On Thursday, December 5, 2024 at 5:35:35 AM UTC-7 John Clark wrote:
On Thu, Dec 5, 2024 at 1:19 AM Alan Grayson <[email protected]> wrote: * >But the conclusion that it fits seems to contradict the fact that the length of the garage shrinks from the car's pov* *But 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.* *John K Clark* *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. So if you assume the car's velocity is sufficiently large to fit perfectly within the garage, so that its front and back end are simultaneously positioned at the open garage doors, the garage observer will not agree with that conclusion due to the failure of simultaneity of the front and rear boundaries of the car, as seen by the garage observer. IOW, unless we can establish that there's an objective reality where both observers see the same thing -- the car perfectly fitting inside the garage, or not -- we haven't resolved the apparent paradox. Moreover, 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* -- 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/9e854b26-30cc-4f68-a7b7-108782209604n%40googlegroups.com.
