On Wed, Dec 11, 2024 at 2:05 AM Alan Grayson <[email protected]> wrote:
> > > On Tuesday, December 10, 2024 at 11:58:03 PM UTC-7 Jesse Mazer wrote: > > On Wed, Dec 11, 2024 at 12:08 AM Alan Grayson <[email protected]> wrote: > > > > On Tuesday, December 10, 2024 at 7:23:53 PM UTC-7 Alan Grayson wrote: > > On Tuesday, December 10, 2024 at 6:38:51 PM UTC-7 Alan Grayson wrote: > > On Tuesday, December 10, 2024 at 6:07:51 PM UTC-7 Brent Meeker wrote: > > On 12/10/2024 2:21 PM, Alan Grayson wrote: > > On Tuesday, December 10, 2024 at 1:46:37 PM UTC-7 Brent > Meeker wrote > > On 12/10/2024 1:33 AM, Alan Grayson wrote: > > > > On Monday, December 9, 2024 at > 4:54:34 PM UTC-7 Brent Meeker wrote: > > On 12/9/2024 3:24 PM, Alan Grayson wrote: > > On Monday, December 9, 2024 at 2:01:28 PM UTC-7 Brent Meeker wrote: > > > > > Nothing odd about dilation and contraction when you know its cause. > > But what is odd is the fact that each frame sees the result > > differently -- that the car fits in one frame, but not in the other -- > > and you see nothing odd about that, that there's no objective reality > > despite the symmetry. AG > > The facts are events in spacetime. There's an event F at which the > front of the car is even with the exit of the garage and there's an > event R at which the rear of the car is even with the entrance to the > garage. If R is before F we say the car fitted in the garage. If R is > after F we say the car did not fit. But if F and R are spacelike, then > there is no fact of the matter about their time order. The time order > will depend on the state of motion. > > Brent > > > Since the car's length can be assumed to be arbitrarily small from the > > pov of the garage, why worry about fitting the car in garage perfectly, > and then appealing to difference in spontaneity to prove no direct > contradiction between the frames? It seems like a foolish effort to > > avoid a contradition, when one clearly exists. AG > > > What's the contradiction? > > > The contradiction is precisely this; assuming the initial rest state is > that the length of the car is larger than the length of the garage, we get > the *car* *never fitting* in the garage from the pov of the car, and the > *car* *fitting* in the garage from the pov of the garage. The car can't > fit *and* not fit in the garage. > > You think that because you have not carefully defined "fit", which does > require reference to simultaneity. > > > I defined "fit" to mean the car's length in any frame is *less* than the > garage's length. AG > > Wrong! > > > How would you define fit? By allleging the car perfectly fits within the > garage, even though it is longer than garage? AG > > > The former result is easy to see, since the car's motion shrinks the > garage's length, so the car, initially longer than the garage, can never > fit inside the garage. > > Within the cars reference frame. > > > Yes. AG > > The latter result follows from the fact that from the pov of the garage, > the car's length shrinks, and for a sufficient velocity, it will shrink > enough to fit in the garage. Further, the issue of simultaneity is a > non-issue, > > No it is the essential issue. The car (or the garage) don't actually > undergo some physical shrinkage. > > > Yes. It's all about appearances, or so it seems. > > No, it's all about measurements and simultaneity. > > > But when the measurements give different results depending on which frame > they are made from, the LT de facto tells us how things appear from such > frames, so about appearances. AG > > And yet, physicists claim the LT gives the actual measurements in one > frame, using the measurements in another frame. AG > > If they did they wouldn't keep their dimensions in their own frame. So it > is a question of measurement and simultaneity. > > Why then do physicists agree that the distance to Andromeda will be > immensely shortened if a traveler's velocity is close to c? Never a mention > of simultaneiry in this case. AG > > Because they're not concerned with two events, just with the duration of > the trip. In this case you must consider two events: One when the front of > the car is adjacent to the exit of the garage and the other when the rear > of the car is adjacent to the entrance of the garage. If these two events > are spacelike relative to one another then there is a reference frame in > which they are simultaneous. > > Brent > > > In the case of the car perfectly fitting in the garage, are the ends of > the car spacelike separated? I don't think so, so why bring it up? AG > > > *The above comment is wrong. I was confusing spacelike separated from > events which are not causally connected. AG * > > > The primary flaw in the attempt to model the problem is to assume the car > fits perfectly in the garage (meaning the front and back ends of car are > juxtaposed to back and front end of the garage) in contradicton to the > initial conditions (rest length of car is assumed greater than the rest > length of the garage), so that when the car is moving, and the same gamma > factor applied to yield the transformed lengths observed by each frame, > each of these rest lengths changes in the same proportion, making the > assumed initial perfect fit while moving, impossible. AG > > > In the garage rest frame where the car fits, the gamma factor is not > applied to the garage, only to the car. Likewise in the car rest frame > where the car doesn't fit, the gamma factor is not applied to the car, only > to the garage. Again you seem to want to allude to some frame-independent > notion of what it means for the car to "fit" without ever giving a clear > definition. > > Jesse > > > I didn't apply the gamma factor in the rest frame, since we need relative > motion to apply it. But when motion exists, I can use the gamma factor to > determine the contraction of the motion being observed from either frame, > to the other. I thought I gave a clear definition of fit, namely, the car > length being LESS than the garage. AG > > If your definition is that the car length is less than the garage length, are you defining those lengths relative to whatever frame we're using, for example if we ask whether the car fits in the garage frame are we using the combination of the car's contracted length and the garage's rest length? Jesse -- You received this message because you are subscribed to the Google Groups "Everything List" group. 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