On 1/25/2025 10:13 PM, Alan Grayson wrote:
On Saturday, January 25, 2025 at 9:06:18 PM UTC-7 Brent Meeker wrote:
On 1/25/2025 6:34 PM, Alan Grayson wrote:
On Saturday, January 25, 2025 at 6:47:22 PM UTC-7 Jesse Mazer
wrote:
On Sat, Jan 25, 2025 at 8:07 PM Alan Grayson
<[email protected]> 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
Jesse; it's the last two of Brent's sentences that I find
ambiguous. What
does he mean?
What about them do you find ambiguous?
He's just saying that if there's a spacelike separation
between the events F and R (as there was in his numerical
example), then you can find a frame where R happens after F
(as is true in the car frame where the car doesn't fit), and
another frame where F happens after R (as is true in the
garage frame where the car does fit).
*What does he mean by "But if F and R are spacelike, then there
is no fact of the matter about their time order."? (What you
wrote above?) *
Brent writes > Yes. Just what Jesse wrote above. It means the
two events were so close together in time and distant in space
that something would have to travel faster than light to be at
both of them.
*More important I just realized that in the frame of car fitting,
the events F and R aren't simultaneous, so how does one apply
disagreement on simultaneity when one starts with two events
which are NOT simultaneous? AG*
Brent writes > That's why you should talk about events being
spacelike...the relativistic analogue of simultaneous.
*
*
*I'd like to do that. BUT if the Parking Paradox is allegedly solved
by starting in the garage frame where the car fits, the pair of events
which define fitting are not spacelike since they occur at different
times! *
You didn't read the definition of "spacelike" that I wrote above. You
want everything fed to you in tiny bites of knowledge which you forget
eight lines later, so the questions start all over again.
Brent*
*
*Which pair of events shall we use to allegedly solve the paradox? AG*
Spacelike is an /*invariant*/ concept. It */does not/* depend
the reference frame. If it's true in one frame, it's true in
all. But the time order of two spacelike events is frame
dependent. So the same two spacelike events F and R can be both
simultaneous and not simultaneous. Changing from one state of
motion to another can reverse their time order. They can be in
the order F before R and also R before F. There will be some
intermediate state of motion that makes the two spacelike events
simultaneous in that particular reference frame. The car/garage
paradox doesn't depend on that.
Brent
I also wonder what happens when we transform in the
reverse direction from the pov of simultaneity, from the
car frame to the
garage frame? TY, AG
Brent didn't mention a direction in which the transformation
is being taken, but regardless of whether you start with the
coordinates of F and R in the garage frame and transform to
the car frame, or start with the coordinates of F and R in
the car frame and transform to the garage frame, you get the
same answers about what the coordinates of these F and R are
in each frame. For instance if you start with the coordinates
x,t of F in the garage frame and apply the LT
*But don't you have to start with two events which are
simultaneous in one frame, to get a disagreement in simultaneity
in a second frame, but F and R are not simultaneous in car
fitting frame? AG*
to get the coordinates x',t' of F in the car frame, then
apply the LT to x',t' (this time using a velocity of -0.8c
rather than +0.8c since the garage frame is moving in the -x
direction as seen in the car frame) you will get back the
original coordinates x,t for the garage frame.
Jesse
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