On Tue, Dec 10, 2024 at 5:53 AM Alan Grayson <[email protected]> wrote:
> > > On Tuesday, December 10, 2024 at 3:27:32 AM UTC-7 Jesse Mazer wrote: > > On Tue, Dec 10, 2024 at 4:33 AM Alan Grayson <[email protected]> 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. > > > It would only be a contradiction if "the car fits" and "the car doesn't > fit" were meant in exactly the same sense, but they aren't, they are > referring to different coordinate systems. If I have some geometric shapes > on a plane, and I then overlay one set of x-y coordinate axes to get the > conclusion "the circle has a greater x-coordinate than the triangle", but > then I overlay a *different* set of x-y coordinates and get the conclusion > "the circle has a smaller x-coordinate than the triangle", the two > statements are referring to different coordinate systems which define the x > and y coordinates of both shapes differently, so there is no true > contradiction--do you agree? It's exactly the same with "the car fits" and > "the car doesn't fit", they are made from the POV of different spacetime > coordinate systems so they are not using "fit" in exactly the same sense, > and there is no true contradiction. > > Further, the issue of simultaneity is a non-issue, since measurements of > the front and back end of the car occur in the car's frame, and since the > car never fits in the garage, such measurements can never be made when the > car perfectly fits in the garage, or even loosely, since this condition > never occurs. > > > Yes, but different measurements of simultaneity can be made in the > coordinates of the garage's frame, and it's in these coordinates that the > car *does* fit, so clearly the differing definitions of simultaneity *are* > relevant to understanding why the two frames have different answers. > > Jesse > > > *I don't agree that coordinate systems can resolve the contradiction. > IIUC, measurements of simultaneity are made in car's frame, not in garage's > frame. * > Where did you get that idea? Every inertial frame in relativity has its own definition of simultaneity, based on the assumption that light travels at the same speed in both directions in that frame. And the only reason a physicist would say the car "fits" in the garage frame is that according to the garage frame's definition of simultaneity, if you measure the position of the front and back end of both car and garage simultaneously, you will find at some moments the back end of the car is past the front door of the garage while the front end of the car has not yet reached the back wall (or back door) of the garage. > *From that it's concluded that from garage frame, it's indeterminate > whether the car really fits. But I'm confused on this point. How can the > garage frame know about those measurements in car frame, and know they > differ? AG* > > If you know the coordinates of events in one frame you can simply use the Lorentz transformation to know what they are in a different frame, it's just that the coordinates in the other frame won't correspond to measurements on your own rulers and clocks at rest relative to you. 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/CAPCWU3K7oi2EOrLi%3DC2as13m88pxAHGODEROmTMVuN-gYQpr%3DQ%40mail.gmail.com.
