How To Consistently Explain Electromagnetism With Relativity

[A.T.]

since they always share the same frame

There is no frame (inertial or non-inertial) where all the rockets remain at rest, throughout the acceleration.

- There is a series of inertial frames, where all the rockets are instantaneously at rest, but along that series the distances between the rockets are increasing.

- There are non-inertial frames, where one of the rockets remains at rest throughout the acceleration, but the acceleration of the others is affected by position dependent time-dilation:
https://en.wikipedia.org/wiki/Rindler_coordinates

 

[Ibix]

There is a series of inertial frames, where all the rockets are instantaneously at rest, but along that series the distances between the rockets are increasing.

Perhaps I'm misunderstanding you, but I don't think that's right. There is a series of frames in which one or other of the rockets is always at rest, but the other one is always moving. That's why (or, at least, one way of conceptualising why) the distance is changing.

The other way of putting that is that the spacelike axes of the family of frames are not parallel, and it's only parallel to the spacelike axis of S that the separation is constant.

 

[A.T.]

Perhaps I'm misunderstanding you, but I don't think that's right. There is a series of frames in which one or other of the rockets is always at rest, but the other one is always moving. That's why (or, at least, one way of conceptualising why) the distance is changing.

I conceptualize as each inertial frame in that series seeing a different distance.

But either way, even if you construct a single frame where one rocket remains at rest during the acceleration, the other rocket does not remain at rest in that frame. And if you insist to know why they increase separation according to that frame, you have to take the position dependent time dilation in that frame into account.

 

[Geocentricist]

But either way, even if you construct a single frame where one rocket remains at rest during the acceleration, the other rocket does not remain at rest in that frame. And if you insist to know why they increase separation according to that frame, you have to take the position dependent time dilation in that frame into account.

I still don't see why the rockets aren't at rest with respect to each other throughout the acceleration. Everyone keeps repeating they aren't without really explaining the cause.

 

[PAllen]

I conceptualize as each inertial frame in that series seeing a different distance.

But either way, even if you construct a single frame where one rocket remains at rest during the acceleration, the other rocket does not remain at rest in that frame. And if you insist to know why they increase separation according to that frame, you have to take the position dependent time dilation in that frame into account.

I think this is wrong. Consider the events A has speed .7c, B has speed .7c as described in the original rest frame. These events are simultaneous in this frame. Consider ther frame moving at .7c relative to the original rest frame. These events are not simultaneous in this frame. Thus, when A is at rest in this frame, B is moving, and when B is at rest in this frame, A is moving.

We are not dealing here with any non inertial frames. The statement is that no inertial frame has both rockets at rest at the same time except the original inertial frame. Also, in SR, it is normal practice that frame refers to inertial frame unless one specifically discusses noninertial (and then, as you know, there are multiple valid ways to construct noninertial frames.)

 

[Ibix]

I still don't see why the rockets aren't at rest with respect to each other throughout the acceleration. Everyone keeps repeating they aren't without really explaining the cause.

I told you why in #89. They are the same distance apart in S because in that frame they are always traveling at the same speed at the same time. But no other frame has the same definition of "at the same time", so in any other frame the rockets are traveling at different speeds at the same time (by their definition of "the same time") so are always changing their separation.

 

[A.T.]

I think this is wrong. Consider the events A has speed .7c, B has speed .7c as described in the original rest frame. These events are simultaneous in this frame. Consider ther frame moving at .7c relative to the original rest frame. These events are not simultaneous in this frame. Thus, when A is at rest in this frame, B is moving, and when B is at rest in this frame, A is moving.

Yes, you and Ibix are right. There are no other inertial frames, where they are both at rest, even instantaneously.

We are not dealing here with any non inertial frames.

The OP want's to know what happens in the frame of a rocket throughout acceleration. That frame is non-inertial and has position dependent time dilation.

 

[PAllen]

The OP want's to know what happens in the frame of a rocket throughout acceleration. That frame is non-inertial and has position dependent time dilation.

Somehow, I think th OP is ill equipped to deal with this. Imagine trying to explain why a non inertial frame for rocket A can always include B, but for a noninertial frame for B, A cannot be included after some time (it falls below the Rindler horizon for B).

 

[bob012345]

Yes, you and Ibix are right. There are no other inertial frames, where they are both at rest, even instantaneously.The OP want's to know what happens in the frame of a rocket throughout acceleration. That frame is non-inertial and has position dependent time dilation.

Let me jump in and ask if m getting the point correctly. Since there is no size requirement on what constitutes a valid reference frame, that's defined by velocity, so distance separated events along the direction of relative motion within one reference frame, S, can be seen as non simultaneous in another frame, S', even if they are always moving at the same velocity within frame S?

 

[PAllen]

Let me jump in and ask if m getting the point correctly. Since there is no size requirement on what constitutes a valid reference frame, that's defined by velocity, so distance separated events along the direction of relative motion within one reference frame, S, can be seen as non simultaneous in another frame, S', even if they are always moving at the same velocity within frame S?

Correct.

 

[bob012345]

Correct.

Thanks. So if the only separation were 90 degrees to the direction of motion, simultaneous events in S could be simultaneous in S'?

 

[PAllen]

Thanks. So if the only separation were 90 degrees to the direction of motion, simultaneous events in S could be simultaneous in S'?

Correct.

 

[jartsa]

I still don't see why the rockets aren't at rest with respect to each other throughout the acceleration. Everyone keeps repeating they aren't without really explaining the cause.

Well one thing is that the motor of the trailing rocket burns fuel at slowed down rate. And why does that happen? The vicinity of the Rindler-horizon causes that kind of things. Rindler-horizon is like event horizon of a black hole, in every way, for an accelerating observer, for inertial observers it does not exist.

What do you think is the situation for the observers in the rockets after a long time, if both rockets run out fuel after a quite short time?

 

[A.T.]

I still don't see why the rockets aren't at rest with respect to each other throughout the acceleration. Everyone keeps repeating they aren't without really explaining the cause.

It was explained to you pages ago for the electrons:

If you actually attach a frame to an electron, during it's acceleration, you have time running at different rates along the wire in that frame. This effectively delays the electrons in the back, and speeds up the electrons in the front, so their distances increase.

 

[Geocentricist]

Yes, you and Ibix are right. There are no other inertial frames, where they are both at rest, even instantaneously.The OP want's to know what happens in the frame of a rocket throughout acceleration. That frame is non-inertial and has position dependent time dilation.

A and B share a frame at all times. There may be time dilation in their frame relative to some other frame but they cannot experience time dilation relative to their own frame, so there is still no cause for their separation to increase.

 

[Geocentricist]

It was explained to you pages ago for the electrons:

If you actually attach a frame to an electron, during it's acceleration, you have time running at different rates along the wire in that frame. This effectively delays the electrons in the back, and speeds up the electrons in the front, so their distances increase.

Time running at different rates along the wire? The wire frame is one frame, there cannot be multiple rates of time in this one frame.

 

[Ibix]

A and B share a frame at all times

No they don't. That's the point.

Time running at different rates along the wire? The wire frame is one frame, there cannot be multiple rates of time in this one frame.

Ditto.

 

[PAllen]

A and B share a frame at all times. There may be time dilation in their frame relative to some other frame but they cannot experience time dilation relative to their own frame, so there is still no cause for their separation to increase.

I’ve asked you to define what you mean by sharing a frame. You have refused. If you mean there is any standard type of frame (inertial or noninertial) in which they are not moving relative to each other, this is false (edit: except the original rest frame). There is no (edit: other) such frame.

 

[pervect]

Let me jump in and ask if m getting the point correctly. Since there is no size requirement on what constitutes a valid reference frame,

It might be a nitpick, but I'd add "inertial reference frame" here. There are size constraints on the size of an accelerated frame, as mentioned previously.

that's defined by velocity, so distance separated events along the direction of relative motion within one reference frame, S, can be seen as non simultaneous in another frame, S', even if they are always moving at the same velocity within frame S?

 

[Dale]

A and B share a frame at all times. There may be time dilation in their frame relative to some other frame but they cannot experience time dilation relative to their own frame, so there is still no cause for their separation to increase.

Their frame is non inertial, so the usual rules don’t apply. There can be time dilation at rest, as well as expansion and torsion.

Time running at different rates along the wire? The wire frame is one frame, there cannot be multiple rates of time in this one frame.

There can be “multiple rates of time” in one frame if the frame is non-inertial. This phenomenon is closely related to gravitational time dilation and the equivalence principle.

However, it is not likely (in my opinion) to help you learn electromagnetism. I think you have gone far off track if that is still your goal.

 

[A.T.]

Time running at different rates along the wire?

Yes:

https://en.wikipedia.org/wiki/Gravitational_time_dilation

Gravitational time dilation was first described by Albert Einstein in 1907 as a consequence of special relativity in accelerated frames of reference.

 

[bob012345]

A and B share a frame at all times. There may be time dilation in their frame relative to some other frame but they cannot experience time dilation relative to their own frame, so there is still no cause for their separation to increase.

I think what people are saying is that if the relative velocities were constant, that would, be always true but with acceleration, what one thinks of as an extended reference frame is no longer an inertial reference frame. It's all because of the acceleration not the relative velocity.

 

[Ibix]

I think what people are saying is that if the relative velocities were constant, that would, be always true but with acceleration, what one thinks of as an extended reference frame is no longer an inertial reference frame. It's all because of the acceleration not the relative velocity.

Not quite. The problem is that, when discussing relativity, you have to be precise in a way that sounds pedantic to laypeople. So laypeople leave out the "pointless pedantry" and end up hopelessly confused.

When you ask "is that guy moving at the same speed as me?" you actually mean "is his velocity zero in my rest frame at a time simultaneous with my watch reading 18.15.30 GMT?" Pedantic, right?

Unfortunately one of the more counterintuitive results of relativity is that simultaneity is frame dependent. So although everyone understands what you mean by the time on your watch, they don't agree on what "at the same time as" means for events at different locations. Example: if you use your James Bond watch-mounted gun to shoot someone, everyone will agree what your watch read when you pulled the trigger (same place), but not necessarily what it read when the bullet hit (different place).

Going back to the moving ships - when both are moving at constant speed none of this matters. If the answer to "how fast are they going right now?" is always 700m/s, no one cares what you mean by "now". But if they are accelerating then you will get different answers for the velocity if you mean different things by "now". Which is why there is only one frame where the ships have constant separation, which is their initial rest frame. The situation is made yet more complex by the fact that there are at least two plausible candidates for what is meant by "the rest frame of a ship" once they are accelerating. Neither resolves this problem.

 

[bob012345]

Not quite. The problem is that, when discussing relativity, you have to be precise in a way that sounds pedantic to laypeople. So laypeople leave out the "pointless pedantry" and end up hopelessly confused.

When you ask "is that guy moving at the same speed as me?" you actually mean "is his velocity zero in my rest frame at a time simultaneous with my watch reading 18.15.30 GMT?" Pedantic, right?

Unfortunately one of the more counterintuitive results of relativity is that simultaneity is frame dependent. So although everyone understands what you mean by the time on your watch, they don't agree on what "at the same time as" means for events at different locations. Example: if you use your James Bond watch-mounted gun to shoot someone, everyone will agree what your watch read when you pulled the trigger (same place), but not necessarily what it read when the bullet hit (different place).

Going back to the moving ships - when both are moving at constant speed none of this matters. If the answer to "how fast are they going right now?" is always 700m/s, no one cares what you mean by "now". But if they are accelerating then you will get different answers for the velocity if you mean different things by "now". Which is why there is only one frame where the ships have constant separation, which is their initial rest frame. The situation is made yet more complex by the fact that there are at least two plausible candidates for what is meant by "the rest frame of a ship" once they are accelerating. Neither resolves this problem.

Thanks, but can you rephrase that in one sentence with nontechnical language?

 

[Ibix]

Thanks, but can you rephrase that in one sentence with nontechnical language?

Frames agree on what "here and now" means but not what "now, over there" means, and this difference of opinion has consequences when you ask "what speed is that accelerating person over there doing now?".

That's a total cheat using a run-on sentence and an embedded question, but you'll have to live with it.

 

[bob012345]

Frames agree on what "here and now" means but not what "now, over there" means, and this difference of opinion has consequences when you ask "what speed is that accelerating person over there doing now?".

That's a total cheat using a run-on sentence and an embedded question, but you'll have to live with it.

Thanks. I can live with it till I review my Taylor and Wheeler book Spacetime Physics.

 

[Geocentricist]

I think what people are saying is that if the relative velocities were constant, that would, be always true but with acceleration, what one thinks of as an extended reference frame is no longer an inertial reference frame. It's all because of the acceleration not the relative velocity.

So if I drop two identical rocks from the same height at the same time, the rocks will disagree on who hit the ground first?

 

[Dale]

So if I drop two identical rocks from the same height at the same time, the rocks will disagree on who hit the ground first?

What does this have to do with electromagnetism? If that is still your goal then the answer to this question won’t help and asking it just encourages the thread to get further from your goal.

 

[PAllen]

So if I drop two identical rocks from the same height at the same time, the rocks will disagree on who hit the ground first?

Totally different case because the separation between the rocks is perpendicular to their acceleration rather than parallel. If you are not familiar with how fundamental this difference is in SR, then you really need to read any standard introduction to the subject, because we cannot teach you SR from the ground up.

 

[Geocentricist]

What does this have to do with electromagnetism? If that is still your goal then the answer to this question won’t help and asking it just encourages the thread to get further from your goal.

I've put off the electromagnetism thing for a bit until I understand why the electron spacing increases in their own frame. Also because I spent a lot of time with those graphics only to find they were wrong.

The thing about the rocks falling was supposed to be analogous to the electrons accelerating, but I think I messed that up. So I will rephrase it. If A and B are both stationary and both experience the same gravitational force (for example, a couple rocks sitting on the ground), will they disagree on what events are simultaneous?