On Thursday, December 12, 2024 at 8:08:50 PM UTC-7 Brent Meeker wrote:
On 12/12/2024 5:43 PM, Alan Grayson wrote: On Thursday, December 12, 2024 at 6:34:01 PM UTC-7 Brent Meeker wrote: On 12/12/2024 12:27 PM, Jesse Mazer wrote: So what the hell is going on? It then occurred to me that this situation is somewhat analogous to the Twin Paradox (TP), where the two frames seem identical, yielding an age contradiction when the twins meet. But the solution to the TP is the recognition that the frames are NOT equivalent due to the accelerations of only the traveling twin whose clock can be shown, with SR or GR (although they likely give different numerical values), that the traveling twin's clock ticks at a SLOWER rate than the clock of the Earth-bound twin, accounting for the age difference when they meet. So, how to apply the lesson of the TP to the issue at hand? How is the garage frame different from the car frame? The answer is ACCELERATION! Specifically, in the problem at hand, these frames can only be equivalent if they have *equivalent* *histories.* Acceleration is only relevant to the twin paradox if it happens between the initial and final events you are analyzing, specifically between the moment the two twins depart from a common location and when they reunite at a common location. Any acceleration done by either twin *before* the departure moment would be completely irrelevant to predicting their ages on reuniting, if you know their ages at departure and subsequent paths between departure and reuniting, that's sufficient to get a prediction of their ages on reuniting that doesn't depend in any way on what happened prior to them departing from one another. Similarly, in the car/garage paradox we can assume some initial conditions where the front of the car has not yet entered the garage and both the car and the garage is moving inertially--what happened *before* those initial conditions will be irrelevant to the analysis of what happens after, for example it makes no difference if the car accelerated before that moment, or if we replace the car with space rock with the same rest length that has been moving inertially for billions of years, while the garage is mounted to a rocket and accelerated towards the space rock shortly before the initial conditions. Jesse As is well known the twin's paradox is shown to be independent of any acceleration by the related triplet's paradox: This can't be correct. It not only can be, it is. Remember I've *taught* relativity theory. Acceleration is only required in the sense that the path not be geodesic, which are maximum length paths between give events. This is the same in GR or SR. It's not a question of clocks running slow. That's loose talk; clocks in these thought experiments are always assumed to be perfect and to measure proper time along their world line. Brent *As I see it, the traveling twin must accelerate in order to leave and return, in order to meet his Earth-bound twin, and this is described as the only asymmetry in their paths, non geodesic motion, and is responsible for the asymmetric aging (traveling twin aging slower than his Earth-bound twin). And when I say acceleration slows the rate of clocks, I am applying the Equivalence Principle, that acceleration is equivalent to gravity if one ignores tidal effects. I can't dispute your claim, and must assume it's esoteric and above my head. Finally, I will rethink my position on the subject of this thread, and post it when ready. AG* For example, accelerations in GR cause clocks to slow, and absent accelerations, the traveling twin won't return to meet the Earth-bound twin. Further, using SR, and modeling changes in velocity to connected straight line segments, from the pov of Earth-bound twin, the traveling twin's clock runs slow on each segment or partition, and allowing the partitions to decrease in length to the limit, any acceleration can be modeled. 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/d1b2ddd5-fe0c-4f56-9d3b-c9036ad9a117n%40googlegroups.com.
