# B One way twin

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Summary
time dilation with a one way twin
(I swore to myself I would never ask a relativity question again....oh well)

I don't know why I can't find anything about this in a search so I guess I'll just have to ask. Is a twin that takes off to Mars to stay, younger than a stay at home twin or is it ambiguous? I would think that this could be determined simply by sending the current time to each other and subtracting the data travel time using distance and c, determining in this way if the Martian's clock had slowed. In reading some twin paradox threads it seems this can be ambiguous and is not determinable and that times cannot be compared unless the clocks are in the same location. I'm assuming for the sake of this question the relative velocity between Earth and Mars is 0 and am ignoring any gravitational effects.

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#### Orodruin

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It is ambiguous since the clocks are not colocated.

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That was going to be my guess, but why is my method of determining the clock differences not valid if there is no relative motion? I thought simultaneity issues didn't matter if there was no relative motion.

#### Dale

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Is a twin that takes off to Mars to stay, younger than a stay at home twin or is it ambiguous?
It is ambiguous, or more precisely the answer is frame variant.

#### Ibix

To see if two people have experienced the same elapsed time you need to compare their watches at the beginning and end of the period. If, at either of those comparisons, the watches are not colocated then the relativity of simultaneity means that different frames have different views about what "the beginning and end of the period" actually means.
I thought simultaneity issues didn't matter if there was no relative motion.
But there is relative motion between all the people at rest in all the different frames you could be using.

If you specify a frame then there is a unique answer. But there's no One True Choice Of Frame whose answer is "more right" than any other.

#### FactChecker

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Suppose that clocks on Earth and Mars are synchronized (we are assuming there is no relative motion) and remain synchronized through the entire experiment. Then a clock that traveled with the traveling twin can be compared with the Mars clock and the Earth clock will agree with the result as though they were collocated. The acceleration (and deceleration) of the traveling twin will slow down his clock. He will be younger.

#### phinds

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The acceleration (and deceleration) of the traveling twin will slow down his clock.
No, it will decrease his aging, not slow down his clock. I think this is an important distinction for someone not yet solid on SR because most such people thing those are identical things and it causes them great confusion.

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To see if two people have experienced the same elapsed time you need to compare their watches at the beginning and end of the period. If, at either of those comparisons, the watches are not colocated then the relativity of simultaneity means that different frames have different views about what "the beginning and end of the period" actually means.
I think I see. So it seems that the fact that there was relative motion between the time when the clocks were synchronized (colocated) and the time when the measurements took place that make the determination ambiguous. Is this correct?

So if the Martian determined that the Earth clock had slowed, the Earthling, making the same measurement could conflictingly determine that in fact it was the Martians clock that had slowed? They would not agree on their measurements?

#### Ibix

Suppose that clocks on Earth and Mars are synchronized (we are assuming there is no relative motion) and remain synchronized through the entire experiment.
But synchronised using what synchronisation convention?
The acceleration (and deceleration) of the traveling twin will slow down his clock.
It's not the acceleration that's important here, just the velocity. You can have someone pass Earth at constant speed, zero their clock as they pass, and find that when they pass Mars their clock is not in sync with the Mars clock - no acceleration needed.
He will be younger.
According to Einstein synchronised clocks, yes.

#### Ibix

So it seems that the fact that there was relative motion between the time when the clocks were synchronized (colocated) and the time when the measurements took place that make the determination ambiguous. Is this correct?
No. The point is that anyone in motion with respect to Eargh and Mars will regard their clocks as desynchronised. And they aren't wrong in any sense.

Under the simultaneity convention of Earth and Mars, the traveller is younger than his twin at home. But under other simultaneity conventions he may not be because "on Earth at the same time as the travelling twin gets to Mars" means different things to different frames.

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According to Einstein synchronised clocks, yes.
Wait. I thought we just determined it was ambiguous?

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Under the simultaneity convention of Earth and Mars, the traveller is younger than his twin at home. But under other simultaneity conventions he may not be because "on Earth at the same time as the travelling twin gets to Mars" means different things to different frames.
OK, the Martian and the Earthling will agree, the Martian is younger. This is real? The Martian actually is younger and will live longer?

#### FactChecker

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But synchronised using what synchronisation convention?
By Einstein convention
It's not the acceleration that's important here, just the velocity. You can have someone pass Earth at constant speed, zero their clock as they pass, and find that when they pass Mars their clock is not in sync with the Mars clock - no acceleration needed.
Without taking acceleration into account, both twins think that the other twin is aging slower. It is the acceleration that breaks the symmetry and allows both twins to agree that the traveling twin aged more slowly (and by how much). By the time the traveling twin stops, they both must agree.

#### Ibix

This is real?
It depends on your simultaneity convention. So I'd say it's not real. It's comparable to the statement that you were doing 30mph. You really were doing 30mph relative to the surface of the Earth, but you were also doing a couple of hundred with respect to the Earth's center of mass, and about 20km/s with respect to the Sun. None of those figures is any less real than any other.

In the mutual rest frame of the Earth and Mars (to the extent there is such a thing...) the traveller is younger. In some frames, he's older. Neither answer is more real than the other.

#### Ibix

It is the acceleration that breaks the symmetry
No - as I pointed out, the same effect happens with an always-inertial observer passing Earth and Mars. The difference between the two frames here is that one of them has one clock (on the ship) and the other has two (Earth and Mars) and we do local comparisons between the ship clock and the Earth clock and the ship clock and the Mars clock.

#### hutchphd

No. The point is that anyone in motion with respect to Eargh and Mars will regard their clocks as desynchronised. And they aren't wrong in any sense.

Under the simultaneity convention of Earth and Mars, the traveller is younger than his twin at home. But under other simultaneity conventions he may not be because "on Earth at the same time as the travelling twin gets to Mars" means different things to different frames.
My twin brother moved to Boise. Are you saying that arbitrary observers cannot agree that we are the same age?

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In the mutual rest frame of the Earth and Mars (to the extent there is such a thing...) the traveller is younger. In some frames, he's older. Neither answer is more real than the other.
I'm only interested in the Earthling and Martian since they have no relative velocity when all it said and done. I'm surprised at this answer because of all the discussion that acceleration has nothing to do with it and since the Martian stays, there is also no "turn around" point causing a shift in frames which is usually what is considered to be the reason for the traveler being younger. It certainly does seem that acceleration and not relative velocity is important. With no turn around point, what is causing the definitive aging difference.

#### Ibix

My twin brother moved to Boise. Are you saying that arbitrary observers cannot agree that we are the same age?
For that distance and the speeds involved the relativistic effects are a lot less than the difference in your birth times. But if you both had atomic clocks, synchronised before the move, then different observers would certainly have different opinions about the difference in their readings after it.

If my visualisation is correct you can't actually "swap ages" by changing frames unless you had a near-lightspeed removal service (same goes for the Mars trip). I could be wrong about that - I've just sketched a Minkowski diagram in my head, not done the full maths.

#### Ibix

there is also no "turn around" point causing a shift in frames which is usually what is considered to be the reason for the traveler being younger.
That's not why the traveller is younger. The traveller is younger because your elapsed time is the "length" of your path through spacetime, and the traveller took a shortcut, essentially. And this is why the Earth-to-Mars traveller is younger in the Earth frame - the route he took between the Earth's "now" when he left and the Earth's "now" when he arrived was shorter.

The frame change explains why claiming that "the stay at home twin is always moving for the traveller" and naively applying the time dilation formula gives the wrong answer.

#### FactChecker

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I'm surprised at this answer because of all the discussion that acceleration has nothing to do with it and since the Martian stays, there is also no "turn around" point causing a shift in frames which is usually what is considered to be the reason for the traveler being younger.
It is not necessary to turn around to change the inertial reference frame. The acceleration leaving Earth and deceleration at Mars causes a shift in frames.

#### hutchphd

That's not why the traveller is younger. The traveller is younger because your elapsed time is the "length" of your path through spacetime, and the traveller took a shortcut, essentially. And this is why the Earth-to-Mars traveller is younger in the Earth frame - the route he took between the Earth's "now" when he left and the Earth's "now" when he arrived was shorter.

The frame change explains why claiming that "the stay at home twin is always moving for the traveller" and naively applying the time dilation formula gives the wrong answer.
My point is that this would also be true if the Martian trip were a round trip. It is not the lack of co-location that causes an issue. In fact any movement apart can be done symmetrically.

#### Dale

Mentor
I'm only interested in the Earthling and Martian since they have no relative velocity when all it said and done.
That is fine. The answer is still frame variant, but by specifying the frame you can at least get a unique answer.

In this frame the person who traveled from earth to mars is younger.

It certainly does seem that acceleration and not relative velocity is important.
Why do you think this? The same individual who accelerates is also the same individual who has a non-zero velocity relative to the specified frame. So there is no way your “and not ...” claim can be justified here.

#### Dale

Mentor
It is not the lack of co-location that causes an issue
It is the lack of co-location that makes the age difference frame variant. If they were co-located then all frames would agree on their age difference. But since they are not collocated different frames disagree

#### FactChecker

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When something is true, it can often be proven in multiple ways. Accelerations (including instantaneous changes in velocity) match the path which indicates that the traveling twin is younger. You can't have one without the other. But for the actual physical processes to be have been slower in the traveling twin when they reach a directly comparable state, there must be more profound going on than a simple graph on paper -- even if the graph on paper gives the correct result.
EDIT: I want to correct the prior statement. This graph on paper is a very direct representation of the trade-off between motion in the time axis and motion in the spatial dimensions. As such, it is profound and can account for the different ages.

The spatial separation of Earth and Mars is not enough to prevent comparing the twins. Suppose there is also a "pseudo-twin" on Mars who was born at the exact same time according to Einstein-synchronized clocks. Because there is never any relative motion between Earth and Mars (OP assumption), the Earth twin and the Mars pseudo-twin age identically (by Einstein synchronized clocks). Eventually, the traveling twin slows to a stop at Mars and compares his physical age (how his physical processes have progressed) with that of the "pseudo-twin". Their inertial frames are now identical and there is a moment of truth -- were the physical processes of one slower than the other or not? If so, then one is younger. If not, they are the same age. The traveling twin is younger than the Mars pseudo-twin because of the acceleration (or, if you like, the path which indicates acceleration). Likewise, the traveling twin is younger than the Earth twin.

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#### phinds

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Their inertial frames are now identical and there is a moment of truth -- were the physical processes of one slower than the other or not? If so, then one is younger. If not, they are the same age.
It sounds like you are continuing to promote the falacious point of view that things slow down for the traveler IN HIS FRAME. That is not true. Neither his clock nor his biological processes slow down in his frame, he's just taking a different path through space-time so the NUMBER of ticks of his clock is different but not the rate at which they occur.

I think we need to be careful not to promote this very misleading point of view.

"One way twin"

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