- #1
etotheipi
From the relative velocity equation we can see that two frames will both measure the same relative speed. I don't believe the same is true for relative separations and relative accelerations, but can't find anything useful online to verify this, and was wondering whether someone could point me in the right direction.
I suppose foremost, it doesn't make sense to talk about two observers agreeing on a varying quantity like relative separation, for instance, since the measured time at which the separation equals a certain value will differ between the two frames. This would be the same for relative acceleration in the case that it was not constant, and I'm guessing also for relative velocity in the case that there exists acceleration. The "agreement" in relative velocity between frames seems only to be valid since is constant for all times in both frames.
We can definitely measure the acceleration of one thing relative to another using the acceleration transformation, and the separation of one object from another with the Lorentz transformations, given that we already know what the raw values in another frame are. However, am I right in saying that the only context in which it makes sense to discuss two frames agreeing on their relative 'something' is when that particular something is a constant?
Sorry for the slightly verbose post, I promise I'll add some formulae next time...!
I suppose foremost, it doesn't make sense to talk about two observers agreeing on a varying quantity like relative separation, for instance, since the measured time at which the separation equals a certain value will differ between the two frames. This would be the same for relative acceleration in the case that it was not constant, and I'm guessing also for relative velocity in the case that there exists acceleration. The "agreement" in relative velocity between frames seems only to be valid since is constant for all times in both frames.
We can definitely measure the acceleration of one thing relative to another using the acceleration transformation, and the separation of one object from another with the Lorentz transformations, given that we already know what the raw values in another frame are. However, am I right in saying that the only context in which it makes sense to discuss two frames agreeing on their relative 'something' is when that particular something is a constant?
Sorry for the slightly verbose post, I promise I'll add some formulae next time...!