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.
