Would time dilation be different or the same on a 50lb object going 20,000 or a 2 ton object at 20,000mph?

Question

Does mass play a role in time dilation? If you put an atomic clock on the moon and one of earth and one on mars would they are read different times because of different masses?

Answer 1

In the context of special relativity, the only thing that will cause clocks to run at different speeds when they are moving at different speeds is the difference in speed between the two clocks. So, if you are standing next to clock one, and you watch clock two go by you at half the speed of light (or 20000mph or whatever speed you want), you would notice that clock two would appear to be slow. So, in special relativity, mass doesn't play a role.

However, there is also general relativity, which is Einstein's theory of gravity, more or less. And in general relativity, in addition to relative speed causing a slow down in clocks, the strength of the gravitational field (or actually the magnitude of any acceleration whatsoever) does have an effect on the rate of clocks. So, the clocks on the Earth, Mars, and the Moon would indeed run at different speeds (partially because they do have relative velocities, but also because of the different strengths of gravity). Indeed, this effect is significant enough that GPS couldn't be accurate as it is without taking into account the effects of general relativity. So it's something that not only is a theoretical issue, but something with very real practical significance.

In the case of your 50lb object and 2 ton object, there would be a very, very, *very* slight difference in the speed of the clocks due to the gravity of the two objects. But as I'm sure you've noticed, neither your computer (which might weigh about 50lbs) or your car (which might be a ton or two) exert much of a gravitational pull on you when you're near them, so the effect is very tiny for objects so light (compared to planets, moons, or stars for instance).

Answer 2

I'll give you the exact formula that's called the Lorentz formula for transforming a 4 vector into another one in a different coordinate system. (ie the translator between "fixed space" and moving according to you)

t' = gamma (t-(v/c^2)*x) if say you're moving in the x direction.

gamma is the Lorentz factor of 1/sqrt(1-(v/c)^2) c is the speed of light and v is your speed in the x direction.

Now to answer your question precisely, mass as you can see has no effect on time dilation. It will however have an effect on the Enegy you need to make that 2 ton block go to a relativistic speed.

Answer 3

there is a difference, but you'd have to have your objects travel faster than that for it to become pronounced. the difference between atomic clocks on Earth, Mars, and the Moon would be something you'd notice. it would be tough to synchronize clocks between all 3 places. and keep in mind that the effect works all ways; time dilation, mass, and speed all affect one another.