Twin Paradox in 3-sphere (S^3)

[MeJennifer]

There is exactly one mechanism. If \gamma is the worldline of a twin between the two events where the twins meet, parametrized by u \in [0, 1], then the twin ages

\Delta \tau = \int_{\gamma} || \frac{d \gamma}{du} || \, du.

The amount each twin ages is a different integral, and thus can have different numerical values. We can compare those numbers to tell which twin ages more.

Exactly right, and really, that is all there is to say about this "paradox".

 

[KingOrdo]

I can make it no more perspicuous for you. Consult the arXiv if you need clarification.

So again, I must ask: any ideas? To quote pervect:

"There is a general agreement about the broad details, which is that the two twins won't be the same age.

The disagreement as I read it is how to explain the age difference, i.e. to point to a particular mechanism. The first papers say that it can be addressed in terms of winding number (which is a topological property that doesn't even need a metric). The second papers say that this is not correct, that one needs more than the winding number to properly explain the age difference, that one needs the metric information.

Everyone agrees that there should be an age difference AFAIK."

So: what is the proper resolution? Is the 'winding number' approach right, despite its apparent refutation in the literature? Or do Barrow and Levin have the right idea? Is there perhaps another idea we're missing? And please: I can't explain it any better than I already have; consult the literature if you're unsure about why the paradox may persist in the complex cases.

Any ideas?

 

[Hurkyl]

I can make it no more perspicuous for you. Consult the arXiv if you need clarification.

I'm not aware of anything I need clarified, except maybe precisely what you think, why you think that way, and what criteria an answer must satisfy before you would find it acceptable.

 

[KingOrdo]

I'm not aware of anything I need clarified, except maybe precisely what you think, why you think that way, and what criteria an answer must satisfy before you would find it acceptable.

I can make it no more perspicuous for you. Consult the arXiv (and my earlier posts) if you need clarification.

So again, I must ask: any ideas? To quote pervect:

"There is a general agreement about the broad details, which is that the two twins won't be the same age.

The disagreement as I read it is how to explain the age difference, i.e. to point to a particular mechanism. The first papers say that it can be addressed in terms of winding number (which is a topological property that doesn't even need a metric). The second papers say that this is not correct, that one needs more than the winding number to properly explain the age difference, that one needs the metric information.

Everyone agrees that there should be an age difference AFAIK."

So: what is the proper resolution? Is the 'winding number' approach right, despite its apparent refutation in the literature? Or do Barrow and Levin have the right idea? Is there perhaps another idea we're missing? And please: I can't explain it any better than I already have; consult the literature if you're unsure about why the paradox may persist in the complex cases.

Any ideas?

 

[JustinLevy]

The symmetry demanded by Einstein was local, and it's still present even in these "complex spaces". It's not "broken".

No, it is broken. And it's broken in different ways; cf. the arXiv.

You are misunderstanding the papers. And you are misunderstanding the posters here trying to teach you.

As pervect said:
"IMO Hurkyl isn't saying anything that conflicts with the literature. He is trying (rather patiently) to correct some of King Ordo's misunderstandings of what the literature is saying as far as what the cosmological twin "paradox" is about and what it is not about."

In short, people are trying to be very patient with you and help answer your questions. But you continue to ignore or misunderstand all the help presented to you.

I can understand that you do not believe you are misunderstanding anything, but please entertain the possibility to allow this discussion to move forward.

So again, I must ask: any ideas?

Yes, I have an idea to help this discussion. To clear up some misunderstanding and help everyone see where the root problem is coming from ... and to prevent the discussion from continuing in circles indefinitely ... KingOrdo, please answer these questions:

1) As pervect mentioned, even in a non-closed universe, two distinct inertial paths can cross in two places.
a] So before moving onto closed spaces, do you understand that there is no paradox about how much proper time elapsed on these two world lines?

b] If so, please explain your understanding of the resolution of this "paradox" to give others a starting point to build explanations from.

2) Do you agree that the question of how much proper time elapsed requires a geometry, ie. that until a geometry is defined we cannot ask for the distance between spacetime points? If not, please explain why.

3) Do you agree that specifying a geometry does not specify a coordinate system (ie. the description is still coordinate invarient)? If not, please explain why.

4) Do you agree that once the geometry is specified, there is a unique answer to how much proper time elapsed along a path in spacetime? And therefore there is no "paradox"? If not, please explain why.

 

[KingOrdo]

I simply can't make it any clearer for you. If the fundamentals of relativity theory are still hazy to you, I can recommend some excellent references. Also, consult the arXiv (and my earlier posts) if you need clarification.

So again, I must ask: any ideas? To quote pervect:

"There is a general agreement about the broad details, which is that the two twins won't be the same age.

The disagreement as I read it is how to explain the age difference, i.e. to point to a particular mechanism. The first papers say that it can be addressed in terms of winding number (which is a topological property that doesn't even need a metric). The second papers say that this is not correct, that one needs more than the winding number to properly explain the age difference, that one needs the metric information.

Everyone agrees that there should be an age difference AFAIK."

So: what is the proper resolution? Is the 'winding number' approach right, despite its apparent refutation in the literature? Or do Barrow and Levin have the right idea? Is there perhaps another idea we're missing? And please: I can't explain it any better than I already have; consult the literature if you're unsure about why the paradox may persist in the complex cases.

Any ideas?

 

[JustinLevy]

If you are not willing to entertain the possibility that you are misunderstanding, then you can never learn. In that case, it is pointless to even try to have a discussion about this with you. Is this what you are telling us?

I truly hope not. So please go back and answer the questions asked here:
https://www.physicsforums.com/showpost.php?p=1269327&postcount=105

 

[KingOrdo]

JustinLevy, I simply can't make it any clearer for you. If the fundamentals of relativity theory are still hazy to you, I can recommend some excellent references. Also, consult the arXiv (and my earlier posts) if you need clarification.

So again, I must ask: any ideas? To quote pervect:

"There is a general agreement about the broad details, which is that the two twins won't be the same age.

The disagreement as I read it is how to explain the age difference, i.e. to point to a particular mechanism. The first papers say that it can be addressed in terms of winding number (which is a topological property that doesn't even need a metric). The second papers say that this is not correct, that one needs more than the winding number to properly explain the age difference, that one needs the metric information.

Everyone agrees that there should be an age difference AFAIK."

So: what is the proper resolution? Is the 'winding number' approach right, despite its apparent refutation in the literature? Or do Barrow and Levin have the right idea? Is there perhaps another idea we're missing? And please: I can't explain it any better than I already have; consult the literature if you're unsure about why the paradox may persist in the complex cases.

Any ideas?

 

[MeJennifer]

Any ideas?

Yes, to close this topic, it's going nowhere.

 

[KingOrdo]

Yes, to close this topic, it's going nowhere.

Indeed; but not for want of trying on my part. I've been extremely patient, to the tune of five pages of posts. . . .

 

[JustinLevy]

JustinLevy, I simply can't make it any clearer for you.

Why do you insist on evading the questions? That would make your position abundantly clear. Which currently it is not as you keep stating things that contradict GR as well as the papers you are referring to.

The previous questions and related points have been brought up by other posters and you continue to ignore them or resist acknowledging them. In doing so you ignore the very discussion you repeatedly seek. So if you do not answer those questions, it will be nearly impossible for any poster to help you.

This is a simple request, and the questions are not difficult or time consuming. So please answer the specific questions previously given to you.

 

[KingOrdo]

JustinLevy, I simply can't make it any clearer for you. If the fundamentals of relativity theory are still hazy to you, I can recommend some excellent references. Also, consult the arXiv (and my earlier posts) if you need clarification.

So again, I must ask: any ideas? To quote pervect:

"There is a general agreement about the broad details, which is that the two twins won't be the same age.

The disagreement as I read it is how to explain the age difference, i.e. to point to a particular mechanism. The first papers say that it can be addressed in terms of winding number (which is a topological property that doesn't even need a metric). The second papers say that this is not correct, that one needs more than the winding number to properly explain the age difference, that one needs the metric information.

Everyone agrees that there should be an age difference AFAIK."

So: what is the proper resolution? Is the 'winding number' approach right, despite its apparent refutation in the literature? Or do Barrow and Levin have the right idea? Is there perhaps another idea we're missing? And please: I can't explain it any better than I already have; consult the literature if you're unsure about why the paradox may persist in the complex cases.

Any ideas?

 

[JustinLevy]

Yes, to close this topic, it's going nowhere.

Indeed; but not for want of trying on my part.

How can you possibly say that? It is going no where directly because of your lack of trying.

I have asked repeatedly for you to answer some simple questions. You refuse to acknowledge questions were even asked of you, let alone actually try to answer them.

So stop avoiding the questions, as these relate to the heart of the matter.
Please answer the following:

1) As pervect mentioned, even in a non-closed universe, two distinct inertial paths can cross in two places.
a] So before moving onto closed spaces, do you understand that there is no paradox about how much proper time elapsed on these two world lines?

b] If so, please explain your understanding of the resolution of this "paradox" to give others a starting point to build explanations from.

2) Do you agree that the question of how much proper time elapsed requires a geometry, ie. that until a geometry is defined we cannot ask for the distance between spacetime points? If not, please explain why.

3) Do you agree that specifying a geometry does not specify a coordinate system (ie. the description is still coordinate invarient)? If not, please explain why.

4) Do you agree that once the geometry is specified, there is a unique answer to how much proper time elapsed along a path in spacetime? And therefore there is no "paradox"? If not, please explain why.

 

[KingOrdo]

JustinLevy, I simply can't make it any clearer for you. If the fundamentals of relativity theory are still hazy to you, I can recommend some excellent references. Also, consult the arXiv (and my earlier posts) if you need clarification.

So again, I must ask: any ideas? To quote pervect:

"There is a general agreement about the broad details, which is that the two twins won't be the same age.

The disagreement as I read it is how to explain the age difference, i.e. to point to a particular mechanism. The first papers say that it can be addressed in terms of winding number (which is a topological property that doesn't even need a metric). The second papers say that this is not correct, that one needs more than the winding number to properly explain the age difference, that one needs the metric information.

Everyone agrees that there should be an age difference AFAIK."

So: what is the proper resolution? Is the 'winding number' approach right, despite its apparent refutation in the literature? Or do Barrow and Levin have the right idea? Is there perhaps another idea we're missing? And please: I can't explain it any better than I already have; consult the literature if you're unsure about why the paradox may persist in the complex cases.

Any ideas?

 

[MeJennifer]

You have now repeated that last posting 6 times.
To me that is trolling. Hopefully a moderator can take some action here.

 

[KingOrdo]

I've asked for moderators to intervene pages ago. I ask a simple question and get only evasion. I can explain myself no better than I already have. Any insult/evasion/irrelevance/etc. will be met by boilerplate. You should expect that. I am asking a serious question about a serious topic.

 

[JustinLevy]

I ask a simple question and get only evasion.

You did not get evasion. You got answers from several posters which you preceded to ignore or misunderstand. When people took the time to help resolve this misunderstanding you refused to help in anyway.

I can explain myself no better than I already have.

Yes you can. You can answer the simple questions directly addressed to you to help others understand where the common ground lays and where the disagreement occurs.

The questions are not an insult, nor an evasion, nor irrelevant.

The are simple, reasonable, and relevant. Your evasion of them makes me question your motives here. If you are not here to just troll, please stop evading the questions.

 

[ZapperZ]

Obviously, this thread is going nowhere. Questions have either been answered, or not been addressed, or issues not clear, etc.. etc.

After 8 pages of responses, I believe it is time to stick a fork into this one. Please do not repost this question in another thread.

Zz.