On Tuesday, September 9, 2025 at 7:51:57 AM UTC-6 Alan Grayson wrote:
On Tuesday, September 9, 2025 at 5:10:54 AM UTC-6 John Clark wrote: On Mon, Sep 8, 2025 at 2:19 PM Alan Grayson <[email protected]> wrote: *> I'm not sure the impossibility of absolute simultaneity solves the problem,* *Watch the video! If you follow what he does step-by-step you will see that he is right. It's not difficult. * *I wish I was taught the Twin's Paradox this way! <https://www.youtube.com/watch?v=GsMqCHCV5Xc&t=2s>* *I'll definitely watch it, very soon, but a-priori the impossibility of absolute simultaneity can't solve the paradox because it's not its cause. Can you succinctly state the cause of the paradox?* *Yes, i**t's impossible for all observers to agree that two events are simultaneous unless they happen at the same place. But I'm sure that is a little too succinct to convince you, that's why you need to watch the video, it's only a little longer. And neither acceleration nor General Relativity is the key to resolving the twin "paradox", as far as this matter is concerned you'd do best to forget about them. * *The twins ARE at the same place when the thought experiment begins, and since they're juxtaposed when the thought experiment begins, their clocks are synchronized without anything to do with absolute simultaneity! And second, using a spacetime diagram, the paths are unequal, and that's because only one path represents the accelerating twin who is traveling. If you don't believe me, look at (ds)^2 for each twin to confirm my claim. Take notice of the second order differentials. AG * *CORRECTION: The spacetime path lengths are INVARIANT, but along the path of the stationary twin, the second order differentials are zero since that twin is NOT accelerating, but those second order differentials for the traveling twin are NON-ZERO since he's accelerating. Now look at the proper times along both paths and you'll see that it's greater for stationary twin because the path lengths are invariant. Hence, stationary twin ages more than traveling twin! Note also that this analysis uses SR. If the video is using a simultaneity argument, then the video is wrong. AG* * John K Clark See what's on my new list at Extropolis <https://groups.google.com/g/extropolis>* fai -- 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/b8f54353-cf69-4155-a63f-57b1550ba40bn%40googlegroups.com.
