Hi,
To calculate time dilation in the following example using relative velocities of objects on a line:
mass A: at rest mass B: traveling left at 0.999C mass C: traveling right at 0.999C
Using this online calculator for time dilation:
Relative to mass A, time for mass B and C should be slowed down to about 4.47%.
Now if another mass is added, mass D, and mass A is traveling left at 0.999C as seen from mass A.
mass D: at rest mass A: traveling left at 0.999C mass B: traveling left at 0.999C relative to mass A mass C: traveling right at 0.999C relative to mass A
From the first example, mass C and D time is slowed down to about 4.47% relative to mass A still.
Also mass A should now have time slowed down to about
4.47% relative to mass D now.So the rest mass D has no time dilation, mass A has time slowed down to 4.47% of mass D, and mass B and C, have time slowed down to 4.47% of mass A still, meaning
4.47% of 4.47% of mass D, or in other relative to mass D, time is slowed down for mass B and C to 0.199% of mass D.However another way to look at this, is mass D is not at rest and is traveling at 0.999C to the right relative to mass A, which is still at rest. Using mass A as the rest mass would give mass B and D both traveling at 0.999C to the right, giving the same time dilation answers as in the first example, of 4.47%. I don't think time dilation is arbitrary depending on which mass is called the rest mass, so would appreciate an explanation of my error in understanding this! :D
cheers, Jamie