AG, what your thought experiment highlights is not a dichotomy in the definition of the paradox, but rather a fundamental difference between simultaneity-dependent contradictions and frame-dependent measurements in relativity.
1. Why simultaneity matters in the original paradox The original paradox only appears when people assume there’s a universal "at the same time" across both frames. Once we apply relativity of simultaneity, we see that each frame has its own internally consistent timeline, resolving the contradiction. 2. Why spatial juxtaposition doesn’t create a paradox The observers at the midpoint are not measuring simultaneity-dependent events, they are measuring spatial lengths, which are inherently frame-dependent. There is no expectation in SR that two observers from different frames must agree on length measurements—even if they occupy the same location in space at a given moment. 3. Space and time are similar but not interchangeable Yes, spacetime diagrams treat space and time symmetrically in some respects, but SR does not make space and time fully interchangeable. Time has an asymmetric role in causality (events in the past can influence the future, but not vice versa), while space does not. This asymmetry means that disagreements in simultaneity lead to apparent contradictions if misunderstood, while disagreements in spatial measurements do not—because SR already accounts for them via length contraction. 4. Your thought experiment is just a different way of looking at length contraction The observer in the garage frame sees the car fitting, because in their frame, the car is contracted. The observer in the car frame sees the car not fitting, because in their frame, the garage is contracted. These are not "contradictory" observations, just different frame-dependent measurements—exactly like time dilation or velocity-dependent mass. The original paradox relied on a false assumption of absolute simultaneity—hence why simultaneity "resolves" it. Your thought experiment doesn’t introduce a new paradox—it just reinforces how relativity treats space and time differently and why length contraction, like time dilation, is not paradoxical, just unintuitive. Quentin Hope this discussion about well known facts for about 120 years will end and we can return to everything-list purposes. Le sam. 8 févr. 2025, 08:55, Alan Grayson <[email protected]> a écrit : > > > On Thursday, February 6, 2025 at 2:23:45 PM UTC-7 Alan Grayson wrote: > > 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 > > > What this thought experiment shows is curious *dichotomy *concerning the > definition of the paradox. As long as it's assumed fitting and not fittling > occur at the same TIME, a "timely" form of juxtaposition, we have a paradox > (ostensibly resolved by the disagreement about simultaneity). But when > SPACE is juxtaposed, it's *not* considered a paradox. You'll note that in > the spacetime diagrams we have one dimension of time and one of space, > which have similar properties, albeit not identical. We also know that > given the initial condition, the car never fits from car's frame of > reference, and for a sufficient velocity, it will fit from the garage's > frame of reference. So the model of the spatial juxtapostion of the > observers at the halfway point in garage makes sense. 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/997c5736-cf45-482b-9511-2cccdc7a1b48n%40googlegroups.com > <https://groups.google.com/d/msgid/everything-list/997c5736-cf45-482b-9511-2cccdc7a1b48n%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 [email protected]. 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