On Tue, Dec 10, 2024 at 5:21 PM Alan Grayson <[email protected]> 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 > > 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. And yet, physicists claim > the LT gives the actual measurements in one frame, using the measurements > in another frame. AG > Different frames can define their coordinates in terms of local measurements on a grid of rulers and synchronized clocks like the one in the image at http://www.upscale.utoronto.ca/GeneralInterest/Harrison/SpecRel/SpecRel.html#Exploring -- for example if a collision between two space rocks happens right next to the X=15 meters mark on my ruler, and the clock at that mark reads T=10 seconds when the collision happens right next to it, all observers agree that those events coincide in space and time. But a different frame will have its own parallel set of rulers and clocks, so that the same collision might happen next to say the X'=20 meters on your ruler, with your clock at that location reading T'=5 seconds, and all observers will all also agree that these events coincide. Each set of rulers measures the rulers of other frames to be shrunk, and the clocks of other frames to be running slow and out-of-sync with one another, I gave some illustrations showing how the ruler markings and clock readings of two frames line up with one another at https://physics.stackexchange.com/a/155016/59406 > > > 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 > All length/distance claims do involve simultaneity since one is talking about the distance between two events or ends of an object when both are measured at the same moment in a given frame. Imagine a ruler long enough to stretch from our galaxy to Andromeda which was moving at a high fraction of c relative to the two galaxies, with clocks mounted at regular intervals along it (so at rest relative to the ruler, moving close to c relative to the galaxies) and synchronized in the ruler's frame using the Einstein synchronization convention. Then if you looked for a pair of clocks such that one was passing through our galaxy when it showed a given time T, and the other was passing through Andromeda when it showed the same time T, and looked at the number of light-year markings on the ruler between their two positions, you would find this was greatly shortened relative to the distance to Andromeda as measured by a similar ruler/clock system at rest relative to ourselves. 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]. 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