On Friday, January 10, 2025 at 12:30:01 PM UTC-7 John Clark wrote:
On Fri, Jan 10, 2025 at 2:15 PM Alan Grayson <agrays...@gmail.com> wrote: *>>>If I believe in SR, then I can use length contraction to establish the car won't fit in garage in car's frame.* *>> That depends entirely on what you mean by "the car won't fit in the garage". In the above I've told you exactly what I mean by the term. What do you mean? * *> What do I mean; what any sane person would mean; that the car's length is fixed from the pov of the car's frame when car is moving, but the garage's length is shortened from an initial condition where it starts out shorter. AG * *That's all very nice but that's not what I asked. What exactly do you mean by "the car won't fit in the garage" if it's not "the front of the car is fully within the garage while SIMULTANEOUSLY the back of the car is also fully within the garage"?* *John K Clark See what's on my new list at Extropolis <https://groups.google.com/g/extropolis>* *Length contraction can show that the car won't fit from the pov of the car frame, but won't resolve the possibility of a paradox. But solving the paradox issue with simultaneity is not simple since there are an uncountable number of ways the car can fit in the garage if its velocity is large enough. So the easiest way to approach the solution is to find the velocity which allows the car to fit perfectly in the garage frame, and then transform its endpoint events, the back and front of garage, using the t' transformation formula given by the LT. For higher velocities, the problem is substantially more difficult since now the car will loosely fit in the garage from the pov of the garage frame, in which case we'd have an uncountable number of endpoint events for which we'd have to transform to the car frame. I think it's do-able but more difficult. So the best approach is to determine the velocity such that the car perfectly fits in the garage from the pov of the garage frame, and perform the transformation using the two endpoint events in the garage frame to the car frame. I really can't explain why I thought length contraction alone could also resolve the paradox problem, but I can say it wasn't deliberate. Just an error on my part. AG * *RXT* -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To view this discussion visit https://groups.google.com/d/msgid/everything-list/3a144a79-6032-414e-a0da-fb66cf84b99bn%40googlegroups.com.
