Implications of the statement Acceleration is not relative

[ghwellsjr]

Answers to questions:
Q1. Both the Earth and the rocket claim to be at rest throughout the episode. Can both make good on this claim?
Yes, kinematically. Earth and rocket X coordinates are 0.0 throughout.
Whether this makes physical sense dynamically is unknown, given limited knowledge noted above.

The Earth can claim to be at rest in an inertial frame. The rocket can claim to be at rest in a non-inertial frame.

Q2. What are the clock readings on Earth and rocket at G6?
The Earth clock reads 25.0.
The rocket clock reads 15.0.

Correct.

Q3. Are the clock readings calculated for Q2 unambiguously unique?
Yes.

Correct.

There is only one way to construct the spacetime diagram, due to the unique non-inertial behavior of the rocket.

I don't know why you would say this. Are you referring to the Earth's inertial rest frame? There are an infinite number of ways to construct spacetime diagrams for your scenario, all with different velocities with respect to each other and all just as valid and all producing the same final clock readings and the same things that each observer actually sees.

Visually, the Earth and rocket experiences are symmetric. Each sees the other move away and return. Nevertheless, the rocket is unambiguously younger than the Earth at reunion.

No, they are not symmetric. The rocket sees the Earth move away at 0.8c for a distance of 3.333 units and then remain at that distance for some time and then come back to the rocket. But the Earth sees the rocket move away at 0.8c to a distance of 10 units and then immediately start coming back. It doesn't matter what spacetime diagram you use to depict your scenario, they are all just as valid and produce the same results. The only thing that is different in them are the values of the coordinates (and the geometric shapes of the worldlines).

 

[my_wan]

Einstein tried to relativise acceleration by relativising gravitation, so that it's a matter of free opinion if a rocket accelerates or not. Nowadays few people accept that view.

In a sense I would say Einstein succeeded via the principle of equivalence, with caveats. The first problem is as PAllen stated in his objection to my use of the term "everyone". A gravitational field cannot be globally transformed away unless it is itself globally uniform. The second problem is that, even if you could, any time two inertial observers are accelerated with respect to each other a gravitational field must be involved, such that these two observer cannot be at rest with respect to each other and still be inertial. Everyone can agree that a gravitational field exist even if they may not agree on where the gravitational field is located, its geometry, etc. This issue is the reason energy conservation became so controversial in GR, but it's really more a localization issue than a conservation issue.

The break in the symmetry under both special and general relativity occurs whenever an observer enters a non-inertial state. Sitting motionless on the surface of the Earth is a non-inertial state, which is why you feel weight. By the principle of equivalence you feel this same g-force when you accelerate under special relativity, which breaks the symmetry GregAshmore is wanting to absolutely maintain, leading to his difficulties.

You cannot break this symmetry in either special or general relativity and pretend it is not broken. Once this symmetry, which applies only to inertial observers, is broken it is no longer "matter of free opinion" as to whether it is broken or not. GregAshmore is assuming the symmetry wasn't broken when his spaceship was accelerated. Whether this symmetry is broken by a rocket engine (SR) or a gravitational field (GR) makes no difference, though both break it in a different or inverse manner, breaking this symmetry requires one or the other.

 

[harrylin]

[..] The break in the symmetry under both special and general relativity occurs whenever an observer enters a non-inertial state. [..]
You cannot break this symmetry in either special or general relativity and pretend it is not broken. Once this symmetry, which applies only to inertial observers, is broken it is no longer "matter of free opinion" as to whether it is broken or not. GregAshmore is assuming the symmetry wasn't broken when his spaceship was accelerated. Whether this symmetry is broken by a rocket engine (SR) or a gravitational field (GR) makes no difference, though both break it in a different or inverse manner, breaking this symmetry requires one or the other.

That's correct of course; perhaps I read too much in GregAshmore's issues and is it only a matter of problems with the calculation methods. If so, then that should be easy to fix. So I'll also look into his last attempt.

 

[harrylin]

[..] Here's my best shot at the Twin Paradox. Later this evening, or maybe tomorrow night, I'll see how what I did compares with your suggestions.[..]
Solution of the Twin Paradox - to the degree possible knowing only the Lorentz transform and the usage of the spacetime diagram.

OK - that implies purely SR. As you seem to have solved the equations without issues, I'll skip those.

Given:
G1. Earth and rocket are both at rest at same position. Earth clock and rocket clock are synchronised.
G2. At time 0.0, rocket fires a pulse.
G3. Earth and rocket separate at relative velocity 0.8c.
G4. At distance 10 units from Earth, as measured in Earth frame, rocket fires a pulse.
G5. Earth and rocket approach at relative velocity -0.8c.
G6. Upon reaching Earth, rocket fires a pulse, coming to rest on Earth.
G7. Gravitational effects of mass are to be ignored.

Questions:
Q1. Both the Earth and the rocket claim to be at rest throughout the episode. Can both make good on this claim?

It depends on what they supposedly mean with that. In normal use of the word "in rest", in the context of SR calculations, the rocket cannot claim to be all the time in rest. This is because it's not all the time in rest in any inertial frame. Precision: "inertial frame" in SR means a set of coordinate systems that is in rectilinear uniform motion according to Newton's mechanics; also called by Einstein a "Gallilean" reference system.

Q2. What are the clock readings on Earth and rocket at G6?

Q3. Are the clock readings calculated for Q2 unambiguously unique?

Solution:
The questions are with regard to kinematics only: positions and times. With one exception noted later, the dynamics of the episode need not be considered.

While that is often said, it is only half true, and therefore misleading. The dynamics is inherent by the prescription of reference to inertial frames for the Lorentz transformations. If one purely considered kinematics only then the situation would be symmetrical.

[..]
Earth or rocket must change frames at velocity reversal.
The reversal of velocity in G4 must be represented by a change of frame in the spacetime diagram. Without a change of frame, the worldlines of Earth and rocket can never meet.
Either the Earth or the rocket, or both, must change frames.
The Earth cannot change frames: No unbalanced force acts on it; it is inertial.
The rocket must change frames: It is acted on by an unbalanced force; it is not inertial.

Note my earlier clarifications why such kind of reasoning does not generally hold. What matters for your SR calculation is that the rocket is not all the time at rest in an inertial frame. Also the Earth is not at rest in an inertial frame as it is in an orbit around the Sun; however the effect is small compared to the rocket. That is another simplification of the calculation.

[..] Visually, the Earth and rocket experiences are symmetric. Each sees the other move away and return. Nevertheless, the rocket is unambiguously younger than the Earth at reunion.

Right.
[addendum: kinematically the situation looks symmetrical (which is what I supposed you meant); however next George correctly highlights that of course there are visual differences that can be observed. That is pertinent for understanding the physics. This difference in observations has also been elaborated by Langevin in the article that I linked earlier.]

 

[ghwellsjr]

Given:
G1. Earth and rocket are both at rest at same position. Earth clock and rocket clock are synchronised.
G2. At time 0.0, rocket fires a pulse.
G3. Earth and rocket separate at relative velocity 0.8c.
G4. At distance 10 units from Earth, as measured in Earth frame, rocket fires a pulse.
G5. Earth and rocket approach at relative velocity -0.8c.
G6. Upon reaching Earth, rocket fires a pulse, coming to rest on Earth.
G7. Gravitational effects of mass are to be ignored.

Here is a spacetime diagram for Earth's inertial rest frame:

Earth is shown as the wide blue line and the rocket as a wide red line. Dots along each path indicate one unit of elapsed Proper Time and I have marked most of them. I have also marked the four events that you indicated.

Here is a diagram to show the rocket at rest:

Both Earth and the rocket send a signal to the other one every unit of Proper Time. These signals provide the information that accounts for the visualization that you mentioned at the end of your post. The diagrams make it obvious that the situation is not symmetrical between the Earth and the rocket. They also make it clear that either diagram will provide all the information to determine the visualization of either observer.

You should track a few of the signals, noting the Proper Time (according to the dots) they were sent and received and then go to the other diagram and confirm the same information.

I didn't necessarily use the same coordinates that you used but, again, this will have no bearing on any outcome. The Coordinate Times are not significant when comparing between frames, only the Proper Times matter.

 

[harrylin]

It may be useful to elaborate a little on Langevin's discussion about the fact that acceleration has an absolute sense, as he meant it in a slightly different way than those people in this forum to which your first post relates; however Langevin gave the "twin" example for exactly this purpose, to illustrate the "absolute" effects of acceleration. The way he meant it is made clear by his description (as well as by the text that precedes it, but that's too long to cite here):

Only a uniform velocity relative to it cannot be detected, but any change of velocity, or any acceleration has an absolute sense. [..]
the laws of electromagnetism are not the same in respect to axes attached to this [accelerated] material system as in respect to axes in collective uniform motion of translation.
We will see the appearance of this absolute character of acceleration in another form. [..]
For [..] observers in uniform motion [..]l the proper time [..] will be shorter than for any other group of observers associated with a reference system in arbitrary uniform motion. [..] We can [..] say that it is sufficient to be agitated or to undergo accelerations, to age more slowly, [..]

Giving concrete examples: [..]
This remark provides the means for any among us who wants to devote two years of his life, to find out what the Earth will be in two hundred years, and to explore the future of the Earth, by making in his life a jump ahead that will last two centuries for Earth and for him it will last two years, but without hope of return, without possibility of coming to inform us of the result of his voyage, since any attempt of the same kind could only transport him increasingly further [in time].
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. Returned to Earth he has aged two years, then he leaves his ark and finds our world two hundred years older, if his velocity remained in the range of only one twenty-thousandth less than the velocity of light. The most established experimental facts of physics allow us to assert that this would actually be so.
[etc.]

- starting p.47 of http://en.wikisource.org/wiki/The_Evolution_of_Space_and_Time

 

[GregAshmore]

I don't know why you would say this. Are you referring to the Earth's inertial rest frame? There are an infinite number of ways to construct spacetime diagrams for your scenario, all with different velocities with respect to each other and all just as valid and all producing the same final clock readings and the same things that each observer actually sees.

I was too general in my wording. I only meant that Events A, B, and C have been placed, there is only one way to place Event D.

No, they are not symmetric. The rocket sees the Earth move away at 0.8c for a distance of 3.333 units and then remain at that distance for some time and then come back to the rocket. But the Earth sees the rocket move away at 0.8c to a distance of 10 units and then immediately start coming back. It doesn't matter what spacetime diagram you use to depict your scenario, they are all just as valid and produce the same results. The only thing that is different in them are the values of the coordinates (and the geometric shapes of the worldlines).

Again, poor choice of words. "Similar" would have been better than "symmetry".

 

[GregAshmore]

Right there, that's what I mean. This is the asymetry that is not so easy to explain. And maybe the OP naively thinks that if there is an absolute acceleration it would imply a rate of change of absolute velocity but that can't be because there is no such a thing as absolute velocity in relativity.
At this point I guess I should wait for the OP to confirm if this gets any close to his line of thought.

Well, I did have a thought that might resolve to something like what you say. As I recall, someone defined proper acceleration as the derivative of proper velocity with respect to proper time. I don't understand how there can be proper velocity at all, because proper time is the elapsed time at "the same place". If position never changes with respect to time, it would seem that proper velocity must be zero. I did not say anything about it because my objection was much more basic than that, and I figured there would be a logical explanation for it if and when I get that far.

 

[GregAshmore]

I think that this is probably one of the key topics of modern relativity.

The key concepts of relativity, both special and general, are geometrical (Minkowski geometry for SR and pseudo-Riemannian geometry for GR).

Just like you can take a piece of paper and draw geometrical figures and discuss many things, such as lengths and angles, without ever setting up a coordinate system. The same thing is possible in relativity. The "piece of paper" is spacetime which has the geometrical structure of a manifold. The "geometrical figures" are worldlines, events, vectors, etc. that represent the motion of objects, collisions, energy-momentum, etc.

In this geometrical approach, the twin scenario is simply a triangle, and the fact that the traveling twin is younger is simply the triangle inequality for Minkowski geometry. In a coordinate-independent sense, the traveler's worldline is bent, and that in turn implies that his worldline is necessarily shorter as a direct consequence of the Minkowski geometry.

Now, on top of that underlying geometry, you can optionally add coordinates. Coordinates are simply a mapping between points in the manifold (events in spacetime) and points in R4. The mapping must be smooth and invertible, but little else, so there is considerable freedom in choosing the mapping. It is possible to choose a mapping which maps straight lines in spacetime to straight lines in R4, such mappings are called inertial frames.

It is also possible to choose a mapping which maps bent lines in spacetime to straight lines in R4, a non-inertial frame. Such a mapping does nothing to alter the underlying geometry. The bent lines are still bent in a coordinate-independent geometrical sense, but because it simplifies the representation in R4 it can still be useful on occasion in order to simplify calculations.

Because the mapping is invertible, in many ways it doesn't matter if you are talking about points in the manifold or points in R4. So you talk about things being "at rest" based on R4, and things happening "simultaneously" based on R4, and many other things. However, it is occasionally important to remember the underlying geometry.

I hope this helps.

It does.

It has, in fact, been made clear to you that SR can handle the twins paradox. What obviously hasn't been made clear to you is why. Your repetition of bald assertions that have already been contradicted is unhelpful. It wastes your time in repeating it and it wastes our time in repeating our responses. It also irritates those (maybe only me) who feel like their well-considered and helpful responses have been completely ignored by you.

Not ignored; not understood. Annoying either way, when the reason for not understanding is a failure to work out misunderstandings on paper before making statements.

Another factor on my side was that I thought you did not understand exactly what I was troubled by. Working through the twin paradox, looking for an answer to what troubled me, also led me to understand why SR is valid for solving the problem, at least with respect to kinematics. (I don't say SR isn't valid with respect to dynamics, only that I don't know enough to say it is.) I know that what I did wrt the twin paradox is at the most elementary level. But for me, it was like the transition from saying "ga ga, goo goo" to standing up on two feet and taking a step or two (before stumbling). Hopefully I will be less annoying in future.

 

[GregAshmore]

It depends on what they supposedly mean with that. In normal use of the word "in rest", in the context of SR calculations, the rocket cannot claim to be all the time in rest. This is because it's not all the time in rest in any inertial frame.

I struggled with the issue of whether the rocket is at rest throughout, or not. Part of the struggle has to do with the definition of "frame". If one defines frame to be an inertial frame, the rocket is not at rest while accelerating, while changing inertial frames. However, if one recognizes non-inertial frames, then the rocket is at rest throughout. If a frame is the same thing as the coordinate system whose origin is coincident with an observer, then there is indeed such a thing (in the abstract) as a non-inertial frame. You will note that I hadn't fully thought this through when I posted the calculations: I made sure to say "coordinate system" instead of "frame" when describing the setup. Edit: And it was George's clarification which helped me see this.

I don't say that I fully understand the concept of "absolute proper acceleration" being compatible with "no absolute space". However, it seems to me that this is something that needs to be considered with the dynamics of SR. Kinematically, the spacetime diagram shows that the rocket is at rest in its non-inertial frame.

That, by the way, is the objection that I felt was being dismissed--the call for consideration of the case in which the rocket is at rest. If I (now, or finally) understand George correctly, that objection is intentionally dismissed by Taylor and Wheeler. Indeed, when the objection is raised, it could be shown, using the spacetime diagram that is already under consideration, that the rocket is at rest throughout the episode. What the objector wants (or at least, what I wanted) was for the symmetrical diagram to be drawn, because he thinks that this is the only spacetime diagram in which the rocket is at rest. That thought is based on a misconception of the spacetime diagram--a misconception which I began to perceive as I thought more about the spacetime diagrams I drew for the pole-in-barn paradox.

While that is often said, it is only half true, and therefore misleading. The dynamics is inherent by the prescription of reference to inertial frames for the Lorentz transformations. If one purely considered kinematics only then the situation would be symmetrical.

The "one exception" (which I did not explicitly point out later, I realize now) is the rocket being non-inertial while accelerating. That is a dynamic phenomenon.

 

[GregAshmore]

my_wan said,

Gravity turns this relationship on its head. Note the force felt when accelerating. When on the surface of a gravitational mass, like Earth, the principle of equivalence tells us this weight we feel is the same force we feel when accelerating. Now if you jump off a roof then while accelerating toward the ground you feel no force, effectively weightless. Hence, in your frame of reference you are at rest, i.e., not accelerating, but the Earth is accelerating toward you. Yet everybody in the Universe can agree that your speed is changing, even if not by how much. In this case proper gravity is absolute, while how much gravity and coordinate paths are relative. So in this case gravity is absolute, but the coordinate acceleration due to gravity is relative.

I take it that the bold text above is what harrylin refers to as the modern argument...

Thanks for bringing that up, as it is exactly that modern argument that 1916GR denies; and I had the impression that GregAshmore noticed that point, that it's basically that issue that he discovered. Einstein tried to relativise acceleration by relativising gravitation, so that it's a matter of free opinion if a rocket accelerates or not. Nowadays few people accept that view.

That argument fails in the first version by Langevin, see my earlier remarks as well as elaborations by others.

No, I was not disagreeing with Einstein's contention that it is a matter of free opinion as to whether the rocket accelerates or not.

My understanding is that, even according to modern ideas, it is indeed a matter of free opinion as to whether the rocket accelerates--if one considers acceleration in the usual sense of "rate of change in velocity as measured with respect to a set of coordinates". The statement was, "Coordinate acceleration is relative". (Edit to clarify.)

It is proper acceleration which is absolute; but one may be at rest in a coordinate system while experiencing proper acceleration.

There is at least one person in the universe who will disagree with the claim that the rocket is accelerating: the observer in the rocket who is convinced that he is at rest. (This, I think, is along the lines of another comment on the claim, posted by someone else.)

Still, I don't know anything about how the dynamics of the "resting while accelerating rocket" work, so I'm not making any statement of my own opinion on this issue. I'm only giving my understanding of what I have been told.

 

[Dale]

My understanding is that, even according to modern ideas, it is indeed a matter of free opinion as to whether the rocket accelerates--if one considers acceleration in the usual sense of "rate of change in velocity as measured with respect to a set of coordinates". The statement was, "Coordinate acceleration is relative". (Edit to clarify.)

Yes.

It is proper acceleration which is absolute; but one may be at rest in a coordinate system while experiencing proper acceleration.

Correct.

There is at least one person in the universe who will disagree with the claim that the rocket is accelerating: the observer in the rocket who is convinced that he is at rest. (This, I think, is along the lines of another comment on the claim, posted by someone else.)

It seems like you get the distinction between coordinate and proper acceleration.

 

[harrylin]

[..] As I recall, someone defined proper acceleration as the derivative of proper velocity with respect to proper time. I don't understand how there can be proper velocity at all, because proper time is the elapsed time at "the same place". If position never changes with respect to time, it would seem that proper velocity must be zero. I did not say anything about it because my objection was much more basic than that, and I figured there would be a logical explanation for it if and when I get that far.

I somewhat agree with that; I quickly looked around for definitions and if I see it correctly the definition by Smoot of "proper acceleration" relates to the coordinate acceleration with respect to an instantaneously co-moving inertial frame (thus there is a change of velocity from zero to non-zero) and that makes sense to me.
In contrast, for me the definition of "proper acceleration" as given in Wikipedia is a misnomer for what I would call apparent gravitation. - http://en.wikipedia.org/wiki/Proper_acceleration
It may be that such different definitions bugged you (they did bug me in earlier discussions).

 

[harrylin]

I struggled with the issue of whether the rocket is at rest throughout, or not. Part of the struggle has to do with the definition of "frame". If one defines frame to be an inertial frame, the rocket is not at rest while accelerating, while changing inertial frames. However, if one recognizes non-inertial frames, then the rocket is at rest throughout.

Of course it's always possible to be at rest relative to oneself and to define non-inertial reference frames and coordinate systems. However such a reference frame isn't what is implied with "at rest" in the context of SR, which relates the physics to inertial frames: you have remarked that yourself. And saying that something is in rest in a frame in which we define it to be in rest ("the rocket is at rest in its non-inertial frame") is simply meaningless.

[..] I don't say that I fully understand the concept of "absolute proper acceleration" being compatible with "no absolute space".

Not sure to parse that correctly; some of the text of Langevin that I omitted argues for absolute space. That's a matter of opinion.

[..] it could be shown, using the spacetime diagram that is already under consideration, that the rocket is at rest throughout the episode.

Once more, "at rest" in SR normally means at rest in an inertial coordinate system that one chooses as "rest system". In no SR space diagram is the rocket continuously "at rest", because it is moving during part of the voyage no matter which inertial system one chooses as "rest" system.

 

[ghwellsjr]

There is only one way to construct the spacetime diagram, due to the unique non-inertial behavior of the rocket.

I don't know why you would say this. Are you referring to the Earth's inertial rest frame? There are an infinite number of ways to construct spacetime diagrams for your scenario, all with different velocities with respect to each other and all just as valid and all producing the same final clock readings and the same things that each observer actually sees.

I was too general in my wording. I only meant that Events A, B, and C have been placed, there is only one way to place Event D.

Actually, Event B is of no consequence in the definition of your scenario. As long as we know the rocket's speed and where (or when) it turns around, that defines the end point.

However, I'd like you to consider an issue related to the one you just raised here and that is, how does the rocket know when to turn around? The rocket cannot know from any direct measurement when the Earth has traveled 10 units away in the rocket frame. That distance is the difference between the spatial components of Event B and C which are simultaneous in the Earth frame but which have a distance between them of 16.67 in the rocket frame. Even if the rocket had instant access to the remote information, it would still have to do some calculation if it's based on distance to determine when to fire its rockets.

To me, a much cleaner way to specify the Twin Paradox is to state the Proper Time on the traveler's clock when he should fire the rockets to turn around. This has the advantage that it doesn't require the specification of any reference frame. In fact, it doesn't even require fully specifying any events since we don't care about the spatial component. So if we know how long it takes for the traveler to get to the turnaround point and we know how fast he is traveling, those two parameters fully specify the complete Twin Paradox scenario (assuming of course that he is returning at the same speed he left at). I fully explained this in the thread you linked to in your opening post.

 

[harrylin]

my_wan said, [..]
I take it that the bold text above is what harrylin refers to as the modern argument...

Quite so; with the demotion of pseudo gravitational fields one returns to Langevin's argument that acceleration has "absolute" effects that everyone can observe -even for the case that the accelerometer reading remains zero.

[..]My understanding is that, even according to modern ideas, it is indeed a matter of free opinion as to whether the rocket accelerates--if one considers acceleration in the usual sense of "rate of change in velocity as measured with respect to a set of coordinates". The statement was, "Coordinate acceleration is relative". (Edit to clarify.)

It is proper acceleration which is absolute; but one may be at rest in a coordinate system while experiencing proper acceleration.

One can always choose a coordinate system to be always at rest in; once more, that is meaningless for the physics. However, it is certainly true that proper acceleration (both definitions of it) is quantitatively agreed upon by all. If that's all you wanted to understand, then you have certainly achieved your goal.

There is at least one person in the universe who will disagree with the claim that the rocket is accelerating: the observer in the rocket who is convinced that he is at rest. (This, I think, is along the lines of another comment on the claim, posted by someone else.) [..]

That person, if indeed he denies to be changing his state of motion, will have to explain the physical causes for the observed effects; and I mistakenly thought that you were contemplating the different physical explanations that are given in the literature. If and when you come to that point, you may want to read earlier comments and references that were provided in this discussion.

 

[ghwellsjr]

That, by the way, is the objection that I felt was being dismissed--the call for consideration of the case in which the rocket is at rest. If I (now, or finally) understand George correctly, that objection is intentionally dismissed by Taylor and Wheeler. Indeed, when the objection is raised, it could be shown, using the spacetime diagram that is already under consideration, that the rocket is at rest throughout the episode. What the objector wants (or at least, what I wanted) was for the symmetrical diagram to be drawn, because he thinks that this is the only spacetime diagram in which the rocket is at rest.

T&W never consider non-inertial frames or a frame in which the traveler is at rest, at least not when discussing the Twin Paradox. What they are dismissing is the explanation that I gave in post #23 of the thread you linked to in your OP. I considered three Inertial Reference Frames which included different rest states of the two twins. I attempted to show that anyone of them was adequate to explain everything about the scenario, which is pretty much the classic way of explaining the Twin Paradox. But they think they have a better way which involves any observer calculating the spacetime interval between pairs of events. I don't think that helps at all but since they are writing the book, they get to decide when the objectors are happy. But real objectors, like you, remained unhappy.

 

[GregAshmore]

Once more, "at rest" in SR normally means at rest in an inertial coordinate system that one chooses as "rest system". In no SR space diagram is the rocket continuously "at rest", because it is moving during part of the voyage no matter which inertial system one chooses as "rest" system.

True. But no one is claiming that the rocket is at rest in an inertial frame--not even the twin in the rocket. The twin in the rocket feels the unbalanced force of the rocket engine, and he knows (or would know upon reunion) that the twin on Earth feels no such force. Even without the formal definitions of inertial and non-inertial, the rocket twin would recognize that his situation is fundamentally different than that of his twin. Fully aware of that difference, he claims that he is at rest throughout the episode.

I don't see how the claim is disproved by pointing out that the rocket changes inertial frames during the firing of the engine. The change of inertial frames only confirms what everyone knows: the rocket is non-inertial. From the Earth twin's point of view, the rocket is in an inertial frame, accelerates, and comes to rest in another inertial frame. The rocket twin disagrees with this assessment. He can point to the spacetime diagram (which the Earth twin accepts as valid) and show that he remains at rest in his own frame, even while not at rest in anyone inertial frame. To prove the rocket twin wrong, it must either be shown that his frame moved with respect to some absolute position marker, or that the laws of dynamics are violated if he does not move. There is no absolute position marker, and the laws of dynamics are not considered in my analysis. [If these statements are wrong, at least they are not bald statements; I've done my homework. ]

 

[GregAshmore]

T&W never consider non-inertial frames or a frame in which the traveler is at rest, at least not when discussing the Twin Paradox. What they are dismissing is the explanation that I gave in post #23 of the thread you linked to in your OP. I considered three Inertial Reference Frames which included different rest states of the two twins. I attempted to show that anyone of them was adequate to explain everything about the scenario, which is pretty much the classic way of explaining the Twin Paradox. But they think they have a better way which involves any observer calculating the spacetime interval between pairs of events. I don't think that helps at all but since they are writing the book, they get to decide when the objectors are happy. But real objectors, like you, remained unhappy.

I read that post in its entirety before opening this thread. I didn't catch on to what you were doing because in each of the diagrams the rocket twin is spoken of as moving for part of the trip.

What helped me was to realize that in the typical two-frame spacetime diagram, the world line of an inertial particle shows the particle both as moving and at rest. It is moving in one frame, and at rest in the other frame. Thus, the one spacetime diagram actually shows the case I wanted to see-the case in which the rocket twin considers himself at rest. The symmetrical diagram (which is invalid) is not needed.

 

[GregAshmore]

Actually, Event B is of no consequence in the definition of your scenario. As long as we know the rocket's speed and where (or when) it turns around, that defines the end point.

It would be of consequence for the person who mistakenly believes that because either object can be the one that appears to turn around, the spacetime diagram can be drawn with either object having the bent worldline. Event B is where the Earth would turn around. I chose to show at this juncture that the Earth cannot change inertial frames because it experiences no unbalanced force; because it is inertial.

However, I'd like you to consider an issue related to the one you just raised here and that is, how does the rocket know when to turn around? The rocket cannot know from any direct measurement when the Earth has traveled 10 units away in the rocket frame. That distance is the difference between the spatial components of Event B and C which are simultaneous in the Earth frame but which have a distance between them of 16.67 in the rocket frame. Even if the rocket had instant access to the remote information, it would still have to do some calculation if it's based on distance to determine when to fire its rockets.

To me, a much cleaner way to specify the Twin Paradox is to state the Proper Time on the traveler's clock when he should fire the rockets to turn around. This has the advantage that it doesn't require the specification of any reference frame. In fact, it doesn't even require fully specifying any events since we don't care about the spatial component. So if we know how long it takes for the traveler to get to the turnaround point and we know how fast he is traveling, those two parameters fully specify the complete Twin Paradox scenario (assuming of course that he is returning at the same speed he left at). I fully explained this in the thread you linked to in your opening post.

It is a cleaner solution. Yet even now I feel the [vestigial] reflexive urge to tune it out because it says the rocket twin "travels", "turn around", "return". The doubter has been told that in relativity the rocket has the same right to be at rest as the Earth has. Langauge of motion applied to the rocket speaks so loudly that it drowns out the perfectly valid point that is being made.

For perspective, I have read two or three explanations of the twin paradox to my 30+ son. He has some technical training, has a job that requires him to evaluate contractual language. He had exactly my reaction, without me making any comment.

 

[Dale]

I somewhat agree with that; I quickly looked around for definitions and if I see it correctly the definition by Smoot of "proper acceleration" relates to the coordinate acceleration with respect to an instantaneously co-moving inertial frame (thus there is a change of velocity from zero to non-zero) and that makes sense to me.
In contrast, for me the definition of "proper acceleration" as given in Wikipedia is a misnomer for what I would call apparent gravitation. - http://en.wikipedia.org/wiki/Proper_acceleration

The two definitions are equivalent. The Smoot definition basically just pushes the use of accelerometers one step further. Instead of reading the proper acceleration directly off the accelerometer, you define an inertial frame by strapping accelerometers to your clocks and rods, ensuring that they read 0, and then reading the proper acceleration off the clocks and rods.

 

[Dale]

That person, if indeed he denies to be changing his state of motion, will have to explain the physical causes for the observed effects;

Which he can do quite easily simply by stating the laws of physics in a covariant form and then using any coordinates where his state of motion does not change.

 

[harrylin]

True. But no one is claiming that the rocket is at rest in an inertial frame--not even the twin in the rocket.

The physical meaning of "in rest" is very well clarified in Einstein's 1918 paper.

The twin in the rocket feels the unbalanced force of the rocket engine, and he knows (or would know upon reunion) that the twin on Earth feels no such force. Even without the formal definitions of inertial and non-inertial, the rocket twin would recognize that his situation is fundamentally different than that of his twin. Fully aware of that difference, he claims that he is at rest throughout the episode.

Once more, that is true for Einstein's example and completely wrong (even in two ways) for Langevin's example. "At rest" in the sense that you adopt here only makes sense in the way Einstein elaborates - and that isn't SR.

The rocket twin [..] can point to the spacetime diagram (which the Earth twin accepts as valid) and show that he remains at rest in his own frame, even while not at rest in anyone inertial frame. To prove the rocket twin wrong, [..]

For a last time, as we've been here twice before: everyone can always claim to be at rest in his own frame; such a statement cannot be disproved. You could just as well state that you're in your own world. That's physically meaningless.

 

[harrylin]

The two definitions are equivalent. The Smoot definition basically just pushes the use of accelerometers one step further. Instead of reading the proper acceleration directly off the accelerometer, you define an inertial frame by strapping accelerometers to your clocks and rods, ensuring that they read 0, and then reading the proper acceleration off the clocks and rods.

I prefer his definition as he doesn't confound a displacement with a force; and it does make a difference when using it in SR, due to the different definition of "inertial frame" in SR.

 

[my_wan]

It would be of consequence for the person who mistakenly believes that because either object can be the one that appears to turn around, the spacetime diagram can be drawn with either object having the bent worldline.

What has been repeated here is that either object CANNOT be the one that appears to turn around because all observers MUST agree on which one accelerated, just as the one that accelerated is also the only one to experience a g force as a result.

You are confusing Einstein's term, most probably with respect to the explanation given for the principle of equivalence. IF every agrees on what happened, even if not to what degree, we are by definition talking about an absolute, not relative event. The relative terms of that absolute involve only the quantitative value associated with it. That is the point we are trying to make with the distinction between coordinate acceleration and proper acceleration.

 

[harrylin]

Which he can do quite easily simply by stating the laws of physics in a covariant form and then using any coordinates where his state of motion does not change.

As I suspect that you also don't copy Einstein's physical explanation, I'm curious to know which physical explanation that you found in the literature you fancy for the moving and faster aging Earth with a stationary rocket (let's stay away from personal ideas). How can the firing of the rocket engine move the rest of the universe while keeping the rocket's state of motion unaffected?

 

[Dale]

it does make a difference when using it in SR, due to the different definition of "inertial frame" in SR.

Any way you can determine if your frame is inertial or not is a way of determining your proper acceleration, i.e. it is an accelerometer. You cannot get away from using accelerometers.

 

[harrylin]

Any way you can determine if your frame is inertial or not is a way of determining your proper acceleration, i.e. it is an accelerometer. You cannot get away from using accelerometers.

We have discussed that before, and I found that your definition of "inertial frame" is at odds with that of classical mechanics wrt which SR is defined; as a matter of fact, it's already at odds with Einstein's 1905 paper and Langevin's 1911 paper. So, let's agree to disagree; but if you even disagree to agree to disagree, then I'll just add some links to earlier discussions later, as IMHO everything has been said already.

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

 

[Dale]

What has been repeated here is that either object CANNOT be the one that appears to turn around because all observers MUST agree on which one accelerated

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.

 

[Dale]

We have discussed that before, and I found that your definition of "inertial frame" is at odds with that of classical mechanics; as a matter of fact, it's already at odds with Einstein's 1905 paper and Langevin's 1911 paper. So, let's agree to disagree; but if you even disagree to agree to disagree, then I'll just add some links to earlier discussions later.

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

 

[Dale]

As I suspect that you also don't copy Einstein's physical explanation,

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.

I'm curious to know which physical explanation that you found in the literature you fancy for the moving and faster aging Earth with a stationary rocket (let's stay away from personal ideas). How can the firing of the rocket engine move the rest of the universe while keeping the rocket's state of motion unaffected?

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?

 

[stevendaryl]

We have discussed that before, and I found that your definition of "inertial frame" is at odds with that of classical mechanics wrt which SR is defined

What Einstein said by way of defining inertial frame was in his 1905 paper:

Let us take a system of co-ordinates in which the equations of Newtonian mechanics hold good.

Presumably, since he is suggesting a modification to Newtonian mechanics, he means "approximately", in the low-velocity limit.

The way I interpreted Einstein's words are that an inertial coordinate system satisfies:

1. Objects that are not acted upon by physical, external forces travel so that $\dfrac{d^2 x}{dt^2} = \dfrac{d^2 y}{dt^2} = \dfrac{d^2 z}{dt^2} = 0$
2. 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 $F^i = m \dfrac{d^2 x^i}{dt^2}$
3. If an object exerts a force $\vec{F}$ on a second object, then the second object exerts a force $-\vec{F}$ on the first.

These conditions characterize an inertial Cartesian coordinate system. They imply that an accelerometer at rest in that coordinate system will show no acceleration. 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.

 

[ghwellsjr]

T&W never consider non-inertial frames or a frame in which the traveler is at rest, at least not when discussing the Twin Paradox. What they are dismissing is the explanation that I gave in post #23 of the thread you linked to in your OP. I considered three Inertial Reference Frames which included different rest states of the two twins. I attempted to show that anyone of them was adequate to explain everything about the scenario, which is pretty much the classic way of explaining the Twin Paradox. But they think they have a better way which involves any observer calculating the spacetime interval between pairs of events. I don't think that helps at all but since they are writing the book, they get to decide when the objectors are happy. But real objectors, like you, remained unhappy.

I read that post in its entirety before opening this thread. I didn't catch on to what you were doing because in each of the diagrams the rocket twin is spoken of as moving for part of the trip.

What helped me was to realize that in the typical two-frame spacetime diagram, the world line of an inertial particle shows the particle both as moving and at rest. It is moving in one frame, and at rest in the other frame.

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?

Thus, the one spacetime diagram actually shows the case I wanted to see-the case in which the rocket twin considers himself at rest.

Are you talking about this one spacetime diagram?

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 symmetrical diagram (which is invalid) is not needed.

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.

 

[ghwellsjr]

Actually, Event B is of no consequence in the definition of your scenario. As long as we know the rocket's speed and where (or when) it turns around, that defines the end point.

It would be of consequence for the person who mistakenly believes that because either object can be the one that appears to turn around, the spacetime diagram can be drawn with either object having the bent worldline. Event B is where the Earth would turn around. I chose to show at this juncture that the Earth cannot change inertial frames because it experiences no unbalanced force; because it is inertial.

But when I drew the (non-inertial) spacetime diagram showing the Earth as the object that turns around, it doesn't happen at Event B, it happens at two other events. The Earth's bent worldline has two bends in it, not just one.

However, I'd like you to consider an issue related to the one you just raised here and that is, how does the rocket know when to turn around? The rocket cannot know from any direct measurement when the Earth has traveled 10 units away in the rocket frame. That distance is the difference between the spatial components of Event B and C which are simultaneous in the Earth frame but which have a distance between them of 16.67 in the rocket frame. Even if the rocket had instant access to the remote information, it would still have to do some calculation if it's based on distance to determine when to fire its rockets.

To me, a much cleaner way to specify the Twin Paradox is to state the Proper Time on the traveler's clock when he should fire the rockets to turn around. This has the advantage that it doesn't require the specification of any reference frame. In fact, it doesn't even require fully specifying any events since we don't care about the spatial component. So if we know how long it takes for the traveler to get to the turnaround point and we know how fast he is traveling, those two parameters fully specify the complete Twin Paradox scenario (assuming of course that he is returning at the same speed he left at). I fully explained this in the thread you linked to in your opening post.

It is a cleaner solution.

Please note that I did not say it was a cleaner solution-just a cleaner specification. The cleaner specification does not imply any particular solution or explanation of the Twin Paradox.

Yet even now I feel the [vestigial] reflexive urge to tune it out because it says the rocket twin "travels", "turn around", "return". The doubter has been told that in relativity the rocket has the same right to be at rest as the Earth has. Langauge of motion applied to the rocket speaks so loudly that it drowns out the perfectly valid point that is being made.

Well let's review your entire specification:

Given:
G1. Earth and rocket are both at rest at same position. Earth clock and rocket clock are synchronised.
G2. At time 0.0, rocket fires a pulse.
G3. Earth and rocket separate at relative velocity 0.8c.
G4. At distance 10 units from Earth, as measured in Earth frame, rocket fires a pulse.
G5. Earth and rocket approach at relative velocity -0.8c.
G6. Upon reaching Earth, rocket fires a pulse, coming to rest on Earth.
G7. Gravitational effects of mass are to be ignored.

It's obvious that you are trying to specify the scenario in such a way that it does not imply which object is moving. However, G6 implies that it is the rocket that was moving because you say it comes to rest on Earth. Maybe you should say: At closest approach of Earth and rocket, rocket fires a pulse and once again, both are at rest at the same position.

But there are still problems. Saying that the rocket "fires a pulse" three times throughout the scenario implies that it is exactly the same pulse fired three times in the same direction which, of course, won't work. What could work is if you leave G2 alone and change G3 (using my suggestion) to say: "At time 7.5 according to the rocket's clock, the rocket turns around and fires two pulses" and then at G6 you could say: "At closest approach of Earth and rocket, rocket turns around again and fires a pulse and once again, both are at rest at the same position." If you don't like the term "turns around" then you will have to provide the rocket with thrusters at both ends and state which thruster is being used at each point.

For perspective, I have read two or three explanations of the twin paradox to my 30+ son. He has some technical training, has a job that requires him to evaluate contractual language. He had exactly my reaction, without me making any comment.

I'm all for providing better explanations that actually communicate and maybe we could enlist your son in making that happen. Did he offer any suggestions such as the point you made that my explanation in post #23 was confusing because you expected two frames in one diagram? I can use that suggestion to improve my explanations in the future. More suggestions would be welcome.

 

[ghwellsjr]

As a side note with regard to my diagrams showing only one frame compared to the more traditional Minkowski diagram showing two frames, let me show you what happened when I tried to make the point that my type of diagram was not a Minkowski diagram:

By the way, your graphs are not Minkowski diagrams, they are simply conventional position versus time graphs. And I'm not saying that simply because you are interchanging the time versus distance axes that is more common for a Minkowski diagram.

Read the posts following that one and you'll see why I no longer made a distinction between my one-frame spacetime diagrams and the more common two-frame Minkowski diagrams.