AG, your latest claim about "an uncountable number of solutions" is yet another attempt to complicate something that is already well understood. The "paradox" you keep referencing is entirely resolved through the principles of special relativity, specifically length contraction and the relativity of simultaneity. Let’s address your confusion point by point.
1. The paradox is fully resolvable The car’s position in both frames is fully determined by the Lorentz transformations. These transformations provide exact relationships for space and time coordinates between frames. There’s no ambiguity or "uncountable number of solutions" because the math directly links events in one frame to events in another. Your assertion that it’s "impossible to determine the car’s exact location" is baseless. 2. Simultaneity provides the necessary information The disagreement between frames arises because simultaneity shifts the ordering of events. In the garage frame, the back of the car enters the garage while the front is still inside. In the car frame, the back enters after the front has already exited. The Lorentz transformations calculate these relationships precisely. There is no missing information. 3. Your "length contraction only" approach is incomplete Length contraction shows that the garage is shorter in the car frame, but without simultaneity, you can’t determine how events align in time. This alignment is critical to resolving the disagreement. The so-called paradox exists only when you refuse to account for simultaneity. 4. There’s no "uncountable" problem The problem is entirely countable and deterministic. The Lorentz transformations give you precise equations for determining the position and timing of events. If you’re struggling to see this, it’s not because the problem is unsolvable—it’s because you’re either misunderstanding or overcomplicating it. Your suggestion that the paradox remains unresolved because of a supposed infinite ambiguity is simply wrong. The tools of special relativity, including length contraction, time dilation, and simultaneity, resolve the problem completely. If you truly want clarity, work through the Lorentz transformations instead of inventing unnecessary complications. Le sam. 11 janv. 2025, 18:08, Alan Grayson <agrayson2...@gmail.com> a écrit : > > > On Friday, January 10, 2025 at 2:46:16 PM UTC-7 Alan Grayson wrote: > > 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 * > > > *Clark, thanks for clearly defining the paradox. Somehow, in the course of > this discussion, I lost contact with its meaning. However, when > contemplating the solution, using a specific configuration of fitting from > the pov of the garage frame, and then trying to mathematically solve the > location of the car in the car frame using the disagreement of > simultaneity, I just came to a disquieting conclusion; namely, that the > mathematical problem seems insoluble. The reason is that there is an > uncountable number of solutions of the car NOT fitiiing from the pov of the > car frame. We know it can't fit using length contraction, but it seems > impossible to determine its exact location due to the uncountable number of > soluttions. There's simply not enough information to solve the problem > exactly, which I think is necessary to resolve the paradox. I'd like your > opinion in this matter, and anyone who has an interest in the solution. TY, > AG * > > *X* > > -- > 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/4daa6be8-459b-4424-a813-6ec77b001871n%40googlegroups.com > <https://groups.google.com/d/msgid/everything-list/4daa6be8-459b-4424-a813-6ec77b001871n%40googlegroups.com?utm_medium=email&utm_source=footer> > . > -- 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/CAMW2kAqmcVL%2B05Hpdy2OLAoX0V3XFRQb7hC7GDN5faRsueGzjg%40mail.gmail.com.
