Clocks don't measure time!What clocks actually measure is the space-time interval between events on the clock's world-line. That turns out to reduce to what we call "time" if you and the clock are not moving relative to each other. But if you and the clock are moving relative to each other, then things get weird because, well, clocks don't measure time. In fact, time is not even a well-defined concept when things are moving relative to each other!
Two surprising consequences of this: first, the speed of light is not constant. In fact, "the speed of light" is not even a well-defined concept because time is not a well-defined concept, and speed is defined in terms of time. (In fact, "the speed of X" is not a well-defined concept for any X, because, well, you know.)
(What is true is that the measuring the "speed" of light will give you the same result no matter what reference frame you're in. But that turns out to be a consequence of the fact that clocks measure space-time intervals rather than time. It is not, as is often taught, the foundational principle of relativity. Einstein himself got this wrong.)
The second surprising consequence is that the most common resolution of the "twin paradox" is mistaken. Maudlin quotes Feynman as the prototypical example:
This is called a “paradox” only by people who believe that the principle of relativity means that that all motion is relative; they say “Heh, heh, heh, from the point of view of Paul can’t we say that Peter was moving and should therefore appear to age more slowly? By symmetry, the only possible result is that both should be the same age when they meet.” But in order for them to come back together and make the comparison Paul must either stop at the end of the trip and make a comparison of clocks, or, more simply, he has to come back, and the one who comes back must be the man who was moving, and he knows this, because he had to turn around. When he turned around, all kinds of things happened in his space-ship—the rockets went off, things jammed up against one wall, and so on—while Peter felt nothing.
So the way to state the rule is that the man who has felt the accelerations, who has seen things fall against the walls. and so on, is the one who would be the younger; that is the difference between them in an absolute sense, and it is certainly correct.Maudlin then minces no words:
Everything in this "explanation" is wrong.That sort of clarity is rare.
(It's actually easy to see that any explanation in terms of acceleration must be wrong because it is easy to set up a "twin paradox" that involves no accelerations: use three clocks all moving in inertial trajectories along the same line. Clock A starts to the left of clock B and is moving to the right (relative to B). Clock C starts to the right of clock B and is moving to the left (relative to B). The initial positions are such that A will be co-located with B before it is co-located with C. When A meets B, A is set to the time shown on B. Then, when A meets C, C is set to the time shown on A. When C meets B, the reading on C will be less than the reading on B despite the fact that none of the clocks have undergone any acceleration.)
Anyway, I thought this was cool and so I thought I'd take a moment to share it.