Implications of the statement Acceleration is not relative

[harrylin]

Some links would help. I don't remember that discussion.

Done.

What Einstein said by way of defining inertial frame was in his 1905 paper: [..] Presumably, since he is suggesting a modification to Newtonian mechanics, he means "approximately", in the low-velocity limit. [..]

Indeed, SR is defined wrt the same reference systems as Newton's mechanics.

The way I interpreted Einstein's words are that an inertial coordinate system satisfies:
[*] Objects that are not acted upon by physical, external forces travel so that $\dfrac{d^2 x}{dt^2} = \dfrac{d^2 y}{dt^2} = \dfrac{d^2 z}{dt^2} = 0$[..]

Not sure if you mean that correctly; a coordinate system of reference is not "objects". For example the surface of the Earth is approximately a valid "Galilean" reference frame (neglecting its rotation and orbit), in which a cannon ball is acted upon by the force of gravity in accordance with Newton's second law. That is a classical textbook example of motion wrt to a valid reference system for classical mechanics, as your second point also stresses:

[*]For objects moving slowly compared with the speed of light, the response of an object to a physical external force $\vec{F}$ is given (approximately, ignoring correction terms of order $\dfrac{v^2}{c^2}$) by $F^i = m \dfrac{d^2 x^i}{dt^2}$
[..]
These conditions characterize an inertial Cartesian coordinate system. They imply that an accelerometer at rest in that coordinate system will show no acceleration.

It may however show gravitational force.

But the other way around may not be true. An accelerometer at rest showing no acceleration doesn't imply that your coordinate system is an inertial Cartesian coordinate system.

Right - as illustrated by Langevin. Note that neither he or Einstein would call that "at rest" (without qualifier) in the context of SR.

 

[stevendaryl]

Not sure if you mean that correctly; a coordinate system of reference is not "objects".

I didn't say otherwise. But the path of an object that is not acted on by any force can be described using a coordinate system, and if that coordinate system happens to be an inertial Cartesian coordinate system, then the path $x^i(t)$ will satisfy

$\dfrac{d^2 x^i}{dt^2} = 0$

For example the surface of the Earth is approximately a valid "Galilean" reference frame (neglecting its rotation and orbit), in which a cannon ball is acted upon by the force of gravity in accordance with Newton's second law.

I don't see how that contradicts what I said. Of course, if you think of gravity as a force, then you get one inertial coordinate system, and if you don't think of it as a force, then you get a different inertial coordinate system.

That is a classical textbook example of motion wrt to a valid reference system for classical mechanics, as your second point also stresses:

It may however show gravitational force.

So are you saying that whether or not an accelerometer correctly identifies an inertial frame depends on whether you consider gravity to be a force or not?

 

[harrylin]

Physical explanation of what? You never clarified exactly what you thought he meant by "gravitational field", and he wasn't explicit about it. Until you have defined your terms you are just giving physical explanations of flubnubitz.

It strikes me now that, incredible as this is to me, you actually have no idea what Einstein or his critics were discussing... Basically the whole clock paradox is flubnubitz for you.

I feel like a policeman at a crossroad who shouts at a motorist to stay put - the motorist speeds away and after a chase he's arrested. To his defence the guy states that he stayed put on his bike. and it turns out that he's an English teacher. What to think? Can such a lack of understanding really exist, or is the biker just trying to talk his way out of it by stripping the term from its obviously intended contextual meaning?

The firing of the rocket engine doesn't move the rest of the universe, the choice of coordinates does. The state of motion or rest is a coordinate-dependent quantity. Do you disagree that I can give any object any velocity profile I like simply by choosing the coordinates appropriately?

While I certainly agree with the second sentence, the first one is plain nonsense to me: your choice of coordinates cannot physically move (affect) the universe. "In rest" has in this context the physical meaning that the laws of nature are valid wrt the object; its state of motion is null. Only a force can change its state of motion. We can ascribe a different state of motion to the object by a different choice of reference system; however you can of course not affect my state of motion by changing your choice of coordinates - imaginations of our brains cannot physically affect objects. That is what Einstein clarified as I mentioned to you earlier already in this thread:

To be sure, the accelerated coordinate systems cannot be called upon as real causes for the field, an opinion that a jocular critic saw fit to attribute to me on one occasion.

 

[harrylin]

I didn't say otherwise. [..] Of course, if you think of gravity as a force, then you get one inertial coordinate system, and if you don't think of it as a force, then you get a different inertial coordinate system. [..]

Yes indeed, that's what I meant.

So are you saying that whether or not an accelerometer correctly identifies an inertial frame depends on whether you consider gravity to be a force or not?

I gave 4 ways of identifying an inertial frame in SR, incl. how to interpret an accelerometer in that context. Isn't that all very basic, elementary physics??

As this is probably deviating from GregAshmore topic, I'll limit myself to this.

 

[Dale]

ADDENDUM: see
https://www.physicsforums.com/showthread.php?p=4117808
In post #190 I provided three operational ways with which such reference frames can be defined/determined.
See also post #200 there and a 4th defintion (by Einstein) in post #264:
https://www.physicsforums.com/showpost.php?p=4122201&postcount=264

In post #190 the first definition was "Newton defined it as in uniform straight line motion wrt the 'fixed stars'" which of course is a bad definition since the stars aren't fixed (which Newton couldn't have known at the time).

The second definition was "the definition of inertial motion at places far away from massive bodies". Simply being away from massive bodies doesn't give you an inertial frame, so this definition is incomplete and would require something like an accelerometer to complete it.

I didn't see a third definition.

The fourth definition was "coordinate systems relative to which sufficiently isolated, material points move in straight lines and uniformly". That is an equivalent definition to the accelerometer definition. Any way that you can think of determining whether or not a material point is "sufficiently isolated" winds up being an experiment to whether or not its proper acceleration is 0, hence an accelerometer.

 

[Dale]

What to think? Can such a lack of understanding really exist, or is the biker just trying to talk his way out of it by stripping the term from its obviously intended contextual meaning?

So, in your opinion, what is the "gravitational field's" obviously intended contextual meaning? In my opinion, it is the Christoffel symbols, but you seem to have a different opinion that you are strangely secretive about.

While I certainly agree with the second sentence, the first one is plain nonsense to me

Then you are being logically inconsistent. The second sentence implies the first.

"In rest" has in this context the physical meaning that the laws of nature are valid wrt the object; its state of motion is null.

Well, this is probably the source of the confusion. You are using terms in non-standard ways. The term "at rest" simply means v=dx/dt=0, and the term "moving" simply means v=dx/dt≠0.

Since the laws of nature can be written in a coordinate independent form they are valid wrt any object, so according to your definition all objects are "in rest".

 

[PeterDonis]

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.

Ah, I see that instead of changing the topology of spacetime, Langevin changes its curvature to allow the traveling twin to return without feeling any force. This scenario could not be set up in flat spacetime as he sets it up, because in flat spacetime there is no gravity, so an encounter with a star could not turn the traveling twin around while still having him feel no force.

 

[GregAshmore]

The phrase "appears to turn around" (emphasis added) seems to refer to coordinate acceleration, in which case it would not be true that all observers must agree on it. If you intended the statement to refer to proper acceleration then it is a little confusing.

I think that GregAshmore understands the distinction between coordinate and proper acceleration, so I think that the rest is just miscommunication about which "flavor" of acceleration is being discussed at anyone moment.

Correct. I meant coordinate acceleration.

 

[GregAshmore]

So because my spacetime diagrams only show one frame instead of the two that are more commonly shown in a Minkowski diagram, that prevented you from grasping what I was presenting, correct? But now that you realize the difference, does post #23 make perfect sense to you? Could you use it with further explanation to get your son to understand what I was presenting there?

No, it was not that only one frame was shown. It was the description of the rocket as moving. The application of motion words to the rocket is a trigger. The objector is under the mistaken impression that if the rocket does not move, the traveling Earth twin will be younger on reunion. All talk about inertial vs. non-inertial is not exactly denied; it is just ineffective. He feels he is entitled to a review of the case in which the rocket is stationary; he wants to see how it works out. Any description of the rocket as moving triggers the rejection of the explanation and the repeat of the objection: I want to see the case in which the rocket is stationary.

It is difficult to avoid motion words. As you observed, I tried to use neutral descriptors, so that I did not give the reader any room to infer that one or the other object is "really" moving. And, as you also observed, I did not fully succeed. I will revise the text, because I think it is important, in this problem more than others, to avoid the "motion" trigger.

Are you talking about this one spacetime diagram?

No, I mean the ordinary spacetime diagram, the one showing the Earth's worldline as a single line segment, and the rocket's worldline as two line segments, forming a triangle.

The "aha" moment for me was the realization that this spacetime diagram shows both cases at once. The worldline of the Earth shows the Earth at rest in its inertial frame; that same worldline shows the Earth moving relative to the rocket's inertial frames. Similarly, the two worldlines of the rocket show the rocket in motion with respect to the Earth's inertial frame, and at rest in its two inertial frames.

So, when the objector says, "I want to see the case in which the rocket is at rest", the response can be, "We have that case already in front of us, in the spacetime diagram that we have been studying."

This will come as a surprise to the objector. He believes that the only way to show the rocket at rest is with one line segment.

Having gotten his attention, it can now be shown that the rocket is indeed at rest in its inertial frame during separation, just as the Earth is at rest in its inertial frame.

When the separation ends and approach begins, a choice must be made. One or the other object must change frames. It would be helpful, I think, to show provisionally the Earth changing frames, with the worldline drawn to the "northeast" to meet the rocket, which continues along its original line. This is where the inertial/non-inertial distinction becomes meaningful to the objector. It can be pointed out that Earth is (or would be) at rest in this new inertial frame, just as it was in the original inertial frame. But the Earth cannot change inertial frames, because it is inertial throughout--the Earth twin feels no unbalanced force.

The rocket does feel an unbalanced force; it is non-inertial. It can therefore change inertial frames. But it does not move in its frame, even during the period of "non-inertiality"; its coordinate is zero throughout.

Now the objector (this one, at least) has not only seen the case of the stationary rocket, he understands why the inertial/non-inertial distinction proves that the rocket twin must be younger, and the Earth twin cannot be younger.

If so, wouldn't it have been just as confusing to you if you had not previously figured out that it was not a conventional Minkowski diagram with two frames in it?

The drawing was confusing, but not because it has only one frame. (Arguably it has four, though without axes shown for two?) It is not clear why the Earth's worldline has three segments. Also, it is not obvious why the timing of received light signals is important to the argument. I don't doubt that these issues go away if your explanation is studied with due diligence. It's just that by the time I got that far (in the first reading), I was already overloaded with detail, and fighting the "motion trigger" reflex.

What are you calling a symmetrical diagram? A Minkowski diagram? And why would it be invalid? And why is it not needed? Now I'm confused.

Consider the valid triangular spacetime diagram: the Earth's single-segment worldline is drawn vertically; the rocket's bent worldline is on the right. The symmetrical diagram has the rocket's worldline drawn vertically, and the Earth's bent worldline on the left. That is the diagram the objector expects to see in the case that the rocket is stationary. It is invalid because the Earth in inertial. It is not needed because the valid diagram shows the case of the rocket at rest.

 

[my_wan]

The phrase "appears to turn around" (emphasis added) seems to refer to coordinate acceleration, in which case it would not be true that all observers must agree on it. If you intended the statement to refer to proper acceleration then it is a little confusing.

The term "appears" was in effect quoted from GregAshmore post stating "either object can be the one that appears to turn around". In essence I was objecting to the same thing you are here.

I think that GregAshmore understands the distinction between coordinate and proper acceleration, so I think that the rest is just miscommunication about which "flavor" of acceleration is being discussed at anyone moment.

That's what I thought to, but still not sure why previous responses have not resolved the issue.

 

[GregAshmore]

For a last time, as we've been here twice before: everyone can always claim to be at rest in his own frame

Yes. That is the practical meaning of the principal of relativity. "I am at rest. At rest in this position, I will deduce from observation the laws of physics. Those laws will be of the same form as the laws developed by all other resting observers, no matter the type of their motion with respect to me." {Edit: I made a statement similar to this a week or so ago. I seem to remember it was corrected. I'll stand by the gist of it, even if it is not correct in every technical particular. I could look up Einstein's exact words for GR, but I don't think it necessary to make my point.}

such a statement cannot be disproved.

Of course it can. Show that I have moved with respect to an absolute position marker, and you have disproved the claim. Show that the claim violates a law of physics, and you have disproved the claim. For example, the claim that the rocket is at rest requires some cause for the Earth's coordinate acceleration, its reversal of motion. If there is no cause, then the claim that the rocket is at rest is proven wrong. You yourself have argued against the claim that the rocket is at rest in its non-inertial frame on the grounds that a change of coordinates alone cannot cause the reversal of the earth.

You could just as well state that you're in your own world. That's physically meaningless.

See above.

 

[Dale]

For example, the claim that the rocket is at rest requires some cause for the Earth's coordinate acceleration, its reversal of motion. If there is no cause, then the claim that the rocket is at rest is proven wrong. You yourself have argued against the claim that the rocket is at rest in its non-inertial frame on the grounds that a change of coordinates alone cannot cause the reversal of the earth.

Why not? The change of coordinates causes coordinate acceleration and reverses the coordinate velocity of the earth. What is in the least bit objectionable about any of that?

 

[Dale]

The drawing was confusing, ... It is not clear why the Earth's worldline has three segments. Also, it is not obvious why the timing of received light signals is important to the argument.

Those are both answered here:
http://arxiv.org/abs/gr-qc/0104077

The importance of the timing of the signals is described on page 3 in the section "Radar Time and Radar Distance". The three segments are explained on pages 7 and 8 in the section "Gravity Doesn't Matter".

 

[GregAshmore]

Why not? The change of coordinates causes coordinate acceleration and reverses the coordinate velocity of the earth. What is in the least bit objectionable about any of that?

I didn't actually make that argument. (Not in this thread, at least.) Nor do I wish to participate in the argument--it goes against the new rule of me not making statements that I can't verify by calculation.

 

[Dale]

I didn't actually make that argument.

My apologies, I got confused with the back and forth.

 

[harrylin]

Yes. [everyone can always claim to be at rest in his own frame] is the practical meaning of the principal of relativity. "I am at rest.
At rest in this position, I will deduce from observation the laws of physics. Those laws will be of the same form as the laws developed by all other resting observers, no matter the type of their motion with respect to me."

No to your first sentence, yes to your next sentences; obviously this is a matter of careful formulation. One can always design a reference system relative to which one is in rest. That fact is generic (valid for all theories) and has nothing to do with the PoR. The PoR concerns laws of nature.

[..] the claim that the rocket is at rest requires some cause for the Earth's coordinate acceleration, its reversal of motion. If there is no cause, then the claim that the rocket is at rest is proven wrong. You yourself have argued against the claim that the rocket is at rest in its non-inertial frame on the grounds that a change of coordinates alone cannot cause the reversal of the earth.

The rocket is certainly "at rest in its non-inertial frame", but yes you seem to understand what Einstein meant with "in rest".

 

[ghwellsjr]

I want to see the case in which the rocket is stationary.

Are you talking about this one spacetime diagram?

No, I mean the ordinary spacetime diagram, the one showing the Earth's worldline as a single line segment, and the rocket's worldline as two line segments, forming a triangle.

Ok, then are you talking about this spacetime diagram?

I thought we agreed that my diagrams show only one frame with Earth as the blue line and the rocket as the red line. So now I need an "aha" moment in order to understand what follows:

The "aha" moment for me was the realization that this spacetime diagram shows both cases at once. The worldline of the Earth shows the Earth at rest in its inertial frame; that same worldline shows the Earth moving relative to the rocket's inertial frames. Similarly, the two worldlines of the rocket show the rocket in motion with respect to the Earth's inertial frame, and at rest in its two inertial frames.

So, when the objector says, "I want to see the case in which the rocket is at rest", the response can be, "We have that case already in front of us, in the spacetime diagram that we have been studying."

This will come as a surprise to the objector. He believes that the only way to show the rocket at rest is with one line segment.

It comes as a surprise to me.

Having gotten his attention, it can now be shown that the rocket is indeed at rest in its inertial frame during separation, just as the Earth is at rest in its inertial frame.

When the separation ends and approach begins, a choice must be made. One or the other object must change frames. It would be helpful, I think, to show provisionally the Earth changing frames, with the worldline drawn to the "northeast" to meet the rocket, which continues along its original line. This is where the inertial/non-inertial distinction becomes meaningful to the objector. It can be pointed out that Earth is (or would be) at rest in this new inertial frame, just as it was in the original inertial frame. But the Earth cannot change inertial frames, because it is inertial throughout--the Earth twin feels no unbalanced force.

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

The rocket does feel an unbalanced force; it is non-inertial. It can therefore change inertial frames. But it does not move in its frame, even during the period of "non-inertiality"; its coordinate is zero throughout.

Now the objector (this one, at least) has not only seen the case of the stationary rocket, he understands why the inertial/non-inertial distinction proves that the rocket twin must be younger, and the Earth twin cannot be younger.

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.

The drawing was confusing, but not because it has only one frame. (Arguably it has four, though without axes shown for two?)

My drawings have only one frame--didn't we agree on that? I thought the issue for you had nothing to do with my diagrams not being typical Minkowski diagrams with more than one frame depicted? I'm really confused.

It is not clear why the Earth's worldline has three segments.

It actually has five. I just didn't draw the vertical segments at the top and the bottom where the Earth and the rocket are "at rest at same position". But to understand why there are those three segments for the non-inertial diagram in which the rocket is at rest, read posts #92 and #93 of this thread.

Also, it is not obvious why the timing of received light signals is important to the argument. I don't doubt that these issues go away if your explanation is studied with due diligence. It's just that by the time I got that far (in the first reading), I was already overloaded with detail, and fighting the "motion trigger" reflex.

The timing of those all-important light signals is how the rocket twin creates the spacetime diagram. That is explained in the link in the previous post.

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

Consider the valid triangular spacetime diagram: the Earth's single-segment worldline is drawn vertically; the rocket's bent worldline is on the right. The symmetrical diagram has the rocket's worldline drawn vertically, and the Earth's bent worldline on the left. That is the diagram the objector expects to see in the case that the rocket is stationary. It is invalid because the Earth in inertial. It is not needed because the valid diagram shows the case of the rocket at rest.

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.

 

[harrylin]

So, in your opinion, what is the "gravitational field's" obviously intended contextual meaning? In my opinion, it is the Christoffel symbols, but you seem to have a different opinion that you are strangely secretive about.

Einstein was a physicist, but you try to interpret his physical explanations mathematically. 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.

[..] Well, this is probably the source of the confusion. You are using terms in non-standard ways. The term "at rest" simply means v=dx/dt=0, and the term "moving" simply means v=dx/dt≠0. Since the laws of nature can be written in a coordinate independent form they are valid wrt any object, so according to your definition all objects are "in rest".

I'll try one last time. Please explain how the Earth can be accelerated with effect back in time due to the firing of the rocket engines. Which law of nature permits that?

 

[harrylin]

Ah, I see that instead of changing the topology of spacetime, Langevin changes its curvature to allow the traveling twin to return without feeling any force. This scenario could not be set up in flat spacetime as he sets it up, because in flat spacetime there is no gravity, so an encounter with a star could not turn the traveling twin around while still having him feel no force.

No, in 1911 there was no GR. SR assumes flat spacetime and handles gravitation classically. The mistake that you ascribe to Langevin is due to you projecting modern GR concepts on him teaching SR correctly in 1911.

 

[stevendaryl]

I'll try one last time. Please explain how the Earth can be accelerated with effect back in time due to the firing of the rocket engines. Which law of nature permits that?

The modern way of saying it is that physical effects cannot propagate faster than light, but that coordinate acceleration is not (purely) physical. Coordinates are a system of book-keeping for events, and whether an object has zero or nonzero coordinate acceleration is as much a fact about your coordinate system as it is about the object. The point of introducing the notion of "proper acceleration" is to tease apart what's physical about an object's motion from what's an artifact of your coordinate system.

 

[stevendaryl]

No, in 1911 there was no GR. SR assumes flat spacetime and handles gravitation classically. The mistake that you ascribe to Langevin is due to you projecting modern GR concepts on him teaching SR correctly in 1911.

But SR, together with classical (Newtonian) gravity is inconsistent, I believe.

 

[Dale]

Einstein was a physicist, but you try to interpret his physical explanations mathematically. 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.

Yes, of course. Einstein was an excellent theoretical physicist, so he spent a great deal of time and effort to put his physical explanations into a mathematical framework. So his physical explanations refer to mathematical terms in his physical theory.

The question to you, which you continue to avoid, is which specific mathematical term in Einstein's theory do you think is he talking about when he says "gravitational field"? I think he is talking about the Christoffel symbols. You disagree, so please be explicit.

I'll try one last time. Please explain how the Earth can be accelerated with effect back in time due to the firing of the rocket engines. Which law of nature permits that?

I really enjoy the hypocrisy of your "I'll try one last time" statement. As though I have been evasive on this point at all. I answered in 109, 114, and most explicitly in 171. However, since I want to foster clear communication, I will repeat the answer again.

It is not the firing of the rocket engine which causes the (coordinate) acceleration of Earth, it is the choice of coordinates. If you used the same coordinates without a rocket then the Earth would (coordinate) accelerate just the same. If you used different coordinates with the rocket then the Earth would not (coordinate) accelerate the same. The (coordinate) acceleration of the Earth therefore depends on the choice of coordinates, and does not depend on the firing of the rocket engines.

 

[harrylin]

The modern way of saying it is that physical effects cannot propagate faster than light, but that coordinate acceleration is not (purely) physical. Coordinates are a system of book-keeping for events, and whether an object has zero or nonzero coordinate acceleration is as much a fact about your coordinate system as it is about the object. The point of introducing the notion of "proper acceleration" is to tease apart what's physical about an object's motion from what's an artifact of your coordinate system.

Yes, agreed.

 

[harrylin]

But SR, together with classical (Newtonian) gravity is inconsistent, I believe.

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 should be quite small in the given example, perhaps less than the effect of Earth's gravitation on that of the stay-at-home. Commonly that is neglected in such examples.

 

[harrylin]

[..] The question to you, which you continue to avoid, is which specific mathematical term in Einstein's theory do you think is he talking about when he says "gravitational field"? I think he is talking about the Christoffel symbols. You disagree, so please be explicit.

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.

I really enjoy the hypocrisy [SNIP]

Enough, that ends our discussions.

 

[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.