Implications of the statement Acceleration is not relative

[PAllen]

I don't know if it is inconsistent; for sure SR ignores effects from gravitation on time.
Coincidentally the effect of the star's gravitation on the traveler's aging is quite negligible in the given example, and probably less than the effect of Earth's gravitation on that of the stay-at-home. Commonly that is neglected in such examples.

It is inconsistent because it posits spacelike causal influence. This was recognized by 1906, possibly earlier. Newtonian gravity + galilean relativitity are consistent (whether conventionally expressed, or in a generally covariant formulation like Newton-Cartan). But Newtonian gravity + SR are fundamentally inconsistent.

Independent of the how much 'gravitational time dilation' contributes to a scenario, it is GR that provides the basis for speaking of looping inertial paths. Without GR, with gravity as a force, a flyby path is not inertial - it is accelerated. Further, GR explains that there can be multiple geodesics (inertial paths) between two points, with different clock time experienced (this is generally true of curved manifolds, never true of flat, topologically trivial, manifolds). GR math also implies that whatever the maximum clock time path between two events is, it will be a geodesic (while allowing other geodesic paths that are not maximal).

Langevin's paper must be taken in the historical context of 'before there was any consistent way to treat SR + gravity'.

 

[harrylin]

It is inconsistent because it posits spacelike causal influence. This was recognized by 1906, possibly earlier. Newtonian gravity + galilean relativitity are consistent (whether conventionally expressed, or in a generally covariant formulation like Newton-Cartan). But Newtonian gravity + SR are fundamentally inconsistent. [..]

You seem to refer to the fact that the speed of gravitation is neglected in classical mechanics. Yes indeed, SR imposes a maximum speed of c on gravitation, thanks for pointing that out. However, such considerations are irrelevant in the context of standard SR twin scenarios despite a stay-at-home on Earth. Such aspects are rather off-topic in this thread as well as in most examples of that kind.

With gravity as a force, a flyby path is not inertial - it is accelerated.

Yes, exactly.

 

[PeterDonis]

SR assumes flat spacetime and handles gravitation classically.

I.e., incorrectly. As stevendaryl pointed out, SR is inconsistent with Newtonian gravity. I don't know whether Langevin knew this in 1911, but he should have, as Einstein had already pointed it out and was already working on how to construct a new theory of gravity that would be consistent with SR.

The mistake that you ascribe to Langevin is due to you projecting modern GR concepts on him teaching SR correctly in 1911.

I wasn't trying to ascribe a "mistake" to him; I was simply pointing out that his scenario does not show that you can have multiple free-fall paths between the same pair of events in the absence of gravity. The bolded phrase is true regardless of whether you interpret "gravity" as a force or as the curvature of spacetime. Either way you have to bring in gravity to allow the traveling twin to return without feeling any force. I put the argument in modern terminology because that's what I'm used to, but you could rephrase it in 1911 terminology that would have made sense to Langevin; in fact I just did.

 

[PeterDonis]

Without GR, with gravity as a force, a flyby path is not inertial - it is accelerated.

But the traveling twin following this path still feels no force; he is in free fall the whole time. Newtonian gravity knew enough to make that prediction. (That's actually part of the reason that Newtonian gravity is inconsistent with SR; the kinematics aren't right.)

 

[PeterDonis]

I don't know if it is inconsistent; for sure SR ignores effects from gravitation on time.
Coincidentally the effect of the star's gravitation on the traveler's aging is quite negligible in the given example, and probably less than the effect of Earth's gravitation on that of the stay-at-home. Commonly that is neglected in such examples.

No, it's much worse than that. Consider Langevin's twin paradox scenario in the inertial frame of the stay-at-home twin. The traveling twin follows a curved path in this frame, hence he is accelerated (in the sense of coordinate acceleration), yet he is inertial--he is in free fall the whole time, feeling no force. The kinematics of SR do not permit this possibility; in an inertial frame in SR, coordinate acceleration *must* correspond to proper acceleration, i.e., to feeling a force. This is true even if nobody had yet realized it in 1911 (which they had--at least, Einstein had).

 

[Dale]

I disagreed with your assumption that he was discussing mathematical symbols when he wrote "gravitational field"; regretfully all my attempts to clarify the misunderstanding were in vain. I won't try anymore.

If he is discussing his theory of gravity, general relativity, then the things he discusses must have some correspondence to elements of the theory and hence can be identified with one or more of the mathematical symbols of GR. If he is not discussing his theory of gravity then his discussion is irrelevant to this thread.

Personally, I think that he is discussing his theory of gravity, GR, when he talks about "gravitational fields". When I look at the comments that he makes about "gravitational fields" the only element of his theory that seems to match are the Christoffel symbols. It is therefore my opinion that Einstein refers to the Christoffel symbols when he uses the term "gravitational field". An opinion to which you have not been able to provide a viable alternative.

It is a fact that the Christoffel symbols depend on the choice coordinate system (not on rockets) and also that they do not generate a wave equation. Therefore it is not surprising to me that there is a lack of literature about rockets producing gravitational waves or causing gravitational fields.

Enough, that ends our discussions.

That is certainly your perogative. I am willing to continue the discussion, should you change your mind.

 

[harrylin]

I.e., incorrectly. As stevendaryl pointed out, SR is inconsistent with Newtonian gravity. I don't know whether Langevin knew this in 1911, but he should have, as Einstein had already pointed it out and was already working on how to construct a new theory of gravity that would be consistent with SR. [..]

Right, and nevertheless irrelevant here; see my comments to PAllen.

[..] Consider Langevin's twin paradox scenario in the inertial frame of the stay-at-home twin. The traveling twin follows a curved path in this frame, hence he is accelerated (in the sense of coordinate acceleration), yet he is inertial--he is in free fall the whole time, feeling no force.

That's a continued mix-up of modern GR jargon and concepts with SR. That the traveler feels no force is irrelevant for Langevin's SR calculation; he will come back younger than the stay-at-home on Earth.

PS. I'm afraid that such discussions deviate from the topic; I'll wait for GregAshmore's comments on that, if any.

 

[Dale]

There is no secret about a field in physics being a zone of influence where a force is exerted by a physical cause; that's the meaning of "field" at the time that Einstein used the term, and he didn't modify its meaning.

One further comment on this. The problem is still that, in GR, there are several quantities which could warrant the name "gravitational field", even by this definition of "field". So the term still needs clarification, and thus it is reasonable to ask for such clarification in any discussion of "gravitational fields" in GR.

 

[Jano L.]

Yes, this is a good point.

I think there are at least two views on what is the manifestation of presence of gravitational field. For some people it is the acceleration of test bodies - this probably lead Einstein to his principle of equivalence. The field, as force, is then relative coordinate dependent concept and can be locally transformed away. Thus in the frame of our rocket, there would be non-zero gravitational field.

There are also people who prefer to say that field is present only when curvature is non-zero; in this view, in the rocket there is no gravitational field, since the acceleration is uniform and curvature zero...

 

[Dale]

I think there are at least two views on what is the manifestation of presence of gravitational field. For some people it is the acceleration of test bodies ... There are also people who prefer to say that field is present only when curvature is non-zero

Exactly. My personal preference, and I believe Einstein's preference, is the first view (Christoffel symbols). But it is only a mild preference and I am content with either approach, as long as people are clear about which one they are using.

 

[PeterDonis]

That the traveler feels no force is irrelevant for Langevin's SR calculation

What "SR calculation"? The "calculation" that the traveling twin is younger implicitly uses flat spacetime (and don't say flat spacetime wasn't known in 1911; Minkowski published his spacetime formulation of SR in 1907). But in flat spacetime, the traveling twin can't swing around the star without feeling a force. The fact that Langevin hand-waved this by supposing that the star's "gravity" somehow changes that does not make his "calculation" correct; it just means it was a hand-waving error that he was able to get away with in 1911. There is no consistent way to formulate a theory of "gravity" in flat spacetime that makes Langevin's hand-waving calculation valid; the correct version of his calculation uses GR, i.e., it uses curved spacetime.

such discussions deviate from the topic

Not really; they bear on the question of what the physical asymmetry is between the twins. You were the one who originally claimed that Langevin's version is a counterexample to the claim that proper acceleration--feeling a force--is the asymmetry. I am simply pointing out that this claim only works in the presence of gravity, and the standard formulation of the twin paradox assumes that gravity is negligible. If we allow gravity to be present, the whole thing becomes much more complicated because there are so many more possible scenarios; Langevin's is actually one of the simplest ones involving gravity.

 

[harrylin]

What "SR calculation"? The "calculation" that the traveling twin is younger implicitly uses flat spacetime (and don't say flat spacetime wasn't known in 1911; Minkowski published his spacetime formulation of SR in 1907). But in flat spacetime, the traveling twin can't swing around the star without feeling a force.

Sorry that doesn't make any sense to me; free-fall has been well known since Newton.

The fact that Langevin hand-waved this by supposing that the star's "gravity" somehow changes that does not make his "calculation" correct; it just means it was a hand-waving error that he was able to get away with in 1911. [..]

He assumed the correctness of SR and gave a straightforward application without handwaving. It would however be interesting if you demonstrate that the error in his calculation (according to GR) was considerably more than in usual SR examples in which the effect of Earth's gravitation on clock rate is neglected; that will certainly warrant starting a new thread.

ADDENDUM: as an afterthought, such an attempt would probably be doomed from the outset, as in the example the turnaround time was intended to be negligible compared to those of the inertial phases, so as to allow easy calculation. That's the standard assumption, also with Einstein's rocket.

 

[stevendaryl]

There are also people who prefer to say that field is present only when curvature is non-zero; in this view, in the rocket there is no gravitational field, since the acceleration is uniform and curvature zero...

The problem is that there is already a notion of "gravitational field" used in nonrelativistic physics. With many nonrelativistic notions, there is a corresponding relativistic notion that approximately coincides with the nonrelativistic notion in limiting cases. Spacetime curvature does not reduce the Newtonian notion of "gravitational field" in any kind of limit.

What does happen in the limit is this:

Connection coefficients in GR → Newtonian gravitational field + fictitious forces

There is no good way (as far as I know) in GR to tease apart exactly the quantities that become the Newtonian gravitational field in the nonrelativistic limit, except in special cases such as spherical symmetry.

 

[stevendaryl]

Sorry that doesn't make any sense to me; free-fall has been well known since Newton.

He assumed the correctness of SR and gave a straightforward application without handwaving. I invite you to demonstrate that the error in his calculation (according to GR) was considerably more than in usual SR examples in which the effect of Earth's gravitation on clock rate is neglected; that will certainly warrant starting a new thread.

I have to say that the point of your example is a good one. What I think the point was, in the context of this thread, anyway, that it is possible to have a twin paradox type situation in which neither twin "feels" any acceleration. That of course is true in General Relativity, but Langevin's example shows that it's not necessary to use General Relativity to get an approximate answer to the question: What happens in a twin paradox situation where neither twin feels any acceleration?

In the Langevin example, we can break the "traveling" twin's path into three legs:

1. Far from the distant star, traveling toward it.
2. Traveling near the distant star.
3. Far from the distant star, traveling away from it.

Einstein, even before he developed GR, claimed that legs (1) and (3) can be approximately handled using SR alone. The "stay-at-home" twin, in contrast, is always far from any big masses, and so SR is always adequate for computing his age.

But we can't compute the aging of the traveling twin during leg (2). However, what we can do is to simply let it be an unknown quantity \delta \tau. Then for the entire trip, the stay-at-home twin ages by an amount

\tau_{sah}

the traveling twin ages by an amount

\tau_{trav} = \tau_1 + \delta \tau + \tau_2

We can compute the ratio \dfrac{\tau_{sah}}{\tau_{trav}} in the limit as the distance to the star gets very large. (Assuming, which seems pretty sensible, that \delta \tau, the aging during the time orbiting the star, is a constant, independent of how long the twin traveled getting to the star.)

 

[PAllen]

Sorry that doesn't make any sense to me; free-fall has been well known since Newton.

A mathematically true statement in SR (flat spacetime, trivial topology - e.g. no cylindrical topology), for two world lines between to events to show differential aging, one or both must incur proper acceleration. This is an invariant quantity in SR, the same in all frames or generalized coordinates. Where things get dicey is whether an accelerometer measures proper acceleration. If you allow some ad hoc mixture of SR + gravity, you have the feature that there is proper acceleration not detectible by an accelerometer.

GR changes definitions so that proper acceleration is always corresponds to what is measured by an accelerometer; and inertial paths = free fall paths.

Of course independent of any theory, it was known since Newton that our universe allows multiple free fall paths between a pair of events (e.g. crossing orbits).

He assumed the correctness of SR and gave a straightforward application without handwaving. It would however be interesting if you demonstrate that the error in his calculation (according to GR) was considerably more than in usual SR examples in which the effect of Earth's gravitation on clock rate is neglected; that will certainly warrant starting a new thread.

No, his calculations were methodologically just wrong, though he didn't know it. That his specific example lead to small errors doesn't hide the fact he had no idea there was potential for his treatment to be way off.

Consider how he would have handled the following simple example all in our solar system:

a) A rocket firing thrusters so as to maintain a stationary position relative to the sun without falling or orbiting.

b) a circular orbital craft meetng (a) once per orbit

c) a bullet probe launched by the rocket radially outwards at an event of (a) and (b) meeting, such that it returns for the next (a) and (b) meeting.

Langeven's methods would say (a) ages the most. In fact, (c) ages the most, despite its having high speed for a good part of its trip. The fact that SR only calculation works for (a) and (b) is because these paths are all at the some potential - so gravitational time dilation does not apply at all. For a flyby around a a star, gravitational time dilation would not cancel, and a pure SR calculation is clearly an error, that Langevin was completely unaware of. That the error could be reduced by making the inertial parts of the journey long is irrelevant to the error of method. Alternatively, you could say that Langevin had no idea to even inquire about the error and argue that it could be made small - he had no concept of the parameters to make such an argument.

 

[PeterDonis]

Langevin's example shows that it's not necessary to use General Relativity to get an approximate answer to the question: What happens in a twin paradox situation where neither twin feels any acceleration?

I disagree; you are doing the same hand-waving that Langevin did. Your calculation does give a way of getting an approximate answer to the question of relative aging (since the traveling twin's time elapsed during leg (2) becomes negligible in the limit as the distance to the star gets very large). But it's not an approximate answer to the question I put in bold above, because it doesn't account for why the traveling twin doesn't feel any acceleration during leg (2). There is *no* way to consistently account for that using SR (i.e., flat spacetime) with a Newtonian "gravity" force tacked on; there is no such consistent theory. (Langevin may have thought there could be in 1911; I'm not sure. If he did, he was wrong.)

 

[harrylin]

[..] the traveling twin's time elapsed during leg (2) becomes negligible in the limit as the distance to the star gets very large [..]

Yes, that's the standard assumption for such "twin paradox" examples: the turnaround is assumed to be sufficiently fast so that the turnaround phase may be neglected for the calculation.

 

[PAllen]

Yes, that's the standard assumption for such "twin paradox" examples: the turnaround is assumed to be sufficiently fast so that the turnaround phase may be neglected for the calculation.

Actually, no. SR, for a non-gravitational turnaround makes an exact prediction. It also makes an exact prediction for a twin that is undergoing uniform acceleration the whole time. These predictions are correct, so far as is known (e.g. from accelerator experiments).

 

[stevendaryl]

I disagree; you are doing the same hand-waving that Langevin did.

Obviously. At any given time in the history of physics, there are some phenomena that we believe we understand, and there are phenomena that are yet to be explained. In order for a theory of physics to have predictive value, we have to make assumptions about the magnitudes of the effects due to phenomena we don't understand. Such assumptions always have the possibility for error, but how can you do any better than that.

SR was developed for use in describing situations where gravity was negligible. It would have no relevance to the real world if there were no situations in which we could neglect the effects of gravity. But without a theory of gravity, how can you know whether gravity can be neglected in any particular situation? You don't.

Your calculation does give a way of getting an approximate answer to the question of relative aging (since the traveling twin's time elapsed during leg (2) becomes negligible in the limit as the distance to the star gets very large). But it's not an approximate answer to the question I put in bold above, because it doesn't account for why the traveling twin doesn't feel any acceleration during leg (2).

It's not supposed to account for it. We know, for empirical reasons, that a person in free fall doesn't feel acceleration.

 

[Nugatory]

Yes, that's the standard assumption for such "twin paradox" examples: the turnaround is assumed to be sufficiently fast so that the turnaround phase may be neglected for the calculation.

That's done just to simplify the example. It's not a fundamental assumption of the explanation.

With instantaneous turnarounds, the proper distance along each leg is just algebra: \sqrt{\Delta t^2-\Delta x^2}. If we don't assume instantaneous turnarounds, we have to evaluate some sort of line integral. It's fairly easy to prove that in the limit as the turnaround time approaches zero, the line integral reduces to the simple algebraic calculation, so we use the latter when the details of the turnaround aren't important to the problem at hand.

 

[PeterDonis]

In order for a theory of physics to have predictive value, we have to make assumptions about the magnitudes of the effects due to phenomena we don't understand.

But today, we *do* understand GR. Remember how this sub-thread got started: with the claim that Langevin's example shows that you can have different elapsed proper times between events along different worldlines, without one of the worldlines having to be accelerated. This can only happen in the presence of gravity; Langevin obviously knew that since he knew he had to use a star, a large gravitating mass, as the "turnaround mechanism".

But Langevin appeared to think his example showed something useful about flat spacetime; he appeared to think that gravity could be added to SR without changing anything fundamental about spacetime itself. Today we know that can't be done. If the original claim had been phrased something like "Langevin gave an example of the traveling twin going around a star to turn around, which doesn't require him to feel any acceleration; but today we understand that that example requires curved spacetime for a full explanation", I would not have raised the objection I did. But it wasn't.

But without a theory of gravity, how can you know whether gravity can be neglected in any particular situation?

By measuring its effects. We know that in our everyday lives we don't have to take account of gravitational time dilation when we take an airplane flight. We don't need a theory of gravity to tell us that; we know it from our own observations--that our elapsed wristwatch time matches elapsed ground time between takeoff and landing (adjusted for time zone change if necessary). Similarly, in the Langevin example, the traveling twin could measure his elapsed proper time while slingshotting around the star and verify that it was very small compared to his elapsed proper time on the outbound and inbound legs. He doesn't need a theory of gravity to do that.

It's not supposed to account for it.

Then it's not an answer to the question it claimed to be an answer to.

 

[stevendaryl]

But today, we *do* understand GR. Remember how this sub-thread got started: with the claim that Langevin's example shows that you can have different elapsed proper times between events along different worldlines, without one of the worldlines having to be accelerated. This can only happen in the presence of gravity; Langevin obviously knew that since he knew he had to use a star, a large gravitating mass, as the "turnaround mechanism".

But Langevin appeared to think his example showed something useful about flat spacetime; he appeared to think that gravity could be added to SR without changing anything fundamental about spacetime itself.

It seemed to me that Langevin's example was just being used to illustrate that SR could be used (approximately, anyway) in cases where neither twin "feels" any acceleration. If Langevin was using his example for a different purpose, that doesn't change anything.

 

[PeterDonis]

It seemed to me that Langevin's example was just being used to illustrate that SR could be used (approximately, anyway) in cases where neither twin "feels" any acceleration.

Only in a very limited subset of such cases: where the portion of the traveling twin's trajectory that is affected by gravity is very small compared to the total trajectory. And even then you need spacetime curvature in the neighborhood of the gravitating body to consistently explain *why* the traveling twin feels no force there. You can't just say "it's approximately SR" because there is no consistent theory of "SR plus Newtonian gravity" for the actual calculation to be an approximation to.

 

[GregAshmore]

Could you please draw the diagrams that you are describing? I'm totally confused...

I'm afraid I'm going to become the objector now. I just don't understand your reasoning. Please draw diagrams with annotations so that I can follow your line of reasoning...

If you don't doubt that these issues go away if you study my explanations, then why haven't you studied them?

If I saw that symmetrical spacetime diagram, I would not understand why you say it is invalid just because the Earth is inertial or why the valid diagram shows the case of the rocket at rest. I don't think a real objector would be persuaded by your arguments, at least I am not.

I will address the concerns you raise in regard to my analysis of the twin paradox. It will have to wait until the weekend. I will need some time to do a proper job of it; it may not be finished until some time next week.

As to why I have not studied your diagrams, it is my intention to do that, as well read the material that DaleSpam has recommended. It hasn't happened yet due to time constraints. My evenings have been consumed with thinking about the comments directed to me and putting together what I believe to be accurate responses.

 

[harrylin]

Actually, no. SR, for a non-gravitational turnaround makes an exact prediction. It also makes an exact prediction for a twin that is undergoing uniform acceleration the whole time. These predictions are correct, so far as is known (e.g. from accelerator experiments).

The standard "twin" paradox" examples are like Langevin1911 and Einstein1918 with a stay-at-home on Earth, neglecting effects form its gravitation, and assuming negligibly fast turn-around. That is done on purpose, as it's not a sophisticated calculation exercise but an illustration to explain how SR works.

That's done just to simplify the example. It's not a fundamental assumption of the explanation. [..]we use the latter when the details of the turnaround aren't important to the problem at hand

The "twin" example was meant to illustrate the effect of changing direction (acceleration) according to SR. Indeed, the details of the turnaround aren't relevant for that illustration.

 

[Dale]

The "twin" example was meant to illustrate the effect of changing direction (acceleration) according to SR. Indeed, the details of the turnaround aren't relevant for that illustration.

The details are relevant when gravity is used for the turnaround since doing so puts the scenario outside the domain of applicability of SR.

 

[harrylin]

The details are relevant when gravity is used for the turnaround since doing so puts the scenario outside the domain of applicability of SR.

For me and most people a theory is applicable if the estimated error is acceptably small; stevendaryl gave a good elaboration in post #214.
Let's stop the nitpicking: GregAshmore will already find it difficult to find back the for him interesting posts in this thread!

 

[Dale]

For me and most people a theory is applicable if the estimated error is acceptably small; stevendaryl gave a good elaboration in post #214.
Let's stop the nitpicking: GregAshmore will already find it difficult to find back the for him interesting posts in this thread!

I agree, but the error in the accelerometer reading becomes arbitrarily large as the error in the clock reading becomes arbitrarily small. Both readings are important to the resolution of the scenario.

 

[harrylin]

I agree, but the error in the accelerometer reading becomes arbitrarily large as the error in the clock reading becomes arbitrarily small. Both readings are important to the resolution of the scenario.

?? Ideal instrument readings have no error and the scenario doesn't make use of an accelerometer in the capsule, nor does it need it. Please present your issues as a topic in a new thread.

 

[Dale]

?? Ideal instrument readings have no error and the scenario doesn't make use of an accelerometer in the capsule, nor does it need it.

No, the theory (SR) makes errors predicting what ideal instruments would read in the gravitational-turnaround scenario. The accelerometer is the usual method used to identify the asymmetry between the traveling twin and the homebound twin in SR. That error (SR predicted accelerometer) is unbounded as the other error (SR predicted clock) is minimized when using SR as an approximate theory to analyze a gravitational turn around scenario.

 

[stevendaryl]

Only in a very limited subset of such cases: where the portion of the traveling twin's trajectory that is affected by gravity is very small compared to the total trajectory.

I had the idea that that was the intention behind Langevin's thought experiment.

And even then you need spacetime curvature in the neighborhood of the gravitating body to consistently explain *why* the traveling twin feels no force there. You can't just say "it's approximately SR" because there is no consistent theory of "SR plus Newtonian gravity" for the actual calculation to be an approximation to.

The calculation is an ad hoc amalgam of SR and gravity theory. That's true of most (all?) cases in which someone uses a theory to predict what happens in the real world. There will be aspects of the real world that aren't covered by the theory (or whose calculation from first principles is intractible). In those cases, it's actually quite common to split the problem up into subproblems, some of which can be handled using one theory, and some of which require a different (possibly purely phenomenological) theory.

 

[stevendaryl]

No, the theory (SR) makes errors predicting what ideal instruments would read in the gravitational-turnaround scenario. The accelerometer is the usual method used to identify the asymmetry between the traveling twin and the homebound twin in SR. That error (SR predicted accelerometer) is unbounded as the other error (SR predicted clock) is minimized when using SR as an approximate theory to analyze a gravitational turn around scenario.

I'm not sure what you mean by saying that the error is unbounded.

Look, if you took seriously the sorts of objections that are being made to Langevin's calculation, then SR would have been a theory without any empirical content in 1905. It wouldn't make any predictions at all, since it is only valid when the effects of gravity are negligible, and without a theory of gravity, you can't say whether the effects of gravity are negligible. So SR couldn't be used to calculate anything in the real world.

Similarly, in 1915 GR could not be used to calculate any real-world effects, because GR ignores quantum mechanics, and until you have a quantum theory of gravity, you can't precisely say under what circumstances quantum effects are negligible.

And quantum mechanics in 1925 would have no testable consequences, since it neglected relativity, and without a relativistic theory of quantum mechanics, you can't say precisely what the error is from ignoring relativity.

And so forth. No theory would have any testable consequences unless it's the ultimate theory of everything, because without such a theory of everything, you could never say under what circumstances a partial theory was applicable.

The way that this Gordian knot is cut is by trying to develop rules of thumb for the circumstances in which a theory is applicable, and ways to estimate the size of errors due to phenomena not covered by the theory. So any "pure" theory, if it is to have any empirical content at all, must be accompanied by a more-or-less ad hoc theory of the domain of applicability and the order of magnitude of errors. People can call this supplementary theory "hand waving", but it's absolutely critical in empirical science. Without it, science doesn't apply to the real world, at all.

 

[PeterDonis]

The calculation is an ad hoc amalgam of SR and gravity theory.

Yes, an inconsistent and therefore invalid one.

That's true of most (all?) cases in which someone uses a theory to predict what happens in the real world. There will be aspects of the real world that aren't covered by the theory (or whose calculation from first principles is intractible). In those cases, it's actually quite common to split the problem up into subproblems, some of which can be handled using one theory, and some of which require a different (possibly purely phenomenological) theory.

Yes, but there's a difference between using a provisional treatment of a subproblem that is later validated by a deeper theory, and using a provisional treatment of a subproblem that turns out to be inconsistent and invalid once we have the deeper theory. Langevin's treatment is case of the latter, not the former.

 

[Dale]

What does happen in the limit is this:

Connection coefficients in GR → Newtonian gravitational field + fictitious forces

There is no good way (as far as I know) in GR to tease apart exactly the quantities that become the Newtonian gravitational field in the nonrelativistic limit, except in special cases such as spherical symmetry.

I was thinking about this comment. You are correct, that there is no way to tease them apart in GR. I think that is essentially the content of the equivalence principle. The Newtonian gravitational field is equivalent to a fictitious force per GR, and so they are subsumed into a single quantity in GR.

 

[Dale]

I'm not sure what you mean by saying that the error is unbounded.

As you make your \delta \tau small the SR predicted accelerometer reading becomes large while the actual accelerometer reading remains 0.

Look, if you took seriously the sorts of objections that are being made to Langevin's calculation, then SR would have been a theory without any empirical content in 1905. It wouldn't make any predictions at all, since it is only valid when the effects of gravity are negligible, and without a theory of gravity, you can't say whether the effects of gravity are negligible. So SR couldn't be used to calculate anything in the real world.

Einstein and others had to make assumptions about which situations they believed gravity was important and which they believed gravity was not important. Often they were wrong, as Einstein in his 1905 paper with the example of the clock at the pole and equator and Langevin with his gravitational twin paradox. Luckily scientists were able to find a large number of experiments where gravity is negligible in order to empirically verify SR and establish its domain of applicability.

And so forth. No theory would have any testable consequences unless it's the ultimate theory of everything, because without such a theory of everything, you could never say under what circumstances a partial theory was applicable.

I think you are getting things backwards here. The experiments are what determine the domain of applicability, not later theories. You don't need another theory to tell you that your current theory is/is not applicable, all you need is measurements that agree/disagree with your theory.

The way that this Gordian knot is cut is by trying to develop rules of thumb for the circumstances in which a theory is applicable, and ways to estimate the size of errors due to phenomena not covered by the theory. So any "pure" theory, if it is to have any empirical content at all, must be accompanied by a more-or-less ad hoc theory of the domain of applicability and the order of magnitude of errors. People can call this supplementary theory "hand waving", but it's absolutely critical in empirical science. Without it, science doesn't apply to the real world, at all.

OK. According to the Ad-Hoc Domain Of Applicability Theory for SR (AHDOAT-SR), Langevin's example is outside the DOA. The fact that AHDOAT-SR was insufficiently developed for Langevin or Einstein to know is certainly a good reason for us to excuse them for their understandable mistake, but it is certainly not a good reason to repeat the mistake ourselves.

 

[stevendaryl]

I think you are getting things backwards here. The experiments are what determine the domain of applicability, not later theories.

I agree with that; it seemed to me that other people were saying that Langevin's derivation required some kind of theoretical justification. I was pointing that that didn't make any sense, because you would need a theory of everything before you could ever apply any theory.

OK. According to the Ad-Hoc Domain Of Applicability Theory for SR (AHDOAT-SR), Langevin's example is outside the DOA.

I don't think it is. Look, we have plenty of experience with clocks circling a gravitating star, because all of our clocks do that. To the extent that SR has any relevance in our solar system, it has to be the effects of the sun's gravity can be bounded. Before GR, people used SR to explain the Michelson-Morley experiment, which certainly took place in a gravitational field. If the presence of a gravitational field makes SR inapplicable, then it was never applicable.

 

[PAllen]

I don't think it is. Look, we have plenty of experience with clocks circling a gravitating star, because all of our clocks do that. To the extent that SR has any relevance in our solar system, it has to be the effects of the sun's gravity can be bounded. Before GR, people used SR to explain the Michelson-Morley experiment, which certainly took place in a gravitational field. If the presence of a gravitational field makes SR inapplicable, then it was never applicable.

An experiment like Langevin's was never done, and still hasn't been done, so actually neither he nor us really knows the result of such experiment.

I pointed out that earthbound experiments and specifically comparison of orbit versus hovering at an approximately constant distance from sun, and approximately constant distance from Earth's center really are immune to substantial gravitational time dilation effects. The theoretical justification (nearly constant gravitational potential) need not be known to observe this fact.

A stellar flyby is not so immune. I do think the idea of bounding this, and swamping it with very long 'near inertial' travel is valid. However, the flyby, taken by itself, is actually very substantially affected by gravitational time dilation, because you have rapid change of potential. For highly elliptical orbits, gravitational time dilation swamps SR kinematic effects.

 

[Dale]

I don't think it is.

Of course it is. SR predicts a very large accelerometer reading during the turnaround, and real free falling accelerometers read 0.

Look, we have plenty of experience with clocks circling a gravitating star, because all of our clocks do that. To the extent that SR has any relevance in our solar system, it has to be the effects of the sun's gravity can be bounded. Before GR, people used SR to explain the Michelson-Morley experiment, which certainly took place in a gravitational field. If the presence of a gravitational field makes SR inapplicable, then it was never applicable.

Not every measurement in every scenario is sensitive to gravity. This one is.

I am not making a claim that SR is inapplicable in every scenario where there is any gravity present. It is inapplicable in the twin paradox, for the reasons I stated above.

 

[PeterDonis]

it seemed to me that other people were saying that Langevin's derivation required some kind of theoretical justification.

I was not trying to say Langevin's derivation required extra justification at the time he made it; he was basically making a bet that a theory of gravity of the sort he was thinking of would be consistently possible.

I was only saying that that does not allow us, today, knowing that the kind of theory of gravity he was thinking of is *not* consistently possible, to say that his version of the twin paradox, with the traveling twin not feeling acceleration, can be explained "just by using SR". He thought it could, but today we know it can't.

Before GR, people used SR to explain the Michelson-Morley experiment, which certainly took place in a gravitational field. If the presence of a gravitational field makes SR inapplicable, then it was never applicable.

This is a different case. The MM experiment can be analyzed entirely in a single inertial frame that covers the entire experiment. Langevin's twin paradox scenario cannot. So knowing that Langevin's scenario can't be analyzed just using SR, in the light of today's knowledge, does not imply that the MM experiment can't be analyzed just using SR, in the light of today's knowledge.

 

[GregAshmore]

[]SR predicts a very large accelerometer reading during the turnaround, and real free falling accelerometers read 0.

Not every measurement in every scenario is sensitive to gravity. This one is.

I am not making a claim that SR is inapplicable in every scenario where there is any gravity present. It is inapplicable in the twin paradox, for the reasons I stated above.

I am "getting" very little of the discussion concerning the relationship between SR, Langevin's scenario, and GR. That's not surprising, as I understand only the most basic principles of SR (and for all I know that understanding may need fine tuning), have only a vague conception of GR as a theory in which space and time curve to produce relative motion of massive objects without applied force in the presence of a gravitational field--and absolutely no knowledge of Langevin's ideas.

But this much I believe to be undeniably true of a purely SR treatment of a scenario in which two bodies, one inertial and the other non-inertial, separate from each other and then approach to reunion: the non-inertial body must experience unbalanced force at the transition from separation to approach. There is no other way for the period of separation to end. Therefore I agree with DaleSpam's statement in [my] bold, above.

I think I understand the point that even if one posits that the non-inertial twin reverses direction by "swinging around" a star, there must still be an unbalanced force--a non-zero reading on an accelerometer. The unbalanced force is due to the change of gravitational potential during the flyby. However, at this time I am unable to verify my understanding by calculation, so I have no actual opinion in the matter.

I'm about ready to sign off this thread, as the question in the OP has been answered to the extent possible with my current knowledge. My response to George's concerns will be in a new thread, as it pertains specifically to the explanation of the twin paradox, rather than to the more general question of the relativity of acceleration.

What have I learned?

1. Coordinate acceleration is relative; proper acceleration is not.

2. Proper acceleration may be experienced while at rest in a coordinate system. (This follows from 1.)

3. Loosely speaking, the experience of proper acceleration corresponds to the experience of an unbalanced force. I think this is in agreement with the definition of proper acceleration as the phenomenon that occurs when there is a non-zero reading on an accelerometer. However, I personally am not a fan of a definition of a fundamental physical phenomenon that requires the use of a mechanism. It seems to me that this leads to getting bogged down in the details of the design of the mechanism. I'd rather talk about the underlying phenomenon that the mechanism is intended to measure. In engineering, we are constantly aware of the difference between theory (the ideal) and practice (the inability to make actual conditions to correspond to the ideal). Defining proper acceleration as the reading on an instrument blurs that distinction, in my opinion.

4. Formally, proper acceleration is the derivative of proper velocity with respect to proper time. I have no idea how proper acceleration can ever be non-zero, because I cannot understand how proper velocity can ever be non-zero, if one defines proper time as the interval between two events at the same location. However, at this point in my education I am content to let this alone (for now).

5. From 3, only non-inertial bodies experience proper acceleration.

6. In the twin paradox, only the rocket twin is non-inertial. Therefore, the Earth twin must have a straight world line in a spacetime diagram, and the rocket twin must have a bent worldline. By spacetime diagram I mean a diagram that charts the coordinate (Lorentz) transformation between inertial frames. I believe this is the same thing as saying Minkowski diagram. The design of the diagram does not allow a non-inertial body to be represented by a straight worldline, nor does it allow an inertial body to be represented by a bent worldline.

7. Also from 5, and illustrated in 6, the rocket twin must experience less elapsed proper time than the Earth twin; there is no treatment of the episode in SR that can result in the Earth twin being younger than the rocket twin.

8. From all the foregoing (with special emphasis on 2), the "absoluteness" of proper acceleration does not contradict the claim of the rocket twin to be at rest throughout the episode. Therefore, the statement that proper acceleration is absolute does not have any "shocking" implications with respect to the general principle of relativity.

9. The case of the rocket twin at rest is treated in the Minkowski diagram. The typical explanation of the twin paradox does not draw attention to this fact, leaving some good-faith objectors unsatisfied with the conclusion that the Earth twin cannot be younger than the rocket twin. Further elaboration on this point will be given in the new thread that I intend to open; this will also be my response to George's concerns.

10. The discussion above is limited to the kinematics of SR. The essentially dynamic state of being non-inertial is recognized in the solution of the problem, but it is not analyzed with respect to the laws of dynamics.

11. [edited for clarity] In my mind, 10 leads to a question. In the intuitive understanding of the universe, the Earth is absolutely at rest. The Earth, as it were, is anchored in place. The impression one gets from popular books on relativity is that the intuitive understanding of the universe may legitimately be claimed by any observer: Every observer may consider himself to be anchored in place.

What are the implications of the rocket twin being anchored in place? Simply this: How is it that a force applied to the rocket causes the Earth and all the stars to move? Einstein's proposal is that a gravitational field is the cause. Granting that point for the sake of discussion, one must still ask how the rocket produces enough energy to accelerate the immense mass of the Earth and stars at the observed rate.

[Side note: This objection was alluded to by harrylin at one point in this discussion. I believe it is at the root of his claim that few physicists these days accept the idea that the rocket is "really in rest". I find it interesting in this regard (without drawing any conclusions) that DaleSpam says that most physicists these days tend to leave the question of the gravitational field in SR alone.]

Please understand that I am making no claim regarding the validity of the principle of relativity. I am merely stating the question that I wish to be able to answer, and wish (eventually) to be able to verify by calculation.

 

[Dale]

3. Loosely speaking, the experience of proper acceleration corresponds to the experience of an unbalanced force. I think this is in agreement with the definition of proper acceleration as the phenomenon that occurs when there is a non-zero reading on an accelerometer. However, I personally am not a fan of a definition of a fundamental physical phenomenon that requires the use of a mechanism. It seems to me that this leads to getting bogged down in the details of the design of the mechanism. I'd rather talk about the underlying phenomenon that the mechanism is intended to measure. In engineering, we are constantly aware of the difference between theory (the ideal) and practice (the inability to make actual conditions to correspond to the ideal). Defining proper acceleration as the reading on an instrument blurs that distinction, in my opinion.

As is common in physics, there are multiple equivalent definitions. You may prefer the definition in terms of what is called the covariant derivative. Specifically, the proper acceleration can be defined as the covariant derivative of the tangent vector to an object's worldline along the worldline.

Here is a link on covariant derivatives:
http://en.wikipedia.org/wiki/Covariant_derivative#Derivative_along_curve

It is closely related to the concept of parallel transport:
http://en.wikipedia.org/wiki/Parallel_transport

And the concept of a connection:
http://en.wikipedia.org/wiki/Levi-Civita_connection

Sorry about the hard-to-digest math. It is the price you pay for getting rid of the accelerometer definition. It doesn't add anything new (so feel free to skip it until you are ready for GR); it just defines it mathematically instead of physically.

Personally, I prefer the accelerometer one for precisely reasons that you find objectionable. One problem with defining terms in general is that since there are always a finite number of terms you must always either wind up having circular definitions or undefined terms. In physics, we get around that by defining some terms experimentally. Proper time is the thing measured by a clock, distance is the thing measured by a rod, proper acceleration is the thing measured by an acclerometer. That accomplishes two things, first, it makes the link between the mathematical theory and the physical world more clear, and second it avoids the problem of leaving those things undefined. So, I personally prefer those kinds of "measurement based" definitions of fundamental quantities, but I recongnize that is a personal preference and alternative equivalent definitions are possible which hide the problem by pushing the measurements further away or embrace the problem by leaving some things completely undefined.

How is it that a force applied to the rocket causes the Earth and all the stars to move? Einstein's proposal is that a gravitational field is the cause. Granting that point for the sake of discussion, one must still ask how the rocket produces enough energy to accelerate the immense mass of the Earth and stars at the observed rate.

As I explained to harrylin, it doesn't. If you say "A causes B" then that means that the presence of A implies B. So, if we say that "a force applied to the rocket causes the Earth and all the stars to move" that means that a force applied to the rocket implies that the Earth and all the stars must move. In an inertial frame, there may be a force on the rocket without movement of the Earth, so the force on the rocket does not imply movement of the Earth. Therefore the force on the rocket does not cause the Earth to move.

So what does cause the Earth to move? The answer is that specific choice of non-inertial coordinates. That choice of coordinates implies that the Earth moves, regardless of the presence or absence of any rockets with any forces. Every time you use that choice of coordinates the Earth moves. So the choice of coordinates causes the Earth to move, not the rocket.

 

[GregAshmore]

As is common in physics, there are multiple equivalent definitions. You may prefer the definition in terms of what is called the covariant derivative. Specifically, the proper acceleration can be defined as the covariant derivative of the tangent vector to an object's worldline along the worldline.

Here is a link on covariant derivatives:
http://en.wikipedia.org/wiki/Covariant_derivative#Derivative_along_curve

It is closely related to the concept of parallel transport:
http://en.wikipedia.org/wiki/Parallel_transport

And the concept of a connection:
http://en.wikipedia.org/wiki/Levi-Civita_connection

Sorry about the hard-to-digest math. It is the price you pay for getting rid of the accelerometer definition. It doesn't add anything new (so feel free to skip it until you are ready for GR); it just defines it mathematically instead of physically.

Personally, I prefer the accelerometer one for precisely reasons that you find objectionable. One problem with defining terms in general is that since there are always a finite number of terms you must always either wind up having circular definitions or undefined terms.

I hadn't thought about definitions enough to realize this.

In physics, we get around that by defining some terms experimentally. Proper time is the thing measured by a clock, distance is the thing measured by a rod, proper acceleration is the thing measured by an acclerometer. That accomplishes two things, first, it makes the link between the mathematical theory and the physical world more clear, and second it avoids the problem of leaving those things undefined. So, I personally prefer those kinds of "measurement based" definitions of fundamental quantities, but I recongnize that is a personal preference and alternative equivalent definitions are possible which hide the problem by pushing the measurements further away or embrace the problem by leaving some things completely undefined.

Fair enough. But this may also lead to problems. For example, if proper time is measured by a clock, what is the proper time for the life of an individual particle? What clock do we read to measure its proper life span? This is of particular importance with regard to SR, as experiments with high speed particles are offered as evidence in support of the theory. We do not send a clock to accompany the particle on its journey in the accelerator. It seems to me that one is reduced to claiming that the particle is itself the clock. But if the particle is itself the clock, then there is no independent measure of the proper time that the particle existed, and thus no verification of the theory. There is no question that high speed particles live longer, as measured from our perspective. The question would be whether time in the rest frame of the particle is the same regardless of the speed of the particle measured in some other inertial frame, as the theory of SR requires. (I need to think about this some more; perhaps my logic is not entirely sound.)

As I explained to harrylin, it doesn't. If you say "A causes B" then that means that the presence of A implies B. So, if we say that "a force applied to the rocket causes the Earth and all the stars to move" that means that a force applied to the rocket implies that the Earth and all the stars must move. In an inertial frame, there may be a force on the rocket without movement of the Earth, so the force on the rocket does not imply movement of the Earth. Therefore the force on the rocket does not cause the Earth to move.

So what does cause the Earth to move? The answer is that specific choice of non-inertial coordinates. That choice of coordinates implies that the Earth moves, regardless of the presence or absence of any rockets with any forces. Every time you use that choice of coordinates the Earth moves. So the choice of coordinates causes the Earth to move, not the rocket.

Before I give you my initial reaction, I will tell that I intend to think carefully about what you say. It may be that my initial reaction is merely the expression of prejudice.

My initial reaction is: Nonsense. I'm sitting at rest in my rocket the whole time. Don't tell me about choosing coordinate frames--there is only one coordinate frame that matters: mine. (Isn't that the meaning of "absolute space", or "anchored in place"?) When I throw a ball, its acceleration (with respect to the only coordinate system that matters) is determined by its mass and the magnitude of the applied force. When the Earth and the stars move, the same law should apply. {Edit: Not exactly the same law. I realize that gravity will cause coordinate acceleration without applied force. But the moving Earth and stars have acquired kinetic energy with respect to the rocket. That energy must have come from somewhere.}

A secondary (and less emotional) reaction is to ask the original question in a more precise way. What causes the spatial displacement between the rocket and the Earth to change?

 

[Drmarshall]

What statement of mine are you referring to in post #161?

It seems to me you guys are just playing with words - proper, real, coordinate.
Try defining them before hitting one another on the head with them!

I always thought position was x,y,z - whatever they are, they are relative.
And velocity is their first differential with respect to time - so is relative.
And acceleration is the second differential of relative things - so is also relative.

Yes you can invent a special acceleration and use the word "proper" for it.
But how can you MEASURE it in an experiment?
As for "force" it can never be applied to anything without that thing witstanding it (unless it fractures) Hence "action and reaction are equal and opposite" whether acceleration results or not. So the net force at an SURFACE sums to zero!
As for the idea of force "applied at the centre of an object" there is no way to measure it except by the ASSUMPTION that force is mass times "acceleration"

When I stand here on the floor, my acceleration is 32 ft/sec^2 and it is as simple as that!
No need to dream up "force" at all. All we need is the upward acceleration required to cancel my downward acceleration. Fortunately my brain is well used to providing this acceleration.

 

[ghwellsjr]

What statement of mine are you referring to in post #161?

It seems to me you guys are just playing with words - proper, real, coordinate.
Try defining them before hitting one another on the head with them!

I always thought position was x,y,z - whatever they are, they are relative.
And velocity is their first differential with respect to time - so is relative.
And acceleration is the second differential of relative things - so is also relative.

Yes you can invent a special acceleration and use the word "proper" for it.
But how can you MEASURE it in an experiment?
As for "force" it can never be applied to anything without that thing witstanding it (unless it fractures) Hence "action and reaction are equal and opposite" whether acceleration results or not. So the net force at an SURFACE sums to zero!
As for the idea of force "applied at the centre of an object" there is no way to measure it except by the ASSUMPTION that force is mass times "acceleration"

When I stand here on the floor, my acceleration is 32 ft/sec^2 and it is as simple as that!
No need to dream up "force" at all. All we need is the upward acceleration required to cancel my downward acceleration. Fortunately my brain is well used to providing this acceleration.

Why are you dragging me into this? What did I say?

 

[PAllen]

It seems to me you guys are just playing with words - proper, real, coordinate.
Try defining them before hitting one another on the head with them!

I always thought position was x,y,z - whatever they are, they are relative.
And velocity is their first differential with respect to time - so is relative.
And acceleration is the second differential of relative things - so is also relative.

Yes you can invent a special acceleration and use the word "proper" for it.
But how can you MEASURE it in an experiment?.

Your last statement gets at exactly why relativity required new definitions. Precisely when proper acceleration, defined as covariant derivative by proper time along a world line, differs from derivative if (x,y,z) by t, then experiments (using accelerometers) measure proper acceleration and DO NOT measure what you define as acceleration. Similarly, proper time is what clocks measure, NOT the time coordinate difference in some coordinate system.

 

[stevendaryl]

It seems to me you guys are just playing with words - proper, real, coordinate.
Try defining them before hitting one another on the head with them!

I always thought position was x,y,z - whatever they are, they are relative.

The modern way of thinking about it is that a position, such as a location on Earth, is absolute. The top of the Eiffel Tower is a definite spot; there is no ambiguity, or relativism involved. But there are infinitely many coordinate systems that can be used to specify a position.

In relativity, the primary thing is not a position, but an event, a point in space and time. So "the top of the Eiffel tower when Michelle Obama went up it" is an event, and it's absolute. But if I try to describe it using 4 numbers, for example, (latitude, longitude, altitude in meters, time in seconds since 1900), its description is relative to a coordinate system.

A spacetime path, giving the events that a traveler passes through, as a function of the time on his watch, is an absolute thing, because each event is absolute. But to describe the path as a set of 4 functions x(\tau), y(\tau), z(\tau), t(\tau) is relative to a choice of a coordinate system.

The proper velocity of a path is again an absolute thing, while the components of the proper velocity are relative to a coordinate system. Proper acceleration is an absolute thing, while its components are relative to a coordinate system.

Yes you can invent a special acceleration and use the word "proper" for it.
But how can you MEASURE it in an experiment?

Yes, with the notion of "proper acceleration" used in General Relativity, one can measure its magnitude with an accelerometer. A simple accelerometer can be constructed by just taking a cubic box, putting a metal ball in the center, and then connecting the ball to the sides of the box using 6 identical springs. If the ball is exactly in the center, then the box has no proper acceleration. If the ball is closer to one wall, then the box is accelerating in the direction of the opposite wall.

 

[TrickyDicky]

The modern way of thinking about it is that a position, such as a location on Earth, is absolute. The top of the Eiffel Tower is a definite spot; there is no ambiguity, or relativism involved. But there are infinitely many coordinate systems that can be used to specify a position.

That is not the modern way, that is Newton's way, unless you consider Newton's the modern way of thinking (but we're not in the eighteenth century anymore, remember?). Anyway the rest of your post gets it right that the more modern relativist thinking considers events in space time rather that position in space as absolute, so I don't know what you meant by this introduction.

 

[Nugatory]

That is not the modern way, that is Newton's way, unless you consider Newton's the modern way of thinking (but we're not in the eighteenth century anymore, remember?). Anyway the rest of your post gets it right that the more modern relativist thinking considers events in space time rather that position in space as absolute, so I don't know what you meant by this introduction.

I must confess that I'm not reading Stevendaryl's point the way you are. The top of the Eiffel tower absolutely and unambiguously identifies a particular absolute coordinate-independent timelike worldline - and you'll notice that Stevendaryl carefully avoided identifying a "position" with a point in classical three-space.

 

[stevendaryl]

That is not the modern way, that is Newton's way, unless you consider Newton's the modern way of thinking (but we're not in the eighteenth century anymore, remember?). Anyway the rest of your post gets it right that the more modern relativist thinking considers events in space time rather that position in space as absolute, so I don't know what you meant by this introduction.

A position on the earth is absolute. A position in space isn't.

The Earth is a 3D object, while space is 4D in the modern way of looking at it.

 

[PeterDonis]

When I throw a ball, its acceleration (with respect to the only coordinate system that matters) is determined by its mass and the magnitude of the applied force.

Really? When you, standing on the surface of the Earth, throw a ball upward, its motion is determined purely by its mass and the force you apply? Then why does it come back down?

When the Earth and the stars move, the same law should apply. {Edit: Not exactly the same law. I realize that gravity will cause coordinate acceleration without applied force. But the moving Earth and stars have acquired kinetic energy with respect to the rocket. That energy must have come from somewhere.}

The ball changes its kinetic energy with respect to you even though you didn't exert any additional force on it; at some point in its trajectory, it is momentarily motionless with respect to you (up in the air at the instant it stops rising and starts falling back). Where did the kinetic energy you gave the ball go?

You give away the problem with the position you are trying to take when you say "not exactly the same law". That's just the point: if you want "the laws of physics" to be "the same" in all reference frames, so that you can always view yourself "at rest", then the laws of physics have to include counterintuitive things like the Earth and the stars changing direction and speed just because you fired your rocket engine. If you want the laws of physics to always look simple, then you have to restrict yourself to frames in which they look simple (because all the counterintuitive stuff cancels out in those frames). You can't have it both ways; you can't have both simple-looking laws *and* a free choice of frames; your choice of frames determines how simple the laws look in the frames you choose.