harrylin
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PeterDonis said:No, that's not what Einstein explained. [..]

PeterDonis said:No, that's not what Einstein explained. [..]
It is more like Newtonian mechanics with the strong and weak nuclear forces. It doesn't have any mechanism for making predictions where the nuclear forces are important. All you can do is ignore them.harrylin said:I thought that he was clear, but apparently not... it's like Newton's mechanics which can fail at very high speeds because it has no limit speed; that's not the same as saying that Newton's mechanics makes no predictions at the speed of light.
harrylin said:it's like Newton's mechanics which can fail at very high speeds because it has no limit speed; that's not the same as saying that Newton's mechanics makes no predictions at the speed of light.
harrylin said:The question is what SR predicts that an accelerometer in free-fall will read.
Samshorn said:I think the question is ill-posed, because special relativity isn't a theory of gravity, and hence it makes no predictions about the effects of gravity.
PeterDonis said:I agree that any prediction SR makes about accelerometer readings (as with any prediction of SR in general) can only be made on the assumption that [STRIKE]gravity is negligible[/STRIKE] any tidal effects from gravity are negligible.
PeterDonis said:... the concept of free fall makes sense in the absence of gravity...
Samshorn said:The subject of the thread is "Free fall acceleration in SR", which obviously refers to gravity (see the words "fall" and "acceleration")
Samshorn said:unless you are claiming that the very term "free fall" necessarily implies a state indistinguishable from uniform motion in flat spacetime.
Samshorn said:clearly the OP didn't want to assume that tautology, he wanted to know if any "accelerometer" could measure or detect, from within a sealed projectile, the gravitational "acceleration" of the projectile as it loops around a star (for example).
PeterDonis said:Huh? Doesn't "SR" automatically exclude gravity? (Or more precisely tidal gravity, as Nugatory pointed out.)
PeterDonis said:I interpreted the OP's question to mean, what does SR predict that an ideal accelerometer will read? That question can be formulated perfectly well in flat spacetime, without gravity.
PeterDonis said:Yes, I realize that's not the question the OP actually wanted answered...
PeterDonis said:...but the question the OP asked was whether an accelerometer in free fall would read zero. That translates easily to asking whether an accelerometer at rest in some inertial frame in flat spacetime would read zero.
PeterDonis said:So the full response to the OP, IMO, can't just be that "SR can't answer your question"; it has to also distinguish the question the OP actually asked, which SR *can* answer, from the question the OP really wanted answered, which SR cannot answer.
Samshorn said:As discussed previously, one can formulate a nominally viable theory of gravity within the context of special relativity (i.e., a Lorentz invariant theory in flat Minkowski spacetime), and in fact this is precisely what several people did between 1905 and 1915, most notably Nordstrom's second theory of 1913.
Samshorn said:The thing that "automatically excludes" gravity from being operationally modeled within special relativity is the strong equivalence principle
Samshorn said:The OP was obviously asking about gravitational free-fall, and even if we restrict this to homogeneous fields
Samshorn said:I think we have a different perception of the question the OP actually asked.
PeterDonis said:...a basic assumption of SR, the one that allows you to construct global inertial frames, is that if you take two objects at rest with respect to each other, and both of them move inertially--i.e., no forces act on them--then they will stay at rest with respect to each other. Tidal gravity violates this assumption.
PeterDonis said:You can't get any kind of accurate prediction of the twin's proper acceleration using SR, because of the large path curvature at the turnaround point. You need a curved spacetime to get the right answer for proper acceleration in this scenario (i.e., zero).
PeterDonis said:In this context, the OP's question is really something like this: does the large path curvature of the traveling twin at turnaround, in the above SR model of the slingshot scenario, really *have* to correspond to SR predicting (incorrectly) a large nonzero reading on an accelerometer for the traveling twin at turnaround?
PeterDonis said:Is there any way to graft some kind of "gravity" onto SR that would allow SR to somehow predict a zero reading on an accelerometer even on a path with a large ("apparent"?) path curvature in a global inertial frame?
PeterDonis said:The answer to this, it seems to me, is "no"; but that's not because of the SEP. It's because there's no way to model tidal gravity in SR, as I said above.
Samshorn said:I think your reasoning tacitly relies on general relativity and the strong equivalence principle, because you are thinking of gravitational free-fall as force-free inertial motion. You say two objects are moving inertially - subject to no forces - in a gravitational field, and since they drift together or apart due to tidal effects you say this contradicts global inertial frames. But you could also conceivably model gravity as a force in Minkowski space, so that objects in gravitational free-fall are not in inertial motion, and hence this doesn't automatically rule out global inertial frames. (There are "tidal effects" for electromagnetism too, but this doesn't make EM incompatible with special relativity.)
Samshorn said:What people tried to do soon after special relativity was to develop a Lorentz invariant version of Newton's gravitational force, analogous to the electromagnetic force (which certainly isn't incompatible with special relativity). But it turns out there are difficulties with this simple approach when applied to gravity. (Strangely reminiscent of the difficulties in trying to quantize gravity today...)
Samshorn said:But maybe when you say special relativity predicts a non-zero reading you are referring to some other kind of accelerometer, perhaps one using electromagnetic or optical features, and a theory of gravity that violates the strong equivalence principle so that these features would reveal the acceleration? That all seems pretty far-fetched to me. And yet you're talking about it as if it's the default SR prediction... and all the while saying that SR even makes a prediction for the accelerometer readings in a gravitational turn-around in the absence of a theory of gravity... I can't follow your reasoning at all.
PeterDonis said:Can you give any references? This is not an area I'm familiar with, but it looks interesting.
harrylin said:This is a spin-off of a parallel discussion, starting from:
https://www.physicsforums.com/showthread.php?p=4281037#post4281037
The question is what SR predicts that an accelerometer in free-fall will read. This issue may be simply due to different people using a different meaning of "SR", but it could have a deeper cause.
A basic reference for this discussion:
Einstein 1905, http://www.fourmilab.ch/etexts/einstein/specrel/www/
and another one for context:
Langevin 1911, http://en.wikisource.org/wiki/The_Evolution_of_Space_and_Time
SR uses the inertial frames of classical mechanics; in my opinion it's obvious that SR doesn't predict that an accelerometer in free fall will indicate a large acceleration. That conflicts with the known laws of physics, even of classical mechanics.
Arguments in favor of both opinions may help to clarify this issue.
It would make no sense to modify a postulate that doesn't apply and SR is commonly used in the presence of gravity; evidently this is a topic to discuss, although it's not the topic of this thread.PeterDonis said:Newtonian mechanics makes predictions at the speed of light because "speed" is a meaningful concept in Newtonian mechanics; it just doesn't have a limiting speed. SR can't make predictions at all in the presence of gravity because "gravity" is not even a meaningful concept in SR; the presence of gravity (more precisely, the presence of tidal gravity, but the field of any real gravitating mass, like the Earth, includes tidal gravity, so it amounts to the same thing) violates the fundamental assumptions upon which SR is built.
Thanks, that's a constructive take of the question. I'm not familiar with that theory, but of course such a theory can not predict a deflection of light in vacuum wrt a Newtonian reference system. Once more: in contrast to GR, SR based theories of gravitation erroneously predict that a truly optical accelerometer in free fall towards a star will measure its free-fall acceleration.Samshorn said:[..] Probably the closest thing to a viable theory of gravity that is (nominally) consistent with special relativity is Nordstrom's second theory in 1913. This theory arose from Nordstrom's attempt to devise, in the most direct way, a Lorentz invariant theory of gravity, compatible with special relativity. [..] Nordstrom's theory predicts no deflection of light [..]
That was suggested earlier in this thread, but it's an interesting point indeed![..] every attempt to model gravity in a self-consistent way inevitably "breaks" special relativity.
No, that confounds SR with GR - SR has no equivalence principle. Mixing up theories is a persistent problem in this thread...[..] Overall, I suspect the OP was misled by Langevin's 1911 paper, especially the part where Langevin claims (naively, at best) that if an observer and an electric charge were both floating freely inside a sealed capsule in free fall in a uniform gravitational field, the observer (according to Langevin) would detect radiation from the co-moving electric charge (because he says it is absolutely accelerating). Langevin says this "fact" proves the existence of an "ether" (although he doesn't say why). But of course that "fact" violates the strong equivalence principle [..]
Yes, especially when considering that SR uses Maxwell's field interpretation. It goes to show that one should never have blind faith in a theory.He also considers tandem acceleration from other causes, and makes the same assertion, but, again, his naive assumptions in this area are known to have been wrong - although I suppose he can be forgiven, since even today there are endless threads on this forum arguing about whether a co-moving observer will detect radiation from a free-falling charge. It's hard for people to understand that the presence or absence of "radiation" is not an absolute fact (especially for people steeped in the Faraday-Maxwell field interpretation, rather than the Ampere-Weber particle interpretation).
Yes indeed; and we all know that SR was ruled out by experiment, that's why GR successfully replaced it.I don't think the OP asked for "the right answer", he asked what special relativity would predict. As noted above, one would get a prediction of zero for accelerometer readings even for a Newtonian-style force theory of gravity, provided only that the force accelerates all parts of the accelerometer in tandem. This, I suspect, is what the OP was driving at. Indeed the default theory of gravity works exactly this way... the problem is that the only known "force" models of gravity that are nominally consistent with special relativity are ruled out by experiment.
But only when the errors from neglecting gravity are negligible, as in the MMX, not the GST.harrylin said:SR is commonly used in the presence of gravity
harrylin said:SR based theories of gravitation erroneously predict that a truly optical accelerometer in free fall towards a star will measure its free-fall acceleration.
harrylin said:No, that confounds SR with GR - SR has no equivalence principle. Mixing up theories is a persistent problem in this thread...
harrylin said:Yes especially when considering that SR uses Maxwell's field interpretation.
And none of the "SR gravity" theories are consistent with observation (AFAIK). Because of that, all you can justifiably do is use SR in situations where the errors arising from neglecting gravity are small.Samshorn said:I'd say the persistent problem in this thread is the mistaken idea that there is a unique theory of gravity consistent with special relativity, so that questions about accelerometer readings in "gravitational free-fall in SR" have a well-defined answer.
DaleSpam said:And none of the "SR gravity" theories are consistent with observation (AFAIK). Because of that, all you can justifiably do is use SR in situations where the errors arising from neglecting gravity are small.
This is interesting. Do you mean this literally or is this hyperbole?Samshorn said:the equivalence principle, which is the most precisely verified principle in physics.
DaleSpam said:This is interesting. Do you mean this literally or is this hyperbole?
Thanks, I was unaware of that! Do you have a reference, or at least the name of the experiment? It seems like one I should know, but don't.Samshorn said:the equivalence principle, or at least the equality of inertial and gravitational mass, has been established to 1 part in about 100 billion - and that was in 1964.
DaleSpam said:Thanks, I was unaware of that! Do you have a reference, or at least the name of the experiment? It seems like one I should know, but don't.
Yes, I think we all agreed on that, and for me this topic has sufficiently been discussed and so I will not comment further in this thread. What remains is possible spin-offs for other, related topics. For example:Samshorn said:[..] the concept of "SR based theory of gravitation" is inherently ill-defined and counter-factual.
?? GR is developed on top of SR, but is incompatible with SR's second postulate (the one of Einstein, not of some textbooks). If he did not explain that clearly enough for everyone, then we should probably start it as a topic in which I am willing to participate (in that case, please put a link to it here). It's very straightforward really.[..] One can't really claim that an "SR based theory of gravitation" could not possibly satisfy (operationally) the strong equivalence principle. In fact, there is a field interpretation of general relativity in which the curved metric is just an "effective" metric, on top of the "true" (but unobservable) flat Minkowski metric of special relativity. (This is similar to how special relativity can be interpreted in a Lorentzian sense, by invoking a metaphysically defined sense of "truth", adding strictly unobservable elements to the theory.) So, according to this interpretation, general relativity is actually a "SR based theory of gravitation".
Hmm I did not see anyone suggest that idea... never mind, it's a non issue.I'd say the persistent problem in this thread is the mistaken idea that there is a unique theory of gravity consistent with special relativity,
harrylin said:?? GR is developed on top of SR, but is incompatible with SR's second postulate (the one of Einstein, not of some textbooks). If he did not explain that clearly enough for everyone, then we should probably start it as a topic in which I am willing to participate (in that case, please put a link to it here). It's very straightforward really.
harrylin said:?? GR is developed on top of SR, but is incompatible with SR's second postulate (the one of Einstein, not of some textbooks). If he did not explain that clearly enough for everyone, then we should probably start it as a topic... It is really quite straightforward.
harrylin said:Hmm I did not see anyone suggest that idea...