Time dilation

When we observe time dilation, such as on the Space Shuttle or GPS satellites, how can we be sure time is actually changing for those observers, as opposed to just the rate of matter acceleration changing?

Question continued: Every means we have to try and measure time involves the acceleration of matter. Atomic clocks use the rate of radioactive decay, digital clocks use electronic oscillators or crystals, and grandfather clocks use pendulums. All of these clocks require a fixed, predictable rate of matter acceleration in order to measure time accurately. It seems like this creates an artificial relationship between motion/acceleration and time, leading us to conclude that since matter slows down in certain situations, time must also be slowing down. But is time really slowing down for that observer, or is it just an illusion for that observer caused by the slowing of matter acceleration, which is the only means we have for measuring time?

Answer:

It seems like there may be two questions here: (1) how experiments that isolate the effect of time dilation are set up, and (2) is there, within Newtonian mechanics, an effect which mimics time dilation.

To address either, it may be easiest to focus on the pendulum, where classical physics is enough and we don't have to worry about quantum mechanics at the same time! Then, consider two identical pendulums, one on the train and one on the platform, which oscillate at the same frequency. In both the Galilean world and the Einstein world there is a Doppler shift, but the Doppler shifts are different. In the Einstein world, the difference can be attributed to time dilation. This is a simple example of an experiment that isolates the effect of time dilation.

For question (2) we could ask if the change in Doppler shifts between the Galilean world and the Einstein world arises naturally from the Newtonian equations of motion. It does not: a Galilean transformation doesn't change the frequency of a pendulum. The different Doppler shifts between observers is due only to relative motion and not to changing reference frames in Newtonian mechanics.

-Dave Seckel