### Question

Say you have a twin, and you go off into space, traveling near the speed of light, when you return, will your twin have aged more?

You're asking about the famous (infamous?) Twin Paradox and the answer is both yes and no. I'm sure that's unsatisfying but let me give a bit more explanation:

As for 'yes:' When traveling at speeds near the speed of light special relativity says that time is dilated. Thus relative to another inertial frame (where perhaps a stationary twin sits) time for the moving twin is slowing down. Hence the stationary twin is aging faster. While the moving twin remains in an inertial frame (that is, continues to move at a constant velocity) the moving twin will observe time running slower for the stationary twin. If they could ever be at the same place and the same point of time again, someone would have to be wrong! This is the Paradox.

As for 'no:' The rub is in trying to get the twins back together at the same place and the same time so they can compare their ages. That's the 'return' in your question. This will necessarily require a change in velocity -- hence an acceleration. But an accelerating frame is not an inertial frame. Thus, without knowing the details of how we bring the twins together, there really is no way to say for sure who will be older -- but in most cases it will be the travelling twin.

This topic is famous for the confusion it creates and a good explanation requires both some mathematics and some space-time diagrams. The best on-line explanation for these issues can be found at

from UC Riverside's Math department.
Answered by: Brent Nelson, M.A. Physics, Ph.D. Student, UC Berkeley

This is a well-known question, at least for anyone who had a course where special relativity is discussed. It is generally known as the 'Twin Paradox'. Let me first spell out what the apparent paradox is, then try to explain why there is in fact, no paradox.

The question is this. We have two twin brothers. We send one of them to space, traveling at relativistic speeds (speeds close to the speed of light) who then comes back. Now, special relativity predicts (and it is in fact very well confirmed) the phenomenon called 'time dilation', which simply means that a clock in motion relative to an observer seems to run slower than a stationary clock; that is, the seconds on the moving clock seem to get 'stretched out'; the closer the velocity to the speed of light, the greater the effect. Also, it is noteworthy that this is not a feature of the mechanics of the clock, it is actually _time_itself_ that gets dilated. So, a regular clock, our body's biological clock, or elementary particles' decay clocks, all seem slowed down when moving relative to the observer.

So, the argument goes, since the traveling twin was moving at relativistic speeds with respect to the twin left on earth, from the point of view of the twin on earth, the traveling twin must have aged _less_. Which means, on return, the twin which traveled will be younger than the one who stayed on earth.

This is all fine and well. But then, as the argument goes, from the point of view of the traveling twin, the twin on earth was moving at the same speed with respect to him, just in the opposite direction! So, it should be the twin on earth that should be younger!

So, the question is posed, who will be younger, if any twin at all?

The correct answer is, the traveling twin will be younger, and there is really no paradox there. The resolution comes from the fact that the situation is _not_ really symmetric. The twin on earth was at rest and never accelerated (much), while the traveling twin accelerated, felt all the jerks and pressures, and at some point in the travel even had to turn back.

Now, so, why does the twin who _accelerated_ remains younger? The simple answer is as follows. Special relativity states its rules with respect to 'inertial' frames, which means, the frame of reference should _not_ be accelerating. The frame of reference of the twin on earth (to an excellent approximation) conforms to this constraint, therefore any calculations done taking the frame of reference of earth are _correct_. However, the traveling twin, at least during some point in the journey, accelerates. So, the simple special relativistic calculations taking the frame of reference of the traveling twin are incorrect. So, in fact there is no paradox, and the traveling twin will be younger.

For the more interested, the book 'A First Course in General Relativity' by Bernard F. Schutz contains a once-and-for-all very careful dissection of this so-called paradox almost as old as the theory of relativity itself.
Answered by: Yasar Safkan, B.S., Physics Ph.D. candidate, MIT

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