A Special Relativity Quiz from
Uncertain Principles Blog
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I am getting to apreciate sites designed for mobile devices..
My stabs at it :
Q : Two twins, named Alice and Bob in keeping with convention, get into identical rocket ships separated by a distance L, with Alice in front and Bob behind her. At a pre-arranged time, they each start their rocket, and accelerate for a pre-determined time. At the end of the acceleration, they are each moving at a relativistic speed-- 4/5ths the speed of light, say. Which of these twins is older at the end of the acceleration?
A : Not enough info, poorly written question. What does 'in front' and 'behind' mean? They start and finish in inertial frames having been accelerated. But the pattern ( direction, magnitudes and time dependence ) of acceleration(s) is/are not specified - constant or what? As for who is older - from which frame ... etc. In any case all speeds are 'relativistic', just some ( alot ) more than others! :-)
Q : A second question, which may or may not help you think about the answer: At the end of their acceleration, what is the spacing between their ships as measured by Alice and Bob?
A : Ditto. Plus whose time is it that is pre-aranged or pre-determined and how, etc ....
The sneaky underlying bit here is the method of knowing/assuring simultaneity. SR and GR rest upon clock synchronisation using signalling when separated not just making two clocks, synchronising 'in place' and then moving the clocks apart.
Bet ya the author weasels out of all of this by undisclosed assumptions.
Cheers, Mike.
( edit ) Caveat : the twin 'paradox' includes the re-union of the two participants back to a single ( original ) frame ie. a return to a close region of spacetime.
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"I have made this letter longer than usual, because I lack the time to make it short." - Blaise Pascal
The comments refine the questions a bit
Both Alice and bob are traveling in the same direction.
The Observer is in the final reference frame.
The comments refine the questions a bit
Both Alice and bob are traveling in the same direction.
The Observer is in the final reference frame.
Not sure about the comments and it's hard for me to accept the terms characterizing the use of Google as cheating, especially after showing up a second day expecting to see the answer and now it says the answer will be given 'probably tomorrow'. So I cheated then, but failed to find a specific answer. I found enough (edit: see for example, Adding to the paradox: the accelerated twin is older) to hazard a guess, though – er, wait – it's up for a vote :))
Not much to her dismay, Alice will be the older twin, and gravitational time dilation would be main the reason – clocks run slower in regions of lower gravitational potential (closer to the center of a massive object, assuming the earth (& sun) in this case if keeping with convention).
Thanks for posting that one Rod, I hope I voted correctly! :)
(edit again: if they accelerate towards the sun and the end of the acceleration is less than about 10 minutes after they started then Bob will be older. But if they accelerate away from the sun then Alice will be older, however long the acceleration lasts. Not sure I could give a general solution covering all angles & durations to give the distance L on a good day.)
I apologise. I am intmate with the blog and the author. There is no strategy, just fun..
I am on a mobile device so typing is a chore.
Chipper has the right answer :)
Today response
Answer
My first thought was, are they moving in the same direction? Apparently so.
I don't understand how Alice is older. If they both accelerated for the same amount of time, and the same rate of acceleration, how is there any difference? In fact, relative to Bob, Alice never even moved! How did she age?
If someone leaves earth, and ages during their journey, does the aging undo itself on the way home, or does it just get worse?
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My first thought was, are they moving in the same direction? Apparently so.
I don't understand how Alice is older. If they both accelerated for the same amount of time, and the same rate of acceleration, how is there any difference? In fact, relative to Bob, Alice never even moved! How did she age?
If someone leaves earth, and ages during their journey, does the aging undo itself on the way home, or does it just get worse?
It's a lesson on the equivalence principle - acceleration is equivalent to being subject to a gravitational force - clocks will run at slightly different rates with the slower clocks being the ones that are subject to greater gravitational forces - the effect of gravitational time dilation.
I guessed the right answer but I'm not sure it was for the right reasons :)
Relative to both twins is the gravitational field they started out in and for the duration of the acceleration one twin (Bob) was always "lower" than the other (Alice) in that field, and so his clock would run slower. That was my reasoning, anyway.
The relative rates of aging on the way back would depend on the motions of the rocket ships ...