On Friday, December 13, 2024 at 12:54:03 PM UTC-7 Jesse Mazer wrote:
On Fri, Dec 13, 2024 at 8:14 AM Alan Grayson <[email protected]> wrote: On Friday, December 13, 2024 at 4:46:09 AM UTC-7 Alan Grayson wrote: *I misstated the apparent paradox. Specifically, if we have car which in its rest frame fits in a garage, for sufficient v of the car, the garage length is Lorentz contracted, so the car will no longer fit. OTOH, from the pov of the garage frame, the length of the car is Lorentz contracted and will fit even better. (In my original formulation, I began with the car length greater than the garage length, in effect Lorentz contracting the garage length without first stating that in the rest frame, the car fits in the garage.) AG* *I admit it; this is a pretty dumb question after all this discussion. But assuming the resolution involves disagreement between frames about simultaneity, what exactly IS the answer? Does the car fit or not, in which frames, under what constraints or conditions? TY, AG* I think the general answer is that it fits in frames where the event "back of car passes front door of garage" happens earlier than the event "front of car hits back of garage (or passes back door of garage, if we imagine a covered bridge style garage)", and it does not fit in frames where the former event happens later than the latter event. *Do you have this backwards? AG* Which frames would fall into either category would depend on the specific values for relative velocity and rest lengths chosen in the problem, in a typical statement of the problem we are just asked to compare the car rest frame and the garage rest frame without worrying about other frames. Jesse On Wednesday, December 4, 2024 at 2:06:41 PM UTC-7 Alan Grayson wrote: In the case of a car whose rest length is greater than the length of the garage, from pov of the garage, the car *will fit inside* if its speed is sufficient fast due to length contraction of the car. But from the pov of the moving car, the length of garage will contract, as close to zero as one desires as its velocity approaches c, so the car *will NOT fit* *inside* the garage. Someone posted a link to an article which claimed, without proof, that this apparent contradiction can be resolved by the fact that simultaneity is frame dependent. I don't see how disagreements of simultaneity between frames solves this apparent paradox. 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/97e8b477-6080-4ffc-9825-32a39d3e7b02n%40googlegroups.com.
