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!
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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