Here is a traditional derivation of time dilation:
There's a train with a lamp in the ceiling, moving at velocity v with respect to an observer. In the frame of the observer, the path taken by the light from the lamp straight down to the ground is actually diagonal because the train has moved forwards by the time the light hits the ground. Since the speed of light is constant, the time it took for the light to reach the ground must have been GREATER, because the distance traveled was the hypotenuse of a triangle whose side is the height of the lamp and whose base is the distance traveled by the train in the time it took the light to travel.
That's the essence of it, math not included because it's not relevant to my question:
This derivation works for light, yes, but it's based on the fact that the speed of light is identical in all frames, so applying the same procedure to a ball, say, would not work. In short: We calculated that light travel time has been dilated. How does this argument extend for ALL objects, not just light?
Also: I have heard of answers involving light clocks (devices which measure time based on how long it takes light to move some distance), using the following arguments:
- Measuring time with a light clock shows that time clearly dilates.
counter-argument: how do you know that the light clock is accurate then? Maybe other clocks would disagree, and time only dilates for light?
- If one uses both a light clock AND a variety of other clocks: The argument is that if you used both clock types and only the light clock went out-of-sync, you could tell that YOU were the one moving, so this violates the postulate of relativity (all inertial frames are equally valid; none are "THE" rest frame).
counter-argument: this is okay with me if the person observing a difference is in the clock frame. But if they are not, relativity seems satisfied with the condition that, if a train observer and a "stationary" observer both have both types of clocks, each person sees the other person's clocks as out-of-sync with the other person's light clocks (nobody looks at their own clocks).
I am aware of the experimental evidence that particle decays follow time dilation. I'd just like some evidence that it applies to all phenomena, rather than just the set which we have experimentally verified. Best would be a theoretical argument from Einstein's postulates.
I am an undergraduate in my senior year, who has not yet taken General Relativity, so I would appreciate it if that were kept in mind in any explanation!
Best Answer
The empirical answer to the question is simple: radioactive beams have longer half-lives as measured in the lab frame than the same particles have when at rest.
This was first noticed in the context of cosmic-ray muons, and later in the hadronic spray emerging from deep inelastic scattering, and these days we build particle accelerators that run radioactive isotopes up to high energy with malice aforethought.
So, long story short: we measure this stuff all the time.