On Thu, Dec 12, 2024 at 10:08 PM Brent Meeker <[email protected]> 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. > In case Alan is unclear on this, a geodesic path in flat spacetime is always a straight line when depicted on a spacetime diagram (it can represent the worldline of an inertial object), and a non-geodesic is not; if you have two points in spacetime and two paths between them, one geodesic and the other non-geodesic, the geodesic one maximizes the proper time, which is analogous to the fact that in ordinary Euclidean geometry a straight line path between two points minimizes the distance. If the non-geodesic path is interpreted as the worldline of a *single* object, then it will involve an acceleration at some point, but the triplet version of the twin paradox shows how you could also interpret a non-geodesic path as joined segments of the worldlines of two (or more) different objects which pass next to one another. Jesse > 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 > > 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 > > > > > Brent > > -- > 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/296773f2-299a-4423-911a-d0c93b0dd24bn%40googlegroups.com > <https://groups.google.com/d/msgid/everything-list/296773f2-299a-4423-911a-d0c93b0dd24bn%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]. > To view this discussion visit > https://groups.google.com/d/msgid/everything-list/0e415085-4ca9-4e08-b41a-9396be118389%40gmail.com > <https://groups.google.com/d/msgid/everything-list/0e415085-4ca9-4e08-b41a-9396be118389%40gmail.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]. To view this discussion visit https://groups.google.com/d/msgid/everything-list/CAPCWU3JMM_7Kh27sVB7%2BdfEWjXHUB%2BMScXaimy2xZKmN6DUTrg%40mail.gmail.com.
