On Fri, Dec 6, 2024 at 3:23 PM Alan Grayson <[email protected]> wrote:
> > > On Friday, December 6, 2024 at 11:13:36 AM UTC-7 Jesse Mazer wrote: > > On Fri, Dec 6, 2024 at 7:45 AM John Clark <[email protected]> wrote: > > 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. * > > > *I think your claim is mistaken if you're using simultaneity in the car's > frame. If not, then how do you define "fits in the garage"? See my comments > in reply to Jesse. AG* > > > *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. * > > > You didn't really answer my question before about whether you think there > is any way to define the phrase "fits in the garage" in a way that doesn't > involve questions of simultaneity. > > > *Offhand, I don't know how else to structure a replywithout relying on > simultaneity, but using simultaneity is useless since the garage observer > will not agree with the car observer that the car fits in the garage, since > he does not interpret simultaneity as the car observer does. And, in > addition, the garage observer knows that the car's length decreases in the > exact same proportion **as the garage's length decreases, so he will deny > that car fits since the relative lengths haven't changed, regardless of the > car's velocity. AG* > When you say above "the garage observer knows that the car's length decreases in the exact same proportion as the garage's length decreases", presumably the latter refers to the shrinking of the garage in the car's rest frame? If so, why should the shrinking of the garage in the *car's frame* be relevant to the *garage observer's* answer to whether the car fits? In answering the question he uses his own rest frame, where there is no shrinking of the garage length. Below you say something about there being an "objective fact" about the matter (see my response below)--are you assuming in your answer here that the garage observer is not trying to answer the question "does the car fit in my own rest frame" but some other question like "does the car fit in objective terms"? If so, I would say this second question is simply nonsensical, like asking "do two points on a plane share the same x-coordinate in objective terms, independently of our choice of how to orient our x-y axes"--whether two points share the same x-coordinate is inherently a coordinate-dependent question that has no objective answer independent of choice of coordinate system, similarly whether the car fits is inherently a frame-dependent question that has no objective frame-independent answer. > > > If we do use a definition involving simultaneity, the natural one is to > look at the two localized events A="back end of the car passes by the front > door of garage" and B="front end of the car crashes into back wall of > garage" (assuming the car does not brake so that everything is inertial up > to the moment of the crash). In a frame where the crash B happens *after* > the back end of the car entering the garage A, there will be some interval > of time where the car is fully inside the garage and it hasn't yet crashed. > In a frame where B happens *before* A, the car never fit in the garage > because the front end crashed into the back wall before the back end had > entered the garage. > > When you say there is never a contradiction, > > > *I don't recall writing that; nor do I agree with that claim. I am saying > that using simultaneity doesn't seem to solve the problem, since a solution > must have both observers agree on an objective fact; whether the car fits > or not. AG* > You said it in the last part of your older message in bold that I quoted above (right before my response beginning 'You didn't really answer my question before')--your words were "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". Did you say that by mistake, or does the wording need clarification or something? And *why* do you think "whether the car fits or not" is an "objective fact"? Is that just a gut feeling or do you have an argument for it? I would say only local facts are really objective in relativity, like what two clocks read at the moment they pass right next to each other (one could for example compare a clock mounted on the back of the car to a clock mounted on the front of the garage and both frames would agree on what each clock reads as they pass next to each other). Since "does the car fit" cannot be stated in such localized terms, but depends on comparing the position of the front of the car and the position of the back of the car at "the same moment", I'd say any yes-or-no answer to this question is *not* an objective fact but depends on the simultaneity convention. 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/CAPCWU3KehxHCVawJpqmT%3DavxPhYL1WJ84NwHiY5bY1e61TLBLA%40mail.gmail.com.
