B Twin paradox explained for laymen

[Dale]

Ha! I looked that up. I will have to leave that for another lifetime. (A lifetime where I am smarter than I am now.)

It isn't that difficult. You send a radar pulse to an event and collect the radar echo from that event. The radar coordinates of the event are $t=(t_{echo}+t_{pulse})/2$ and $r=(t_{echo}-t_{pulse})c/2$.

 

[PeterDonis]

in this scenario there are no spacelike separated events that are hypothesized to be simultaneous

There are if you are going to make any claims about time dilation. If the only events you consider are "Alex passes Bob" and "Alex passes Alice", then you can make no statements at all about time dilation. You have to consider events like "the reading of Alice's clock at the same time Alex passes Bob" and "the reading of Bob's clock at the same time Alex passes Alice" to make any statements at all about time dilation.

The "stationary" observer (I called him "you") is communicating with a friend in the same IRF who observes the event of the traveler passing.

And this communication (between Alice and Bob) will involve events which are spacelike separated from the first two events, and any claims about time dilation will require a simultaneity convention.

 

[PeterDonis]

Am I wrong?

Yes. You have multiple people now trying to explain to you why. I strongly suggest that you listen to them. It is getting to the point where we are repeating the same explanations over and over.

 

[FactChecker]

I realize now that I have confused a few aspects of the Twins Paradox. Here is a top-level summary of what I think has been said here. I hope that I do not butcher some people's inputs because there are a great many details that I am not qualified to understand or explain.
1) The correct answer to the Twins Paradox can be calculated using only SR and the IRF of the non-traveling twin.
2) Within SR, there is no real symmetry in the twins' situations because the traveling twin can detect that he does not remain in an IRF. So one can not use his non-inertial reference frame and SR to calculate the correct answer.
3) In order to calculate the correct answer using the traveling twin's non-inertial reference frame, GR is required. Two approaches for that are to use pseudo-gravitational potential or to use relativistic Lagrangian dynamics. These approaches are taken in the reference given by @Sagittarius A-Star in Post #17. Both approaches give the same answer as the one calculated with SR using the IRF of the non-traveling twin.

I hope that this is a good representation of the situation. Thanks to all for clarifying it for me.

 

[PeterDonis]

1) The correct answer to the Twins Paradox can be calculated using only SR and the IRF of the non-traveling twin.

Yes.

2) Within SR, there is no real symmetry in the twins' situations because the traveling twin can detect that he does not remain in an IRF.

Yes.

ne can not use his non-inertial reference frame and SR to calculate the correct answer.

No.

3) In order to calculate the correct answer using the traveling twin's non-inertial reference frame, GR is required.

No.

Two approaches for that are to use pseudo-gravitational potential or to use relativistic Lagrangian dynamics. These approaches are taken in the reference given by @Sagittarius A-Star in Post #17.

These aren't two different approaches.

give the same answer as the one calculated with SR using the IRF of the non-traveling twin

Yes.

See my corresponding post in the other thread in which you made an almost identical post for the details behind the above responses.

 

[FactChecker]

See my corresponding post in the other thread in which you made an almost identical post for the details behind the above responses.

Yes. Somehow I switched to that other thread without me noticing it. I have deleted that post from there and put it here. Thanks for your answers.

 

[PeterDonis]

I have deleted that post from there and put it here.

I just undeleted it, since the Post #17 reference you gave is actually in that other thread, not this one. I agree that duplicate posts are normally not a good idea, but in this case I think it's reasonable to have both since similar issues have been discussed in both threads.

 

[Dale]

So one can not use his non-inertial reference frame and SR to calculate the correct answer.

One can use a valid non inertial reference frame and SR to calculate the correct answer. But you have to derive the correct formula anew. You cannot simply use the standard formula derived for an inertial reference frame and just directly apply it in the non-inertial reference frame.

 

[FactChecker]

One can use a valid non inertial reference frame and SR to calculate the correct answer. But you have to derive the correct formula anew. You cannot simply use the standard formula derived for an inertial reference frame and just directly apply it in the non-inertial reference frame.

When you are doing SR in a non-inertial reference frame, I wonder where you would say that SR ends and GR begins. I just think of GR as allowing non-inertial reference frames. From what you, @vanhees71, and @PeterDonis are saying, that is not right. Does it have to do with the curvature of the space?

 

[Ibix]

When you are doing SR in a non-inertial reference frame, I wonder where you would say that SR ends and GR begins. I just think of GR as allowing non-inertial reference frames. From what you, @vanhees71, and @PeterDonis are saying, that is not right. Does it have to do with the curvature of the space?

Flat spacetime = SR
Curved spacetime = GR

I think there was some argument in the early days about which label to apply to non-inertial frames in flat spacetime. But ultimately there's no physics in non-inertial frames that isn't in inertial frames - just the maths is harder. There is new physics in curved spacetime. So it makes sense to draw the dividing line there.

 

[FactChecker]

Flat spacetime = SR
Curved spacetime = GR

I think there was some argument in the early days about which label to apply to non-inertial frames in flat spacetime. But ultimately there's no physics in non-inertial frames that isn't in inertial frames - just the maths is harder. There is new physics in curved spacetime. So it makes sense to draw the dividing line there.

I think that I am finally getting to the bottom reason for my stubbornness on this issue. I had the very definition of SR and GR wrong. Sorry. I think I owe an apology to many people.

 

[PeterDonis]

I had the very definition of SR and GR wrong.

As I commented earlier, so does the Gron paper that was referenced. There are other sources in the literature that also get this wrong; a big reason for that is that it took a fair amount of time after relativity was first discovered for physicists to get clear about this, because of the issue @Ibix mentioned with regard to non-inertial frames. Even Einstein wasn't entirely clear about it in all of his writings.

 

[Dale]

Does it have to do with the curvature of the space?

Yes. Flat spacetime is SR and curved spacetime is GR

 

[vanhees71]

"True gravity", i.e. the gravitational interaction is within GR covariantly characterized by curvature. If there's no gravitational interaction (or rather can be neglected as in particle physics) then SR is valid.

 

[PeterDonis]

I am pointing out that time is is also affected by energy in space. An energytime.

This is personal theory, which is off limits here. You have now been banned from further posting in this thread.