Time Dilation Question: Two Men's Watches Differ after Space Travel

[Julius Ceasar]

TL;DR

After you undergo time dilation do you still exist at the same time?

Sometime in the future two men meet at a space port and they synchronize watches, one boards a spacecraft and goes on a round trip around the solar system, when he returns the two men compare wristwatches to find they have different times.
Q. Do the two men still exist at the same time or not?

 

[weirdoguy]

Do the two men still exist at the same time or not?

What does that even mean?

 

[PeterDonis]

Q. Do the two men still exist at the same time or not?

This question is not answerable as you ask it because "exist at the same time" has no well-defined meaning.

If you ask, do the two men see each other, hear each other, experience each other as being right next to them, have other people agree that they are both standing right there next to each other, etc., etc., the answer is yes.

If you ask, do the two men read the same time on their watches, the answer is no.

 

[Ibix]

Q. Do the two men still exist at the same time or not?

As others have noted, this question doesn't really make sense. I think the underlying thinking is that, if the traveller experiences eight years and the stay-at-home experiences ten years, then somehow the stay-at-home doesn't reach the traveller's return event until two years after the traveller does. The physical model underlying that, I think, is of worldlines as paths through spacetime with objects as animated dots traveling along the worldlines. This is not a correct model. We know this because relativistic effects occur at all speeds. With modern atomic clocks we know that twin paradox effects occur if you pop to the shops for some milk. Your family is still there when you get back.

 

[PeroK]

What does that even mean?

It means the OP is a philosophy student!

 

[vanhees71]

Well, then you have to answer the important question, whether it's possible for two non-existing people to compare clocks . It must be related to the problem, how many angels can be placed at one point...

 

[DiracPool]

Summary:: After you undergo time dilation do you still exist at the same time?

Q. Do the two men still exist at the same time or not?

The short answer is Yes. If the two dudes are hanging out having a beer after one travels around the solar system and the other one was tanking beers for two weeks at the space port then, Yes, they are existing at that moment at/in the same time because they are currently in the same inertial reference frame.

When you say "still" exist in/at the same time as when they did before the one dude took the trip, you complicate the issue. Technically, they are not existing at the same time relative to two weeks ago, as is evidenced by the different times they show on their watches. However, strictly speaking, nobody even at the space port exists in the same time after any average two weeks of time because everyone is moving relative to everyone else at different velocities which changes the values on each of their watches, not to mention if you're on the second level of the space port if it's say, in a microgravity orbit above the Earth.

 

[MikeeMiracle]

I know it's hard to grasp at first but there is no "absolute" time as such. We all experience the flow of time differently depending on our path through "spacetime." You need to look to further your understanding of exactly what "spacetime" is to understand this further and answer your question. I understood it through watching youtube video's containing spacetime diagrams. "TBS Spacetime" and "The Science Asylum" are good resources for those of us who are not comfortable doing the maths.

 

[andrew s 1905]

I don't understand why some senior forum member decided to poke fun at the OP.

The question was answered reasonably by @PeterDonis .

I read it as how do you lable the event of there meeting. It has the same space coordinates (give or take their physical size) but what about the time coordinate given their clocks now differ.

Regards Andrew

 

[FactChecker]

The simple answer is yes, time dilation does not cause anything bizarre. It is the same as if you compare your watch to someone else's and the watches do not agree. The fact that the watches ran at different rates does not cause you great concern. And if your twin has slightly greyer hair, you are not amazed or worried that he does not exist.

 

[Nugatory]

It has the same space coordinates (give or take their physical size) but what about the time coordinate given their clocks now differ.

There’s no reason why the time coordinate of an event must be related to either clock reading. We can choose a coordinate system in which the time coordinate of the event “travelers meet up again” is equal to what one or the other clock reads at that event or something else altogether.

 

[vanhees71]

I don't understand why some senior forum member decided to poke fun at the OP.

The question was answered reasonably by @PeterDonis .

I read it as how do you lable the event of there meeting. It has the same space coordinates (give or take their physical size) but what about the time coordinate given their clocks now differ.

Regards Andrew

Both the space-time coordinates are the same when you want to compare the clocks. As Einstein put it, there is to observe in general-relativistic spacetime are coincidences of events. In this case you read off the times the clocks of the two space travelers show at one space-time point.

 

[andrew s 1905]

Thank you @Nugatory and @vanhees71 I know. I was just pointing out the OP's question made sense and could be answered as you both have done. Regards Andrew

 

[etotheipi]

I think the underlying thinking is that, if the traveller experiences eight years and the stay-at-home experiences ten years, then somehow the stay-at-home doesn't reach the traveller's return event until two years after the traveller does. The physical model underlying that, I think, is of worldlines as paths through spacetime with objects as animated dots traveling along the worldlines. This is not a correct model.

That is the optimal answer; a worldline must be considered in its entirety as a 'history' of a particle, and it is wrong to think that a particle moves along its worldline. Nothing moves in spacetime!

However given any third observer with arbitrary worldline, there's always a spacetime domain where his local rest spaces $\mathscr{E}_{\mathbf{u}}(\tau)$ introduce a regular slicing of the spacetime. This let's you define a perfectly normal Euclidean vector space, where you can now consider the evolution of this reference space as per usual with respect to the affine parameter.

 

[russ_watters]

I don't understand why some senior forum member decided to poke fun at the OP.

Because they are human and sometimes an idea can be so off-base that it is funny? I actually think when an idea is irredeemably wrong there is some value in a a little poke, because the OP needs to understand that the idea needs to be dropped completely, otherwise they may continue down the same line of thinking, trying to adjust it to make sense. The OP (and another recent one) sounds to me like a Star Trek episode where the crew is in a cave with some aliens, but can't see them because they are "out of phase". That's not a thing, it's just gibberish/technobabble. And I really think fiction media is where a lot of these ideas come from.

Time dilation (differential aging) is strange enough without adding extra dimensions to it. But it can be distilled down into simple/mundane examples sometimes, such as where two people are simply standing next to each other looking at each others' watches and seeing that the times are different.

 

[andrew s 1905]

Because they are human and sometimes an idea can be so off-base that it is funny? I actually think when an idea is irredeemably wrong there is some value in a a little poke, because the OP needs to understand that the idea needs to be dropped completely, otherwise they may continue down the same line of thinking, trying to adjust it to make sense. The OP (and another recent one) sounds to me like a Star Trek episode where the crew is in a cave with some aliens, but can't see them because they are "out of phase". That's not a thing, it's just gibberish/technobabble. And I really think fiction media is where a lot of these ideas come from.

Time dilation (differential aging) is strange enough without adding extra dimensions to it. But it can be distilled down into simple/mundane examples sometimes, such as where two people are simply standing next to each other looking at each others' watches and seeing that the times are different.

Human nature or not poking fun at people is unlikely to educate them in the way you claim. It is, I would suggest, more likely to turn them away for the forum and probably to less rigorous sites.

One can be civil in pointing out misunderstanding as others clearly demonstrate.
It is, in my opinion, arrogant to assume any misguided view is due to science fiction influence without any evidence to support it.

Regards Andrew

 

[Ibix]

I don't understand why some senior forum member decided to poke fun at the OP.

Not sure if that was aimed at me. If so, I was not making fun - here's a PF post with someone espousing exactly the model I was criticising. I find it much easier to interpret the OP's question as implying that model than as a confusion over coordinate systems, to the extent that your interpretation never occurred to me. I may be wrong, of course.

 

[andrew s 1905]

@Ibix It was not. Regards Andrew

 

[russ_watters]

Thread reopened on OP request. Let's get back to/keep on topic, thanks.

 

[Ibix]

I think you are using "exist at the same time" without defining what you mean by the phrase. I take it to mean that both observers are present and capable of interacting. Of course there's evidence of that - my "popping to the shops" comment was not an idle one. From your latest comment (edit: which appears to have been deleted), though, I think you just mean that the two twins' watches show different times when they meet up. Yes. So what? Elapsed time, in relativity, is very like distance travelled. You and I can meet up, then you can sit there while I walk away and come back. While you are saying that we now "don't exist at the same time", would you also say that we "don't exist at the same place" because my FitBit shows I walked a hundred paces and yours shows you did not move?

If I can assume you all agree that this family must always exists at the same time as the person popping to the shops; then as far as you are all concerned an actual slowing of time does not result in an actual different time, I don’t know how you can conclude such nonsense, stop drinking the timeflow coolaide and check yourselves, this is just dumb.

...or else you aren't communicating clearly, or aren't understanding correctly what you are communicating about.

Certainly the stay-at-home and the traveller experience different amounts of time between departure and return and their watches will show different times. If you want to phrase that as "they exist at different times" I can't stop you, but as you can see from this thread it causes a lot of confusion. It would be better to use more standard terminology: they have experienced different elapsed times, or their watches are no longer in sync, or they have undergone differential aging, or something of that nature.

 

[FactChecker]

Q. Do the two men still exist at the same time or not?

When they get back together, they disagree on what time it is, and each time is equally legitimate. That is just another way of saying that there is no universal time. But no matter which time you pick, they both exist.

 

[vanhees71]

At the end it always boils down to the fact that one can unambigously compare clock readings only when being at the same position. The twin paradox thus should be always discussed by considering the two twins starting at the same position and there synchronizing their (ideal, e.g., atomic) clocks and then meeting again later. Then the clock readings when meeting again at the same place is simply given by the proper times, which are invariants,
$$\tau_{j}=\frac{1}{c} \int_{\lambda_1}^{\lambda_2} \mathrm{d} \lambda \sqrt{\dot{x}_{j}^{\mu} \dot{x}_{j\mu}}.$$
In this case you have a well-defined frame-independent result answering the question which of the twins aged more from starting at one place and meeting again at one place.

It's of course not a paradox that the aging can be different for the two twins, if seen in this geometrical space-time picture.

It's not more surprising than the analogous case of travel distances of two people traveling from Frankfurt to Paris, one taking the direct connection and the other going to Rome first and then traveling on to Paris. Of course the latter one had a much longer travel distance from Frankfurt to Paris than the former, which is far from being a paradox ;-)).

 

[PeterDonis]

Thread closed for moderation.

 

[russ_watters]

This thread hasn't gotten any better, so we're going to just keep it locked.