On Sunday, September 7, 2025 at 7:49:01 PM UTC-6 Brent Meeker wrote:
On 9/7/2025 5:44 PM, Alan Grayson wrote: On Sunday, September 7, 2025 at 2:38:40 PM UTC-6 Brent Meeker wrote: A complicated explanation of the triplet paradox. Length contraction is consistent, but it's not necessary to understand the effect. AG will reject it because he doesn't "believe in" handing off clock readings. Brent *No, that's not it. Rather, I am uncomfortable with de-facto frame-jumping because I am unsure what happens to time when this is included in a solution. And if the twins are at rest and juxtaposed as the scenario begins -- which, BTW, is how the TP is habitually DEFINED -- the traveling twin MUST accelerate to begin his journey. But in the final analysis it's "your way or the highway", meaning that alternate solutions are unacceptable for you. * Not at all. You think it depends on acceleration. Fine, then here's an alternate version with acceleration. The twins each accelerates exactly the same level for exactly the same duration. But Red is still younger than Blue for exactly the same reason; his path is longer in space and therefore shorter in spacetime. *So, if there is acceleration, there is also gravity by applying the Equivalence Principle, * So did you apply gravitational time dilation to each twin above? *Later I posted why my GR model doesn't work. There's no obvious way for the twins to compare clock and determine their relative ages. It might depend on the paths taken, and I don't see how to do a calculation for any particular path for the traveling twin. Nonetheless, your denial of acceleration is mistaken. In your diagram with two spacetime paths, the proper times differ because along one path all the spatial derivatives are zero, unlike along the other path of the traveling twin. This is your de-facto admission that differences in accelerations is the key to solving the paradox. Your solution is ostensibly simpler because you fail to state exactly why the proper times are different along the two paths. AG* *and clocks in gravitational fields slow down, and this applies solely to the traveling twin. Notice, I never used or applied the concept of force, * Above you seem to think the equivalence principle means acceleration implies gravity Brent *When you're accelerating, it seems as if you're in a local gravitational field; that is, you cannot distinguish your acceleration from local gravity field. If that's not what the EP is, what's your take? AG* *so claiming I did so, shows you didn't understand my solution (using GR!). 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/95583d64-ac5b-4680-9161-df61a98ace16n%40googlegroups.com.
