# Fermilab

## Inquiring Minds

All About Light Main Page  |  Classical  |  Relativistic  |  Quantum

 Relativistic - The Twin Paradox-Who Is Older? c and Einstein  |  c Top Speed  |  Speed & Speed  |  Faster than c? Mass Gain  |  E=m*c^2  |  Age Slower  |  Time Dilation  |  Twin Paradox Dopper Shift  |  Ticketed  |  Simultaneity  |  Competition  |  Fast Strudel Paradox? No!  |  Confusions  |
To be honest with you dear reader, I have to add a little comment to the previous page, which discussed time dilation. There I said that "muons lived longer in our frame of reference." I also said that "the twin on the space ship lived longer than we did on the Earth." I explained this as a consequence of relativity, because the muon and the spaceship twin were MOVING, whereas we were STATIONARY.

On the other hand, the twin in the space ship (or the traveling muons) can say, "No, no, no, you guys on Earth were moving away from me, and I was stationary: therefore you must be younger than I am."

So who is right? When the space ship twin shakes hand, with the Earth twin, ONE MUST BE OLDER!!! But which one?

This is obviously a paradox, because both of them think that the OTHER twin was on the journey and therefore must be the younger one.

The solution to this paradox is that the spaceship's and the muon's frames of reference are NOT INERTIAL. During their journey, they must have accelerated to reach those high speeds, or decelerated and turned around when the space ship twin decided to come back ... . Since frames of reference with non-zero acceleration are not INERTIAL, we can unambiguously declare, that the space ship twin (or the muon) was the one who traveled and therefore would be the younger one.

Please note: I am not saying that the twin traveling in the spaceship aged slower than the twin on Earth because the acceleration slowed down the rate of his aging. It can be proven that the way they accelerate does not affect their aging process (not at least from the point of view of special relativity; of course the rigorous calculation must be done with the tools of general relativity). What matters only is the fact that one accelerates and the other does not.

On the next page I discuss a physicist's attempt to explain to police officer that he did not run red light!

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