On 1/23/2025 1:51 PM, Jesse Mazer wrote:
On Thu, Jan 23, 2025 at 4:28 PM Alan Grayson <[email protected]>
wrote:
On Thursday, January 23, 2025 at 12:41:30 AM UTC-7 Alan Grayson wrote:
On Wednesday, January 22, 2025 at 7:10:56 PM UTC-7 Jesse Mazer
wrote:
On Wed, Jan 22, 2025 at 8:06 PM Alan Grayson
<[email protected]> wrote:
On Wednesday, January 22, 2025 at 2:00:25 PM UTC-7
Jesse Mazer wrote:
Brent hasn't chosen to answer your question, but
my guess would be he just means if you pick some
specific event where part of the car is inside the
garage, like the event A of the back of the car
passing the garage entry door, in the garage frame
the car is fully inside the garage "at the same
time" as event A (using the garage frame
definition of other events simultaneous with A),
while in the car frame the front of the car is
already well past the exit of the garage "at the
same time" as event A (using the car frame
definition of other events simultaneous with A).
He obviously isn't disputing the notion that the
two frames have different definitions of
simultaneity since he made this point many times
in his comments.
Jesse
If that's what Brent means, how is this related to the
breakdown of simultaneity? AG
Are you asking about where to find a breakdown of
simultaneity in my statement 'if you pick some specific
event where part of the car is inside the garage, like the
event A of the back of the car passing the garage entry
door, in the garage frame the car is fully inside the
garage "at the same time" as event A (using the garage
frame definition of other events simultaneous with A),
while in the car frame the front of the car is already
well past the exit of the garage "at the same time" as
event A (using the car frame definition of other events
simultaneous with A)'?
If so, in that statement I'm saying that the two frames
disagree about which event at the front of the car is
simultaneous with A, the garage frame picks an event B on
front of the car's worldline where the front of the car is
inside the garage and hasn't yet reached the exit, the car
frame picks a different event C on the front of the car's
worldline where the front of the car is outside the
garage, having already passed through the exit. In the
garage frame A is simultaneous with B, in the car frame A
is simultaneous with C.
Jesse
OK, let's suppose you've identified events which aren't
simultaneous in both frames, you still have a car, the same
car, which fits in one frame and never in the other. For me
this still seems paradoxical even though I agree that
relativity allows different frames to make different
measurements of the same phenomena such as the B and E fields
in E&M. AG
Here's what I want to know; how exactly do you define the paradox
(what it is), and how does the disagreement about simultaneity
solve it for you? AG
The paradox is the seeming danger that the disagreement about fitting
could lead to differing predictions local physical facts, and the
relativity of simultaneity shows how this danger is avoided.
In particular, if we have a version of the problem where in the garage
frame both garage doors shut simultaneously and then re-open, if both
frames *did* agree about simultaneity this would clearly lead to a
conflict. In the garage frame, since the car fits entirely within the
garage for a short time, that means both doors can close
simultaneously without hitting the car; but in the car frame, since
the car never fits entirely within the garage, if both doors also
closed simultaneously in this frame, one of the doors would have to
smash into some part of the car that was blocking the door frame at
that moment (whether or not the door collides with the car is a local
physical fact). But with the relativity of simultaneity you can show
that if the doors shut simultaneously in the garage frame, in the car
frame the right door closes first before the front of the car has
reached its location so there is no collision, and then the left door
closes later after the back of the car has passed it, so a collision
is avoided there too.
Jesse
Having the doors close and then open seems like a confusing complication
to me. That's why I start with the exit door closed and the entrance
door open. Then there are only two "door" events. The exit door opens
and the entrance door closes. If that's the time order, there's a
period when both doors are open. If, in a different reference frame,
the order is reversed, there's a period when both doors are closed.
Talk of simultaneity is slightly misleading, what we're talking about is
reversal of time order between the car's reference frame and the
garage's reference frame. Of course that implies that there is some
intermediate reference frame in which the exit door opens and the
entrance door closes simultaneously, but that's not the essence of the
seeming paradox.
Brent
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