- #36

Shirish

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- 32

Thanks a ton for the help so far. One more question pops up from this - how do we carry over or modify the argument in bold for special relativity. I think it was mentioned in this thread that the standard spatial force is no longer invariant, but the 4-force is.Ibix said:You just agreed that if ##F'\neq ma## then I can use my spring, mass, clock and ruler to measure my speed from inside a sealed box.

Mathematically, what we're saying is that the only difference between frames is their velocity (assuming Galilean relativity). So if ##F=ma## holds in one frame then the only possible option for other frames (given the invariance of ##m## and ##a##) is that there are some velocity-dependent terms that just happened to be zero or one (depending if they are additive or multiplicative) in the first frame. If those terms don't have those same values in another frame then I can measure them by playing around with different accelerations and masses, and hence deduce my velocity.

This stuff is subtle. You aren't asking stupid questions, so don't worry.

I won't pursue that question too much right now because I haven't studied relativistic dynamics yet. My guess is that even in SR, the force still can't be a function of velocity (since that'll allow us to again play around and deduce the velocity), but the key difference might be that spatial intervals change across IRs, hence the usual 3-force also changes.