around point. All he really said is, the traveler accelerates (by unspecified means) from Earth out to a distant star (for example) at high speed, then turns around (by unspecified means) and returns at the same speed. Readers who realized that a gravitational slingshot could not possibly accomplish the turn-around (for any star known at the time) would have been less likely to assume that he was claiming a gravitational slingshot as the mechanism.
 
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There is another translation of Langevin's paper by B. L. Sykes (published in Scientia, 1973, v. 108). Online freely available on:
http://amshistorica.unibo.it/diglib.php?inv=7&int_ptnum=108&term_ptnum=302

The relevant passage reads:
p. 297: To do this, our traveller would need only to agree to being shut up inside a projectile that the Earth would launch at a velocity sufficiently close to that of light, but still less than it, which is physically possible, arranging for an encounter with, say, a star to take place at the end of one year in the lifetime of the traveller and to send him back towards the Earth at the same velocity.

(Il suffirait pour cela que notre voyageur consente à s’enfermer dans un projectile que la Terre lancerait avec une vitesse suffisamment voisine de celle de la lumière, quoique inférieure, ce qui est physiquement possible, en s’arrangeant pour qu’une rencontre, avec une étoile par exemple, se produise au bout d’une année de la vie du voyageur et le renvoie vers la Terre avec la même vitesse.)
 
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Even if it is a mis-attribution, for the purposes of this thread "Langevin scenario" is a gravitational twins paradox. The translation doesn't eliminate the concept, only possibly correct the misattribution.
 

stevendaryl

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“For this it is sufficient that our traveler consents to be locked in a projectile that would launched from Earth with a velocity sufficiently close to that of light, although lower so that it is physically possible, then arranging an encounter with, for example, a star that happens after one year of life, and then the traveler returns to Earth with the same velocity.”

This is even less suggestive of gravitational sling mechanism.
I can't imagine why it would be important that there be a distant star in the first place, if the star is not supposed to play a role in turning the rocket around. Without the star, how is this any different from the usual twin paradox?
 
I can't imagine why it would be important that there be a distant star in the first place, if the star is not supposed to play a role in turning the rocket around. Without the star, how is this any different from the usual twin paradox?
Well, it simply could play the role of the travel destination, at which the traveler turns around. This doesn't necessarily imply a gravitational influence as the cause of the turnaround. However, even if Langevin thought that a gravitational turnaround can be fully described with SR, it is irrelevant from a modern perspective. Because in 1911 the relation between gravitation and SR was widely unknown, only some speculative, tentative models by Einstein and Abraham were published.
 
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the second postulate of SR implies that light cannot bend in vacuum, as measured with a classical inertial frame.
Then I'm confused; how is an optical accelerometer supposed to register a nonzero reading in free fall?
 

stevendaryl

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Then I'm confused; how is an optical accelerometer supposed to register a nonzero reading in free fall?
I think that Harry is saying that SR predicts no bending of light by gravity. Therefore, the prediction is that light will appear to bend upward inside a falling elevator car (the elevator is falling, but light is not).
 
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I think that Harry is saying that SR predicts no bending of light by gravity. Therefore, the prediction is that light will appear to bend upward inside a falling elevator car (the elevator is falling, but light is not).
That doesn't make sense either, because the prediction that the elevator is falling, if by that we mean falling with respect to the Earth, can't be made in SR; there's no way to model the gravitational field of the Earth in SR. So it isn't that SR predicts no bending of light by gravity; it's that SR can't model gravity at all, it doesn't even yield a prediction, just a "reply hazy, ask again later". :wink:

If instead you say the elevator is "falling" with reference to a uniformly accelerated observer in flat spacetime, then SR *does* predict light bending--for the uniformly accelerated observer, *not* for the observer in the elevator (since the latter is obviously at rest in a global inertial frame, and there is no light bending in such a frame), as I said before. (Of course, then the issue is that SR alone predicts only half the light bending that is actually observed.)
 
There is another translation of Langevin's paper by B. L. Sykes (published in Scientia, 1973, v. 108). Online freely available on:
http://amshistorica.unibo.it/diglib.php?inv=7&int_ptnum=108&term_ptnum=302

The relevant passage reads:
p. 297: To do this, our traveller would need only to agree to being shut up inside a projectile that the Earth would launch at a velocity sufficiently close to that of light, but still less than it, which is physically possible, arranging for an encounter with, say, a star to take place at the end of one year in the lifetime of the traveller and to send him back towards the Earth at the same velocity.
Thanks for that link. This translation seems more consistent with the original Wiki translation, since it doesn't attribute the turn-around to the encounter, it simply says we can arrange to send him to a distant star, say, and then back to Earth at the same speed. Only in the revised translation on Wikipedia by Harald88 do we find wording that seems to have been crafted to suggest a gravitational slingshot mechanism, although of course there is no actual mention of gravitation in any of the translations, nor in the original French. And for good reason, since a gravitational slingshot of a near light speed object would be a contradiction in the context of special relativity (since it would obviously entail superluminal speed at the perigee).

Even if it is a mis-attribution, for the purposes of this thread "Langevin scenario" is a gravitational twins paradox. The translation doesn't eliminate the concept, only possibly correct the misattribution.
I think the subject of this thread is free fall acceleration in the context of special relativity, particularly the scenario involving a gravitational slingshot of a projectile that travels to a star at nearly the speed of light. This is inherently a historical subject, since we don't normally deal with gravity in the context of special relativity today. It's also inherently self-contradictory, since (as Langevin himself observed) the projectile cannot exceed the speed of light according to special relativity, and yet a gravitational slingshot in this context would require the projectile to be moving significantly faster than light at the perigee (and the "star" would have to have a superluminal escape velocity at the surface, and couldn't precisely reverse the projectile's direction in any case).

The OP cites Langevin's 1911 article for this scenario, and if this was true then Langevin was guilty of a rather glaring self-contradiction and error in reasoning. Is it appropriate to attribute this blunder to Langevin (who was a pretty smart guy)? Well, when we read the paper in question, we find no mention at all of gravitation. The idea that Langevin had in mind a gravitational slingshot is based entirely on the fact that he said the projectile travels to a star and then returns. But when he mentions the star as the destination point, he says "for example", implying that the turn-around point need not be a star, and of course he does not state the mechanism for the turn-around, any more than he explains how the projectile was originally accelerated to near light speed when departing the Earth.

The only arguably damning evidence against Langevin is the current Wiki translation (as revised in 2010 by a wikipedia editor named Harald88), which is worded to indicate that the encounter with the star is what sends the projectile back. If that translation is accurate, it might suggest (although certainly wouldn't prove) that Langevin really did have that erroneous idea in mind. However, in two other translations the wording is more neutral. Also, the fact remains that in none of the translations does Langevin actually mention gravity. So, I'd be inclined to give him the benefit of the doubt, and attribute the error in reasoning to some of Langevin's modern day readers, rather than to Langevin himself.
 
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So, I'd be inclined to give him the benefit of the doubt, and attribute the error in reasoning to some of Langevin's modern day readers, rather than to Langevin himself.
That is fine by me. I have never read anything by him and have no opinion about his reasoning. "Langevin scenario" nothing more than a convenient shorthand for "gravitational slingshot turn around twins paradox scenario". No judgement of Langevin is implied by me. But if you find the association objectionable then I can just say "GST" for "gravitational slingshot twins".
 

pervect

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That doesn't make sense either, because the prediction that the elevator is falling, if by that we mean falling with respect to the Earth, can't be made in SR; there's no way to model the gravitational field of the Earth in SR. So it isn't that SR predicts no bending of light by gravity; it's that SR can't model gravity at all, it doesn't even yield a prediction, just a "reply hazy, ask again later". :wink:

If instead you say the elevator is "falling" with reference to a uniformly accelerated observer in flat spacetime, then SR *does* predict light bending--for the uniformly accelerated observer, *not* for the observer in the elevator (since the latter is obviously at rest in a global inertial frame, and there is no light bending in such a frame), as I said before. (Of course, then the issue is that SR alone predicts only half the light bending that is actually observed.)
SR should correctly predict the amount of bending in an accelerating elevator. It's basically a flat space-time situation, so it shouldn't have any problem with it. (I haven't done a detailed calculation, but I don't see how it could possibly come out otherwise).

The problem arises in applying the results to the GR situation.

I'd have to think carefully before I placed the blame for the discrepancy. I don't think one can calculate it light bending correctly without actually knowing the GR field equations (I might be wrong).

We occasionally have had arguments over the best "explanation" for light bending as well. As I recall, I thought most people were convinced that the "extra deflection" of light in GR could be blamed on spatial curvature alone - one argument is that it's only sensitive to the PPN parameter gamma. But I'm not sure if everyone got convinced by this.
 
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SR should correctly predict the amount of bending in an accelerating elevator.
Yes, and this calculation, by the equivalence principle, should also predict bending measured by, for example, an accelerated observer standing at rest on the surface of a planet like the Earth, or "hovering" above the surface of a star like the Sun. But this calculation will be "local"; there is no way to calculate, using SR, the light bending in a "global" scenario such as light from a distant star grazing the Sun and arriving at a telescope on Earth.
 
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There is another translation of Langevin's paper by B. L. Sykes (published in Scientia, 1973, v. 108). Online freely available on:
http://amshistorica.unibo.it/diglib.php?inv=7&int_ptnum=108&term_ptnum=302

The relevant passage reads:
p. 297: To do this, our traveller would need only to agree to being shut up inside a projectile that the Earth would launch at a velocity sufficiently close to that of light, but still less than it, which is physically possible, arranging for an encounter with, say, a star to take place at the end of one year in the lifetime of the traveller and to send him back towards the Earth at the same velocity.

(Il suffirait pour cela que notre voyageur consente à s’enfermer dans un projectile que la Terre lancerait avec une vitesse suffisamment voisine de celle de la lumière, quoique inférieure, ce qui est physiquement possible, en s’arrangeant pour qu’une rencontre, avec une étoile par exemple, se produise au bout d’une année de la vie du voyageur et le renvoie vers la Terre avec la même vitesse.)
Thanks Histspec I did not know that another translation already existence. Nice!
The English there is a bit fuzzy though, for it is unclear what is sending him back in that translation, while Langevin explains by what means all this could be possible in principle. I now checked with two natively speaking French colleagues that the wiki translation is correct on that point (and the one by Sykes inaccurate). I was pretty sure of that but it's always good to double-check.
 
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I think that Harry is saying that SR predicts no bending of light by gravity. [..]
Yes that's the consequence of the second postulate, as Einstein also explained.
 
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Yes that's the consequence of the second postulate, as Einstein also explained.
No, that's not what Einstein explained. You yourself quoted him as saying that SR cannot be used in cases where the effects of gravity cannot be neglected. Light bending by the Sun--i.e., in a global context, where light comes in from infinity, passes close to a gravitating mass like the Sun, and then goes back out to infinity with some change in angle, not a local context like an accelerating elevator (see my post #148)--is a case in which the effects of gravity cannot be neglected. So SR cannot make a prediction in this case; that's not the same as SR predicting no bending.
 

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