On Fri, Dec 6, 2024 at 12:10 AM Alan Grayson <[email protected]> wrote:
*>> from the garage man's POV the garage's length does not shrink but the > car's length does. In Special Relativity time is diluted by the factor γ > which is equal to 1 / √(1 - v²/c²) ; and an object's length will be > reduced by a factor of the inverse of γ. So Length contraction reduces the > length by 1/γ, and Time Dilation increases the time interval by γ. For > example, at 87% the speed of light length contracts to half its original > rest length, and time dilutes by a factor of two.* > *The bottom line is that when two observers are in relative motion, like > the garage man and the car driver are, they measure space and time > differently. An event has a position and a time, and the closing of both > garage doors is an event, so they will not agree if that event happened > simultaneously when the entire car was in the garage or not.* > > > > *> I don't think your proposed solution works. We're assuming the rest > frame length of the car is larger than the rest frame length of the garage.* > *As Jesse Mazer points out, if the car fits in the car driver's frame of reference then it always fits in the garage man's frame of reference. However if it doesn't fit in the garage men's frame of reference then it won't fit in the driver's frame of reference either; this can happen if the car is not going fast enough, and the asymmetry between the two viewpoints occurs because when the car driver and the garage man and the car and the garage are all in the same frame of reference (a.k.a. they are not moving with respect to each other) then they both agree that the car is longer than the garage. So there is never a contradiction, there is never an occasion where one of them predicts the car will fit in the garage and the other predicts it will not. * > *> IOW, unless we can establish that there's an objective reality where > both observers see the same thing * *Just because 2 observers see the same thing does not mean they are necessarily observing "objective reality" because their observation is not unique. If observer-1 and observer-2 are not moving with respect to each other then they will agree about what events are simultaneous and what events are not; however observers # 3 and 4 who are not moving with respect to each other but ARE moving with respect to #1 and 2 will agree with each other about what events are simultaneous but they will not agree with #1 and 2 about what events are simultaneous. * > *> since the car length decreases in the same proportion as the garage > length decreases (from the pov of the garage observer and the car observer, > respectively), both observers would deny, given the initial condition, that > the car can perfectly fits in the garage. AG* > *If they both agree that the car will not fit in the garage then the car will not fit in the garage because the car is not going fast enough, and there is no contradiction. * *John K Clark See what's on my new list at Extropolis <https://groups.google.com/g/extropolis>* 3bv -- 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/CAJPayv2g62c7r1MUEB21%2BKmYF4LMMqYWM7nhjF05UU63ob6uWQ%40mail.gmail.com.
