Two people passing in space

Nov 2019
1
0
ohio
Person A and person B are flying at each other through space
Person A sees himself as stationary and sees person B moving towards him at half the speed of light
So to person A, time is slowing down for person B and person B is aging slower
When they are 10 light years apart they are both 40 years old
20 years later when person B arrives he is only 50 years old since timed moved slower for him while person A is 60 years old

But person B would see the the same thing, when person A arrives, person A is 50 years old and person person B is 60 years old

They can't both happen, so what would happen?

My guess is that person B would not see the same thing as Person A
When they are 10 light years apart, Person B would see himself as 30 years old, and person A as 50 years old
So 20 years later when Person B got there , he would be 50 years old and person A would be 60 years old
Is this correct?
 

topsquark

Forum Staff
Apr 2008
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On the dance floor, baby!
This is an example of the famous "Twin Paradox." When they are passing each other, yes, they do see that the other person is aging slower than they are. But the problem, in a nutshell, is that one of the people (or both) has to accelerate to get back to the other person. Since one is accelerating then we have a distinction between the two people and one of them ages faster than the other at the turn around point.

-Dan
 

ChipB

PHF Helper
Jun 2010
2,361
289
Morristown, NJ USA
I don't think the OP's post involves acceleration, so it's not quite the classic twin paradox.

The issue here is in this statement: "When they are 10 light years apart they are both 40 years old ." According to whom? Remember that under SR you can't say that two events occurring far apart for objects moving at relativistic speeds are "simultaneous" in the same way as you do with every day observations on Earth. So to say that they are both 40 years old at a certain point in time is incorrect. You are correct that A and B each see the other as aging more slowly than they, so if each measures 20 years passing in their own inertial frames, but only ten ten years for the other person's frame, then that means that when they were 10 LY apart each saw the other as being 10 years older than themselves.
 
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physicsquest

PHF Helper
Feb 2009
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474
I agree with Chip . The problem is in the statement "When they are 10 light years apart they are both 40 years old " and as Chip asked according to who's clock? In special relativity the way time measurements are made is as follows. Each frame has a set of clocks stretching from - infinity to + infinity, and they are all synchronized, i.e. read the same time. So all A's clocks read the same time, and so do all B's clocks. But clocks in both frames won’t read the same time even if they were synchronized earlier if they are in relative motion. Whenever the time for an event has to be recorded, the clocks in each frame closest to the event note the time. You can imagine a picture being clicked by both clocks which includes the event, A’s clock and B’s clock. These can be compared later using Whatsapp or whatever. The point is that they can’t disagree on the photographic evidence. So if A reads for example 80, and B 70, this can’t be contested. So one observer feels that the others clocks have also lost synchronization, not just slowed down and makes peace with the difference in readings. Another way is to understand that simultaneity for events separated in space is not absolute. So if A says my clock read t1 and “at the same time” B’s read t2, B will say when my clock read t2, “at the same time” A’s read say t3. The “at the same time” stuff is different for both A and B, so in a sense they, as you said see different things. There is a concept called lines of simultaneity in space-time or Minkowski diagrams. These are very helpful in understanding this sort of question. Do look them up.

Hope this helped.
 
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Jun 2016
1,142
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England
You are implicitly introducing a third observer C at the point where the paths of A and B cross
and defining the observations of observer C as being the "correct" observation.

If everyone agrees that A and B are 50 when the meeting takes place
then they will all disagree when they are 10 light years apart.
 
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