GREAT Question.
First off, it is clear if an object experiences acceleration, something has happened to it, we call that something “velocity”:
\LARGE v=\int a(t)dt
The magnitude of the velocity is speed, so I’ll use the term speed in the direction of motion.
Let’s take a gendanken example where there is little gravitational potential to affect the clock ticks since under GR clock ticks are affected by gravity…
We have two rocket ships near each other, and on fires its engines and the clock in the accelerating rocket ship acquires more velocity/speed according to the equation above. It accelerates to a very high speed and then cuts off it’s engines and coasts and the clocks between the two rockets go out of sync. Now the moving rocket turns around, fires its engines and decelerates to a net zero velocity relative to its original hypothetical “rest” velocity. It’s clock will have ticked slower over the course of the journey as evidenced by comparing the time on the clocks of the rocket that didn’t fire its engines and the rocket that moved relative to the start of the experiment. Agree or disagree?
Ok, but now a subtlety. And this is a testable prediction, at least in principle. Suppose both rockets were accelerated for long time such that their velocity (according to the above equation) is very high relative to the start of the experiment.
Now let on rocket decelerate to the original “rest” velocity and let the other rocket simply cut off it’s engines. The clock of the resting rocket will tick faster than the moving rocket.
Deceleration is really acceleration in the opposite direction, so hypothetically we can’t be decelerating (accelerating in the opposite direction) such that the clock in that rocket starts ticking at an infinity rate! It will reach a minimum rate at which it no longer ticks faster. When it reaches that miniumum, it is at an absolute zero velocity. That’s how we know.
Now, this is a real data dump and maybe I need to draw up diagrams for clarity, but this is the way I conceive of inferring an absolute coordinate system. This leads naturally thoughts of an aether that is based on the zero-point energy of vacuums. If there are slight positional variations in the zero-point energy density throughout space, this suggest also an absolute coordinate system. Vacuums aren’t technically “nothing”.
Anyway, thanks for the question, it motivated me to think about this more carefully.
Also, not trying to totally diss Einstenian relativity since it’s main pillar is the Lorentz transformation which can be deduced from the approximations known as classical electromagnetic theory of Maxwell. I’ll try to derive the Lorentz Transformation (sometimes called the Lorentz-Einstein) transformation as an exercise from Maxwell’s equations since it shows the origin of the idea by Lorentz.
However, I believe the neo-Lorentzian ( which is a variation from Lorentz’s original idea) may be the right kind of relativity. That is to say, I suspect there is an absolute clock, and the relativistic effects are just making clocks tick slower, not that time, in the absolute sense actually flows slower. Rather than “time dilation”, I think the term “clock slowing” is a more accurate term.
Anyway thanks for the conversation.
The clock of the moving astronaut ticks slower than the frame of the launch pad when adjusted for gravity since the higher altitude makes the clock tick faster.
Going back to the clocks. We can compare the tick rates of clocks.