The twin paradox expanded......?

Question

Its well known that as one of two twins relatively approaches the speed of light, the age difference between both will become significant.

However, if one of them remains still relative to the earth and the other runs, say 10 meters, up and back, would there still be a small (even an attosecond) difference in the age of each twin?

Answer 1

Yes, according to relativity, any acceleration at all results in reletavistic time dilation. However, in the situation you described, the velocity is only a few meters per second, and it's only sustained for a few seconds. With v=3 the Lorentz factor is approximately 1+10^-32. You'd need to sustain that velocity for 10^14 seconds (about 3 million years) before the discrepancy amounted to just one attosecond (10^-18 seconds).

On the other hand, there is a theory in quantum mechanics that time itself may have discrete quanta, in which case the uncertainty principle says that there is only a certain probability that the twins would age differently, with this probability getting larger as the predicted value approached the minimum quanta of time. If that's true, then the probability of any discrepancy at all in the situation you described is quite small.

Answer 2

That is correct, although you'd be hard-pressed to measure the age-difference.

Time dialation (the formal term for the phenomenon) has been confirmed for *very* fast objects (like particles in a cyclotron), but has also been shown in far more *realistic* cases. For instance, they have done this experiment with both trains and airplanes, and have indeed found measurable (if very small) differences in atomic clocks carried on the moving object.

The main issue is acceleration (how quickly you change your speed) as well as the actual speed you are traveling... fortunately, going in a circle is a type of acceleration (centripetal) so even running in circles around someone will cause you to age more slowly... although the time gained may not be worth the effort. ;-)

It is also important to note that even though the 'younger' twin looks as though he will 'live longer', his subjective life-time remains unchanged. To him (the younger twin), only a short time as passed. So if both twins were fated to live 80 years, both, at their death-bed, would have each experienced 80 years... one simply took an extended 'time-out', so to speak.

Answer 3

Yes, just like the outside of a rotating CD ages slower than the inside - and people that go on lots of airplane trips are very slightly younger than they would have been if they had driven or taken a train (low speed train).