Metroid

Yes, as per my original formulation of the question, I do not care about the deceleration time since it does not impact the answer. I guess that I need to derive L' for a uniform deceleration. I am sure that this has been done, but I guess I should do it myself. I guess I just assumed that this may not yield the expected result. But I should check this.

By unphysical, I mean the change in the measured length (that C measures) as C decelerates. If space is discrete, then it is discrete at the Planck scale. I have to work through the equations, but I doubt that the length changes from L' to L over an arbitrary time of deceleration. I would appreciate a citation of such a calculation. Namely, uniform deceleration and the associated change in L' to L. Thank you one and all.

Thanks for the response. Yes, I expected someone would say this. This is a good thing to bring up. But alright, let's spread out the deceleration to a small value, say 100x the Planck time. You will then have the measured length changing by the same amount, but not instantaneously. The result is the sam though, and I think that it is unphysical. I am most interested in this issue, in the context of discrete spacetime.

I have a seemingly simple question about length contraction in SR. Suppose that you have two particles (A and B) at rest relative to each other and separated by a distance L. Now suppose particle C traveling at a velocity (4/5)c from A to B. Particle C travels to and arrives at particle B at a later time. We know that time recorded by C (i.e., T') and the length it has traveled L' are reduced relative to those recorded by observers in the reference frame of A & B. Let's focus on L'. From SR, we all know that L' = 1/gamma x L. So particle C, from its perspective, has traveled L' upon arriving at B. Now consider the following -- immediately (or very quickly) stop particle C upon its arrival at B. The instant before particle C stopped, it will have registered a length L', whereas the instant after it has stopped, it presumably registers a length L for the A-B separation. Now I know that SR should only be applied to inertial reference frames (RFs), but we all know that it can also be applied to accelerating RFs. But we do not need the equations to address this issue -- from one instant to the next (i.e., prior to after arrival at B), the measured length changes from L' to L. I also know a second distance measurement is necessary after the arrival and cessation of C's travel. But regardless, are we supposed to believe that the measured length goes discontinuously (i.e., jumps) from L' to L in this short interval of time? Or does a series of distance measurements show a distance the varies somewhat more continuously from L' to L after stoppage? I know that L is the "proper length", but just stating that this length should be applied to C after its stoppage does not fully address the question. Thoughts?