Equivalent Trajectories in Relativity: Observer Effects

[jaketodd]

In relativity, can two sets of trajectories, carried out at different times, be considered equivalent if they only differ by when they change directions as they traverse their sets of trajectories? They traverse the same trajectories. The only difference is the rate at which they traverse the trajectories. Is the answer yes because the observer, during the two times of trajectory traversal, could be going on their own sets of trajectories (different speeds but the same paths for observing each of the two sets of trajectories) that make the two observed trajectories look equivalent? Are the two trajectory sets equivalent to the described observer? ...they are equivalent to the described observer but not to other observers? If the difference between the rate of traversal between the two identical sets of trajectories is a constant, are the two sets of trajectories equivalent to any observer? What if the two sets of trajectories varied in their rate but not by a constant amount...would they be equivalent, and to which observer(s)?

Thanks,

Jake

 

[Dale]

I guess that depends on the definition of "equivalent". If "equivalent" means that the two trajectories take the same form in some coordinate system then I would say that the answer is "yes, provided that the spacetime is static".