On 1/23/2025 9:43 PM, Alan Grayson wrote:
On Thursday, January 23, 2025 at 10:32:17 PM UTC-7 Brent Meeker wrote: 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. JesseHaving 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 So, what IS the essence of the seeming paradox? AG
Apparently it's that some people cannot understand that changing reference frames can change the order of events.
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