On Fri, Dec 13, 2024 at 6:09 PM Alan Grayson <[email protected]> wrote:
> > > On Friday, December 13, 2024 at 3:40:26 PM UTC-7 Alan Grayson wrote: > > 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* > > No, I had it right--if the event of the back of the car passing the front of the garage happens earlier than the event of the front of the car reaching the back of the garage in some frame, then in that frame there will be some finite time period between these events where the car is fully fitting in the garage, in other words the back of the car has already passed the entrance door and is inside, and the front of the car is also inside and hasn't yet reached the back wall (or back door) of the garage. > > > 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 > > > *For some rest length frame parameters, there's a v, such that for > velocities greater than v, won't the car fit in all garage frames, but in > none of the car frames? If this is correct, what's the justification for > saying the solution exists in one set of frames, but not in another? And > what's the argument that in all of these frames, simultaneity of front and > back of car is satisfied? TY, AG * > Why do you say "garage frames" and "car frames" plural? There is only one frame where the car is at rest which is what is generally what is meant by "car frame", likewise only one frame where the garage is at rest. But it is true that for some choice of parameters like the ones Brent gave, the car fits in the garage frame but doesn't fit in the car frame, given the notion of "fitting" I discuss above. Also, what do you mean by the phrase "simultaneity of front and back of car is satisfied"? Each frame has its own definition of simultaneity, and given such a definition, any event A on the worldline of the back end of the car will have some other specific event B on the worldline of the front of the car that's simultaneous with A in that frame (in Brent's diagrams, if you want to find simultaneous events in the car rest frame just draw horizontal lines in the first diagram and see where they intersect the worldlines of the front and back of the car, likewise if you want simultaneous event in the garage rest frame draw horizontal lines in the second diagram and see where they intersect the car worldlines). 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/75b6d1d9-34aa-4329-b34e-70873e720c12n%40googlegroups.com > <https://groups.google.com/d/msgid/everything-list/75b6d1d9-34aa-4329-b34e-70873e720c12n%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/CAPCWU3K5dMsh0-RmgYE5fuEJS9T-4n%3DXZSPf0kSc4_sRtkvasw%40mail.gmail.com.
