On Wednesday, December 4, 2024 at 2:41:25 PM UTC-7 Jesse Mazer wrote: On Wed, Dec 4, 2024 at 4:06 PM Alan Grayson <[email protected]> wrote:
In the case of a car whose rest length is greater than the length of the garage, from pov of the garage, the car *will fit inside* if its speed is sufficient fast due to length contraction of the car. But from the pov of the moving car, the length of garage will contract, as close to zero as one desires as its velocity approaches c, so the car *will NOT fit* *inside* the garage. Someone posted a link to an article which claimed, without proof, that this apparent contradiction can be resolved by the fact that simultaneity is frame dependent. I don't see how disagreements of simultaneity between frames solves this apparent paradox. AG Can you think of any way to define the meaning of the phrase "fit inside" other than by saying that the back end of the car is at a position inside the garage past the entrance "at the same time" as the front end of the car is at a position inside the garage but hasn't hit the back wall? (or hasn't passed through the back opening of the garage, if we imagine the garage as something like a covered bridge that's open on both ends). This way of defining it obviously depends on simultaneity, so different frames can disagree about whether there is any moment where such an event on the worldline of the back of the car is simultaneous with such an event on the worldline of the front of the car. Jesse *I think I've mostly resolved this issue. Firstly, despite the unanimity* *of our resident experts, the importance of simultaneity for solving this problem is way overblown. Obviously, that the frames disagree about whether the car fits in the garage can be immediately and unambiguously determined by length contraction. I was ridiculed by the arrogant fool from Belgium and accused as trolling for not placing greater emphasis on simultaneity for the car fitting frame disagreement, but it isn't needed; one can infer the disagreement qualitatively, directly from how the problem is set up by using length contraction. One of the things Brent did in his plots was to define the problem numerically, or **quantitatively*, *but that wasn't necessary. The statement of the problem easily implies the alleged contested result qualitatively, which is sufficient. Since length contraction, time dilation, and simultaneity all follow from the LT (which follows from the invariance of the Sol), they have the same ontological status; that is the same truth value, so using any of the three phenomena, or any combination thereof, is sufficient to reach the conclusion of fitting disagreement for the two frames under consideration. Brent might have established that disagreement of simultaneity can be used as a factor in the analysis, or he may have known about it beforehand and included it in his plots. I'm not sure which is the case, but it really doesn't matter concerning the result of the analysis; the frame disagreement about the car fitting can be established by applying length contraction alone. I think the problem appears to have an ambiguous paradoxical result because SR gives us hugely non-intuitive results. We tend to think that both frames MUST see the same physical result. But if we accept length contraction as a reality, then IF both frames showed the same physical result, we'd be in a worse situation. It would imply that length contraction is falsified. In fact, one of the videos I posted, ended by concluding just that, the video with a poor sound track at the end, namely, * https://www.youtube.com/watch?v=dDqUbBYpB_k#:~:text=from%20the%20car's%20reference%20rate%20however%20the,will%20get%20smashed%20by%20the%20garage%20doors.&text=in%20order%20to%20find%20out%20we%20must,use%20our%20friends%20the%20lorentz%20transformation%20equations *BTW, I was also confused about the definition of fitting. With all the emphasis about endpoints, and the fact that all clocks in any frame can be sychronized, the ends of the car are always simultaneous whether the car fits or not. I somehow wasn't clear that the event times which were decisive involved the crossing times of the front and rear of garage by the front and rear of the car. The arrogant not-skilled teacher from Belgium was unable to grasp how I misconstrued the fitting conditions and used my error for undeserved accusations. * *AG* -- 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 [email protected]. To view this discussion visit https://groups.google.com/d/msgid/everything-list/fd67e1c7-c68a-4c81-bb4c-066752fc14a8n%40googlegroups.com.
