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.
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.
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. If they did they wouldn't keep their
dimensions in their own frame. So it is a question of measurement and
simultaneity.
Brent
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. In
summary, I think I've done for relativity, what Bertrand Russell did
for Cantor's set theory; proving the existence of a contradiction. AG
Brent
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