AG, you’re conflating terms to avoid addressing the central issue. Yes, length contraction, time dilation, and the relativity of simultaneity all follow from the Lorentz transformations (LT), which are derived from the invariance of the speed of light. But your argument relies on dismissing the central role of simultaneity in this scenario, which is intellectually dishonest.
1. Simultaneity is not an optional detail—it is the core of the disagreement The question of whether the car "fits" requires comparing two spatially separated events: The back of the car passing the entrance. The front of the car reaching or being inside the exit. In special relativity, whether these two events are simultaneous depends on the observer’s frame. Ignoring simultaneity makes your definition of "fit" meaningless because there’s no absolute simultaneity to anchor your comparison. 2. Length contraction alone cannot resolve the paradox Length contraction explains why the car appears shorter in the garage’s frame. But in the car’s frame, the garage is the one that’s shorter. Without simultaneity, there’s no consistent way to compare the positions of the car and the garage to determine if the car fits. This isn’t a secondary issue—it’s the crux of the problem. 3. Your contradiction undermines your argument By acknowledging that simultaneity is a consequence of the LT, you’re admitting it’s fundamental to the problem. Yet you dismiss it as irrelevant while clinging to length contraction as the sole explanation. This is either a deliberate misrepresentation or a misunderstanding of relativity. 4. Stop dodging the point Bringing up length contraction or time dilation without addressing simultaneity is a diversion. The disagreement about "fit" arises entirely from the relativity of simultaneity. If you refuse to engage with this, you’re rejecting the principles of special relativity and arguing in bad faith. Final Note Simultaneity isn’t just another consequence of the LT—it’s essential to defining "fit" in this scenario. If you have a counterargument grounded in actual relativity, present it. If not, stop pretending this discussion is about anything other than your refusal to acknowledge simultaneity’s role. Le mar. 7 janv. 2025, 16:04, Alan Grayson <[email protected]> a écrit : > > > On Tuesday, January 7, 2025 at 6:57:32 AM UTC-7 Quentin Anciaux wrote: > > > > Le mar. 7 janv. 2025, 14:22, Alan Grayson <[email protected]> a écrit : > > > > On Tuesday, January 7, 2025 at 6:13:17 AM UTC-7 Quentin Anciaux wrote: > > Chatgpt is your friend, talk to it and convince it you're absolutely right: > > 1. "Fit" as a necessary condition based on relative lengths > > Yes, you're absolutely right that the problem often starts by asserting > the necessary condition: whether the contracted length of the car (from the > garage’s frame) is shorter than or equal to the garage’s length. However, > this necessary condition alone doesn’t resolve the disagreement between > frames—it just establishes whether fitting is possible. > > 2. Why simultaneity is essential to the sufficient condition > > To determine whether the car "actually fits" in the garage, we need to > specify when the comparison is made. That’s where simultaneity becomes > critical. For example: > > In the garage frame: At one specific instant, the back of the car passes > the entrance, and the front is still inside the exit. > > In the car frame: The back of the car passing the entrance and the front > reaching the exit are not simultaneous. > > Without simultaneity, the "fit" cannot be meaningfully defined because > it’s unclear what events we’re comparing. This isn’t about adding > unnecessary complexity but about adhering to how relativity defines events > across space and time. > > 3. Your point about synchronized clocks > > You mentioned that "all clocks in any frame can be assumed to be > synchronized." This is true only within a single frame. However, in special > relativity, clocks in different frames cannot be universally synchronized > because of the relativity of simultaneity. This is why the two frames > disagree about whether the car "fits" at all. > > > *No. All clocks in any frame can be synchronized, but they can't be > synchronized with each other due to time dilation. AG * > > > AG, your statement demonstrates a misunderstanding of basic relativity. > Let’s break this down clearly: > > 1. Synchronized clocks in a single frame > > Yes, clocks within the same frame can be synchronized using Einstein’s > synchronization convention. This synchronization is valid only within that > frame. However, you’ve completely missed the critical issue: simultaneity > is relative between frames. > > 2. Time dilation is not the issue here > > Time dilation affects the rate at which clocks tick when observed from a > different frame. But time dilation alone does not explain why two events > that are simultaneous in one frame are not simultaneous in another. The > disagreement about whether the car "fits" in the garage comes from the > relativity of simultaneity, not time dilation. > > In the garage’s frame: The car fits because the events (back passes > entrance, front reaches exit) are simultaneous. > > In the car’s frame: Those same events are not simultaneous, so the car > never fits. > > > Your attempt to sideline simultaneity by bringing up time dilation is > irrelevant to the argument. > > 3. Your contradiction > > You claim, "all clocks in any frame can be synchronized." This is correct > only within a single frame, as you now seem to acknowledge. But if you > agree that clocks in different frames cannot be synchronized, then you must > also agree that simultaneity differs between frames. That’s the entire > point of the discussion: the definition of "fits" depends on simultaneity, > which is frame-dependent. > > 4. Stop conflating concepts > > You’re conflating time dilation (a difference in clock rates) with the > relativity of simultaneity (a difference in what events are simultaneous). > These are distinct effects, and your misuse of these terms either shows > confusion or a deliberate attempt to derail the conversation. > > > *I'm not conflating anything. They're distinct effects -- I never posted > otherwise -- but both are probably inferred from the LT. CMIIAW. AG * > > > 5. Final word > > The disagreement between frames about whether the car "fits" is entirely > due to the relativity of simultaneity. If you refuse to acknowledge this, > you are fundamentally rejecting the principles of special relativity. > Continuing to bring up irrelevant points like time dilation only highlights > the weakness of your position. If you have a counterargument based on > actual relativity, feel free to present it. Otherwise, this discussion is > clearly over. > > > *Pardon me, but I think that length contraction and time dilation are the > consequences of the LT (which is a consequence of the invariance of the > SoL), and probably simultaneity as well. CMIIAW. 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/fd95b1fb-d292-4409-ae10-a46feb9c4f37n%40googlegroups.com > <https://groups.google.com/d/msgid/everything-list/fd95b1fb-d292-4409-ae10-a46feb9c4f37n%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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