In the twin paradox without acceleration, who ages less?

[imsmooth]

I know this has been asked so many times, but would someone please answer why to this particular variation to the question.

Tom is moving at constant velocity past Jerry on Earth (assume no acceleration). At the moment they pass each other they agree on the time seen on a clock. Tom thinks Jerry is moving past him; Jerry thinks Tom is moving past him. After a sufficient time moving away from the other at relativistic speed (and no turning around), who is older? Each thinks the other is older.

 

[haushofer]

Yes, each person measures time dilation at the other person. Otherwise the principle that inertial frames are equivalent would be violated.

Who's older? Well, to sensibly answer that question you need to compare their clocks with the lapsed proper times. And for that...well, guess what.

 

[PeroK]

I know this has been asked so many times, but would someone please answer why to this particular variation to the question.

Tom is moving at constant velocity past Jerry on Earth (assume no acceleration). At the moment they pass each other they agree on the time seen on a clock. Tom thinks Jerry is moving past him; Jerry thinks Tom is moving past him. After a sufficient time moving away from the other at relativistic speed (and no turning around), who is older? Each thinks the other is older.

There are a number of issues here.

First, let's tidy this up by having Tom and Jerry synchronise their watches as they pass each other. Then, let's have a well-defined second event, such as Tom reaching Mars.

Now, you can analyse this from either Tom or Jerry's frame and things are clear. Tom's watch will show a definite time as he passes Mars. There is no issue there.

Second, unless Tom and Jerry are at the same location, it's not clear what it means for one to be "older" than the other. Who is measuring age? And how are they measuring it?

Third, unless one of them changes their state of motion, then can never meet again to compare the time on their watches. Time dilation, therefore, is not equivalent to differential ageing. The time dilation in this case is symmetric. Each measures the others clock to be running slow (not fast), but unless one of them change their state of motion, this doesn't lead to any contradiction.

 

[Ibix]

Each thinks the other is older.

Each thinks the other is younger. They don't have the same definition of "at the same time" except when they are co-located. So the question "how old is the other guy at the same time as my clock shows one year since we met" means different things and there isno contradiction in both of them saying the other is younger.

 

[Nugatory]

After a sufficient time moving away from the other at relativistic speed (and no turning around), who is older? Each thinks the other is older.

That is correct, but when you remember to consider the relativity as well as time dilation, there is no paradox. We have a number of older postings explaining the relationship between time dilation and relativity of simultaneity and how you need both to make sense of this apparently contradictory situation.

Be aware that what you're describing here is not the twin paradox. The twin paradox arises when the traveller turns around and returns to earth. In that situation, and for reasons that have nothing to do with time dilation, the traveller will unambiguously be younger at the reunion - and the apparent paradox is that at every step of the traveller's journey time dilation suggests that they should find the Earth twin to be aging more slowly. In this case the paradox comes from erroneous misapplication of the time dilation formula.

 

[FactChecker]

Each is observing the other at a moving location along the relative path. Each one thinks that the other is moving behind him on that path. The discrepancy in their clocks is being determined in opposite directions in different locations. So there is no paradox. Each one thinks that the other is aging slower (clocks going slower) than it should. So the problem really is all about how each one has synchronized his own clocks along the path of relative motion.