Folks, apologies for reviving a thread that I know has been picked over, but I am a bit confused. I understand the explanation that "solves" the Twin Paradox -- Twin B in the rocketship flying close to light speed undergoes acceleration and deceleration on his outbound trip away from earth and on his inbound trip, and that accounts for his slower aging. But.... let's do a thought experiment where we're in a future time where "Star Trek"-style teleportation has been invented. Persons A & B are on Earth, and as a rocket zooms by, B is beamed into it, hence undergoes no acceleration (except perhaps some momentary action involved in the beaming?). Each person has a camera capable of tracking the other. According to Einstein's logic of reference frames, neither person can tell if he or the other is the one traveling or the one stationary. Now, for the kicker, there is no return trip; the rocket's speed remains constant. So, why wouldn't each person see the other person's clock slowing down? How could it be independently determined which person was undergoing time dilation? Thanks, Dave
Each person does see the other person's clock slowed down, why would you think otherwise? In each person's rest frame, the other one is undergoing time dilation. And I'd like to take issue with your statement that it is the acceleration and deceleration that accounts for the slower aging, instead they account for changes in speed from the original and final rest condition shared with the other twin, and it is spending time traveling at a speed relative to the other twin and then returning that accounts for the slower aging.
You don't really need any "beaming" here, you could just imagine that the rocket traveled at constant velocity past the Earth, with B always having been on board the rocket, and they made a local comparison of ages at the moment the rocket passed next to A and found they were both the same age at the moment they passed one another. In this case, you have to keep in mind the relativity of simultaneity--once they are no longer next to one another, they can no longer agree about what both their ages were "at the same time", because different frames disagree about which pairs of events at different spatial locations happened at the same time. For example, suppose they are age 20 when they pass one another, and each is moving at 0.6c relative to the other one. Then in A's rest frame the event of A turning 30 is simultaneous with the event of B turning 28, so in A's frame B is only aging at 0.8 the normal rate. But in B's rest frame the event of B turning 28 is instead simultaneous with the event of A reaching an age of 26.4 (and likewise the event of A turning 30 is simultaneous with reaching an age of 32.5 B's rest frame), so in B's frame it is A that is only aging at 0.8 the normal rate.
Just for fun, we could put Earth Twin in a centrifuge so he experiences the same acceleration as Space Twin, and bring a camera to their happy reunion...
Thanks for the helpful reply, Jesse. But if what you say is true, than I guess we really do have a paradox. What still confuses me is this: Special relativity says that traveling through space slows down the time of the traveler. This can be measured. But if it's impossible to say who's doing the traveling (as in the case we're discussing), what meaning is there in saying someone's undergoing time dilation? Let's say our space traveler B was traveling at .999c. Wouldn't each observer then be long dead after, say, 10 years of time elapsed by the other's clock? I'm having difficulty with the implications of that.
No, I mean same acceleration. I thought a centrifuge would be a little easier to get a hold of than a teleporter. But, then again - these days, maybe not...
Go back to basics. The twins paradox is a fiction employed in discussions of time dilation. Time dilation is a perceptual consequence of employing Einstein's definition of synchronicity. Acceleration and deceleration were not involved, though Einstein himself seems to have become confused on this point. I urge you to return to an exploration of the implications of the synchronicity definition for observers that change relative motion. This is something Einstein did not do; he stated, without justification, that a given speed along a closed polygon path would effect the same time dilation as the same speed on a straight path.
But you said the Earth Twin was going into the centrifuge, not the Space Twin. I thought your point was that if the Earth Twin could experience the same speed relative to the earth that the Space Twin was experiencing in traveling away from the earth, then when the Space Twin returned to earth and the Earth Twin got out of the centrifuge, they would be the same age. If that's not your point, then I have no idea what you are trying to say or what your point is.
AND, IF... I have no idea what you are trying to say or what your point is... EITHER - Do we have a paradox??
The topic: twins paradox. Yes? The twins paradox is about time dilation. Yes? You mentioned acceleration and deceleration when you started the thread. Am I off topic to refer to the origins of the ideas being dicussed?
No it doesn't, it only says that traveling relative to a given frame causes one's clock to run slow relative to that frame. When discussing inertial motion, there is no "objective" frame-independent sense in which any particular clock is running slow. It just means that relative to the synchronized clocks at rest in a given frame which are used to define the "time" of events by a local comparison with the reading on the clock next to the event, the clock moving relative to that frame is running slow. Take a look at this thread where I posted some illustrations of two sets of clocks which define the time of two different frames, and how each frame's clocks sees a given clock from the other set (say, the clock with the red hand) running slow. You can see from the illustrations that the effect is completely symmetrical--each set of clocks measures a clock in the other set to be running slow by the same amount. Only in the sense that each observer's frame says the event "my clock shows 10 years elapsed" is assigned the same time-coordinate as the event "other guy's clock shows 223.66 years elapsed, therefore other guy is long dead". But the fact that different frames disagree about which pairs of events share the same time-coordinate is fundamentally no different from the fact that two different spatial coordinate systems which have their axes tilted relative to one another can disagree about whether a pair of points in space share the same x-coordinate.
Experiencing the "same acceleration" does not mean they should age the same amount, though, it has to do with the overall geometry of their paths through spacetime. To illustrate, here is a nice spacetime diagram created by DrGreg: Here we have three objects A, B, C, with C moving inertially while A accelerates away from C and B in 2000, then B remains at rest relative to C until 2010 when B also accelerates away, then later B and C both accelerate back towards A and finally accelerate together to come to rest relative to C in 2020. In this case B and C both have three periods of acceleration which each last the same amount of time and involve the same G-forces, but C will have aged less than B in this case (and of course both age less than A). There is a close analogy between the geometry of paths through space and paths through spacetime--just as a straight-line path through spacetime (like C's) always involves the most aging, a straight-line path through space always has the least distance. And just as B's aging is closer to C's than A's, so the spatial length of path B on the diagram is closer to that of the straight-line path C than path A's spatial length is. For a detailed discussion of the analogy between the time of paths in spacetime and the lengths of paths in space, see [post=2972720]this post[/post].
Time to digest the information helpfully provided on this thread. Then I'll come back, if anyone is still interested...
(replying to gswellsjr) gswellsjr, I think Lightheavyw8t conceived of the centrifuge as a control on acceleration so both would experience the same acceleration and only speed would have been different.