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
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