On Thursday, February 6, 2025 at 5:28:34 AM UTC-7 Quentin Anciaux wrote:
AG, this is the closest you’ve come to an actual discussion, so I’ll give you a straight answer. Your question boils down to whether simultaneity alone is enough to resolve the paradox, or if there's still an issue when two observers, co-located in space but in different frames, observe contradictory outcomes. Why Simultaneity Resolves the Paradox: 1. The "paradox" only exists if you expect a single, universal answer to the question, "Does the car fit?"—which would require a preferred frame of reference. But SR explicitly denies the existence of such a frame. 2. Simultaneity isn’t just a technicality—it’s fundamental to how events are ordered in each frame. In the garage frame, the car is fully inside at one moment because simultaneity in that frame aligns the back entering and the front still inside. In the car frame, simultaneity shifts, meaning by the time the back enters, the front has already exited. The disagreement is built into SR itself. Addressing Your "Co-Located Observers" Thought Experiment: You suggest that if two observers are spatially co-located but in different frames, they would observe contradictory facts. But this is where you’re making an error. 1. Frame membership matters: Each observer is still bound to their own frame’s simultaneity rules. Just because they are momentarily at the same point in space does not mean they share the same perception of simultaneity or event ordering. 2. Contradictory observations are expected, not paradoxical: In relativity, observers in different frames frequently measure different physical quantities for the same event (lengths, time intervals, etc.). This is no different. The garage observer measures the car fitting because their simultaneity rules allow it. The car observer measures it not fitting because their simultaneity rules say otherwise. Each observer’s measurement is internally consistent in their own frame—so there’s no contradiction within SR. 3. Would additional observers change anything? No. Additional observers in each frame will confirm their own frame’s version of events, reinforcing the idea that simultaneity dictates different conclusions. There is no paradox because neither frame’s measurement is "more real" than the other. The mistake is assuming that because two observers are momentarily co-located, they must agree on event sequences. They do not. Their velocity relative to each other still dictates their simultaneity slicing of spacetime, and that’s what resolves the paradox. If you truly accept that simultaneity is relative and that SR allows for frame-dependent measurements, then you should see why "fitting and not fitting" is not a contradiction but a natural consequence of relativity. If you still think there’s a paradox, then ask yourself: what fundamental assumption are you making that requires a single absolute answer to "Does the car fit?" Because that’s where the actual mistake lies. Quentin FWIW, I wasn't seeking to prove in this thought experiment that there's an absolute answer to whether the car fits. In fact, I was alleging the opposite, that with juxtaposed observers at the midpoint of the garage, the car fits in one frame, and doesn't fit in the other. What I was alleging is that this result seems curiously similar to the paradox when using "at the same time" erroneously, whereas in this thought experiment only"same space" is involved, not same time. AG Le jeu. 6 févr. 2025, 11:36, Alan Grayson <[email protected]> a écrit : On Wednesday, February 5, 2025 at 4:23:46 PM UTC-7 Alan Grayson wrote: On Wednesday, February 5, 2025 at 3:37:31 PM UTC-7 Quentin Anciaux wrote: AG, the fact that your only response is to repeat "PRICK" like a broken record says everything about your inability to engage in actual discussion. FWIW, we can engage in a rational discussion if you would cease making accusations about my motives and state of mind. I've reviiewed some of your earlier explanations of the alleged paradox, and your more or less constant complaint that I downplay the role of simultaneity in the resolution. While I admit that my initial proposed solution was mistaken -- that length contraction was alone sufficient to resolve the paradox -- I still fail to see why simultaneity does the trick. I say this because all it does is show that fitting and not fitting cannot occur "at the same time". But once it's acknowleged that each frame in SR has its own set of clocks, not synchronized with the clocks in some other frame, the concept "at the same time" is meaningless. So, if you agree so far, the question becomes whether fitting and not fitting "at different times" remains a paradox to resolve. Although, "at the same time" is meaningless, it's possible to imagine the car midway within the garage, and two juxtaposed observers, one in each frame, which observe the car fitting and not fitting, now NOT simultaneous, but spatially co-located. Can this mean another form of the paradox is alive and well, since each observer has contradictory observations (where additional observers are added where necessary to confirm the observations)? Although SR allows measurement to be frame dependent, why isn't this stuation* essentially identical *to the one which requires simutaneity arguments to allegedly resolve? 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/2e03f30c-10d4-4010-83ae-e5a9d07d4105n%40googlegroups.com.
