On Sun, Dec 15, 2024 at 1:17 PM Alan Grayson <[email protected]> wrote:
> > > On Sunday, December 15, 2024 at 9:41:15 AM UTC-7 Jesse Mazer wrote: > > On Sun, Dec 15, 2024 at 8:31 AM Alan Grayson <[email protected]> wrote: > > On Sunday, December 15, 2024 at 6:20:47 AM UTC-7 Alan Grayson wrote: > > On Sunday, December 15, 2024 at 5:41:54 AM UTC-7 John Clark wrote: > > On Sat, Dec 14, 2024 at 11:01 PM Alan Grayson <[email protected]> wrote: > > * > What bothers me is the disagreement between frames about fitness or > not, and why the alleged lack of simultaneity resolves the apparent > contradiction. AG * > > > *In this thought experiment I think even you would agree that no matter > how fast or slow the car is going there will always be times when the front > of the car is in the garage, and times when the back of the car is in the > garage; so the question of the day is " Is there any frame of reference in > which those two events occur SIMULTANEOUSLY?" Einstein's answer is "yes", > provided the car is moving fast enough. And as proof that Einstein's answer > was correct, in this thought experiment, above a certain speed, there is NO > frame of reference in which there is a car shaped hole in the back door of > the garage. * > > *John K Clark See what's on my new list at Extropolis > <https://groups.google.com/g/extropolis>* > > > No. Above a certain speed, since the car is length contracted from the pov > of the garage frame, the car will fit in the garage, and waiting some time, > then being in a different reference frame, it could hit the back door. AG > > > But the real question is this; if from the pov of the car frame, there is > a v such that the car never fits in the garage for this v and greater, why > is it claimed that lack of simultaneity between frames solves the problem, > since we're only considering simultaneity in garage frame where the car > fits? AG > > > Do you understand that when people talk about the relativity of > simultaneity in the context of the car/garage problem, they are referring > not just to events which are actually simultaneous in some frame, but also > the fact that different frames can disagree about the time-ordering of > events with a spacelike separation (i.e. neither event is in the past or > future light cone of the other event)? The events A and B I was talking > about earlier are not simultaneous in either the car frame or the garage > frame (at least not with the numerical values for rest lengths and relative > velocity given by Brent), but they happen in a different order in the two > frames, and the relativity of simultaneity is key to understanding how > that's possible, in Newtonian physics where all inertial frames agree about > simultaneity there could be no disagreement about the order of any events. > > Jesse > > > What I understand is that from the pov of the garage frame, the car's > length is contracted so can fit in the garage. And, of course, "fit" > requires simultaneity of the car's endpoints. This seems sufficient to > solve the problem. > What do you mean by "simultaneity of the car's endpoints"? The answer I gave involved looking at two events, A="back of car passes front of garage" and B="front of car reaches back of garage", that are *not* simultaneous in either the garage rest frame or the car rest frame (one could find some third frame where they're simultaneous but this is irrelevant to the problem). I suppose it's true that if you're in a frame (like garage rest frame) where A happens before B, then in that frame if A happens at an earlier time T0 and B happens at a later time T2, then if you pick some intermediate time T1 between T0 and T2, and look at events on the worldline of the front and back of the car at T1, then both events will be within the garage (ie both endpoints are simultaneously between the front and back end of the garage in this frame). Did you mean something like that, or are you talking about something different? > But the so-called explanations involve another frame where simultaneity > fails. So, I was wondering; why bring in a second frame, and that > simultaneity fails in this other frame, to explain why the car will > eventually fit in garage frame? > Because the "paradox" is precisely the fact that it fits in one frame and doesn't fit in a different frame, if you just told a student "look at this scenario and notice that the car fits in the garage frame", they wouldn't learn anything new about relativity that differentiates it from a classical scenario where a car fits in a garage. > Anyway, I see my main problem all along has been my inability to *believe* > that different frames can yield different measurements, even the case of a > larger car fitting in an initially smaller garage. > Do you agree with the point I made earlier that they agree on all local measurements of what different clocks read at the moment they are next to each other (like the clock mounted to the back of the car and the clock mounted to the front of the garage), that the basic disagreement is which set of clocks each observer chooses to use to define the time coordinate in their own rest frame? Other disagreements, like the disagreement about whether the car fits, all follow from that initial disagreement about which set of clocks to use to define time. > BTW, I still want to know if clocks in different frames can be > synchronized, and if so, whether the synchronization persists. > If by "synchronized" you just mean they can be set to read the same time at the moment they pass next to each other (so Einstein synchronization isn't needed), then yes you can do that, but in that case the synchronization does not persist in either frame. If I have two clocks A and B which have been synchronized with each other by the Einstein procedure, and your clock C is set to read the same time as A at the moment they pass each other, then C will *not* read the same time as B at the moment it passes B, instead it will show a lesser time so I will conclude that C is running slow relative to my frame. Did you take a look at the diagram I gave at https://physics.stackexchange.com/a/155016/59406 showing the two sets of clocks in motion relative to one another so you can see which pairs of clock readings coincide, and can also see that each frame defines the clocks in the other frame to be both running slow and out-of-sync with one another? > I appreciate your patience throughout this discussion. Are you the physics > graduate of Brown University? AG > No problem. And yes, I got my undergrad degree in physics, but I didn't go on to grad school. Jesse > -- > 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/c9fab5d0-f11f-43d4-8cde-14ed5bef07e2n%40googlegroups.com > <https://groups.google.com/d/msgid/everything-list/c9fab5d0-f11f-43d4-8cde-14ed5bef07e2n%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/CAPCWU3JH7zW3%3Do_PjztZUbdqotJEeyEgfUoiJtk_b1wEeS3KWw%40mail.gmail.com.
