Time dilation is probably the best-known of the relativity effects because of the twin paradox. Here is the scenario: An astronaut leaves on a rocket ship traveling at close to the speed of light. After whizzing around the galaxy she returns to find that her (non-identical) twin brother on Earth is an old man with a long beard while she herself is still young. Now this is certainly mind-boggling. Why should time pass more slowly just because you’re moving? What physical explanation can we find for that?
Intuitive explanation. The explanation is again based on the field nature of matter, described by the field equations. Consider two atoms in a rocket ship (or in its contents). Suppose that one atom creates a field disturbance and when that disturbance reaches the second atom something happens. (It is the interaction among atoms, after all, that causes everything to happen.) Now if the rocket ship is moving, the second atom will have moved farther ahead, so the disturbance must travel a greater distance to get there, even after taking the F-L contraction into account. Since fields travel at a fixed rate, it will therefore take longer for the disturbance to reach the second atom. (Disturbances that propagate in the backward direction have a shorter distance to travel, but this effect turns out to be not as great.) In short, things happen more slowly when you’re moving because the fields have to travel a greater distance.
An analogy. Consider two men on a raft who exchange information by calling back and forth to each other. Suppose further that this exchange of information determines the evolution of events on the raft. That is, when B receives information from A he makes certain things happen, and when B calls back to A, other things happen. The problem is, it takes time for the sound waves to travel from A to B and by the time the sound reaches B, he will have moved to a new position B’. Therefore the sound must travel through a greater distance and the communication will take longer than if the raft were at rest.
If the line between the two men is transverse to the motion (upper sketch) the calculation is not hard to do. The result, as it happens, is exactly the same as Lorentz’s result from Maxwell’s equations. The result is the same if the men are aligned in the direction of motion (lower sketch), although the calculation is harder because the time for forward communication is different from the time for backward communication.
NASA routinely observes time dilation in orbiting satellites and corrections are applied to keep atomic clocks on the GPS satellites in sync with clocks on earth. Time dilation has also been seen in particle accelerators. At the CERN accelerator radioactive particles traveling at 99.9% the speed of light are observed to decay 30 times more slowly than they do at rest (S1986, p. 57).
Another analogy. The idea of length contraction and time dilation may be easier to accept when you consider that objects contract and processes slow down when cooled. The only difference between the effect of temperature and the effect of motion is the mechanism: In a cooler chest it is the slowing down of atomic motion that affects rates and interatomic distances, while in moving objects it is the extra distance through which fields must propagate. Would we think it paradoxical if a twin was placed in a cold chamber for 50 years and then emerged to find that her brother was old and she was young? No, we would not; in fact there are firms that offer to preserve people by freezing them. Why then should we not accept that motion can have a similar effect on chemical and physical processes? As Lorentz himself said,
We may, I think, even go so far as to say that… the conclusion is no less legitimate than the inferences concerning the dilatation by heat. – H. Lorentz (L1916, p. 196)