On Fri, Jan 24, 2025 at 12:06 AM Alan Grayson <agrayson2...@gmail.com> wrote:
> > > On Thursday, January 23, 2025 at 6:03:17 PM UTC-7 Jesse Mazer wrote: > > On Thu, Jan 23, 2025 at 5:55 PM Alan Grayson <agrays...@gmail.com> wrote: > > On Thursday, January 23, 2025 at 2:51:50 PM UTC-7 Jesse Mazer wrote: > > On Thu, Jan 23, 2025 at 4:28 PM Alan Grayson <agrays...@gmail.com> 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 <agrays...@gmail.com> 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. > > > How do you define the local physical facts that both frames must agree to? > AG > > > I explained the concept in a number of posts on the "ATTN: Jesse" thread > you started earlier, like > https://groups.google.com/g/everything-list/c/vcrAzg4HSSc/m/xCpbnK-AAgAJ > and > https://groups.google.com/g/everything-list/c/vcrAzg4HSSc/m/IENKOmsaAwAJ > > > > 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. > > > Can the above result be obtained by simply using the LT time translation t > --> t' applied to the endpoints of the car fitting in garage from the pov > of the garage frame, or is more required? TY, AG > You would want to first apply the LT to the garage door closing events in the garage frame, in order to find the coordinates of the closing events (both position and time) in the car frame. No *single* pair of events on the endpoints of the car would be sufficient to get an understanding of fitting vs. not fitting, since checking if the car fits at some time coordinate in a given frame requires knowing the *simultaneous* position of the front and back of the car in that frame, but a pair of events at the front and back of the car which are simultaneous in one frame will be non-simultaneous in the other. But you could take the x(t) functions for front and back of the car in one frame and substitute them into the LT and solve the resulting equations to find the x'(t') functions for front and back of the car in the other frame. You can also figure out x(t) and x'(t') for the back and front of the car with less algebra just by using the length contraction equation. For example if in the car frame the back end of the car has fixed position x'=0 and the front end has fixed position x'=10, this tells you the car has length 10 in its own frame, so if the car has velocity 0.6c in the garage frame it should have a contracted length of 10*(1/sqrt(1 - 0.6^2)) = 8 in the garage frame. That tells you that in garage frame the back of the car should have x(t)=0.6c*t and the front of the car will have x(t)=8 + 0.6c*t (these equations ensure that the distance between front and back is always 8 at any value of t, and that both have a velocity of 0.6c in this frame; the equation for the back of the car also ensures that at t=0 it has position x=0, which has to be true if it had position x'=0 at t'=0 in the garage frame, since the LT maps x=0,t=0 to x'=0,t'=0). And then if you want, you can double check these equations by taking a particular value of x,t for any event along the worldline of the back of the car (say, t=5 seconds and x=3 light-seconds, which is along the line x(t)=0.6c*t) and applying the LT position translation equation x' = gamma*(x - vt) to verify it gives a value of x'=0 in the garage frame (in this example gamma = 1.25 and v=0.6, so you get x' = 1.25*(3 - 0.6*5) = 1.25*(3 - 3) = 0), likewise with applying the LT position translation equation to any event on the worldline of the front of the car and verifying it gives a value of x'=10. Jesse > > Does the resolution of the paradox require the existence of garage doors? > If you imagine a garage with no doors, does the paradox continue to exist? > AG > > > You can define it in any other way that allows you to physically identify > specific events on the worldlines of different parts of the garage (like > the front and back openings) and different parts of the car (like front and > back end of the car), like if you imagine clocks attached to them so you > can identify points an a worldline by the readings on the attached clock. > And the paradox is about a theoretical situation anyway (we don't have the > practical ability to shoot a car through a garage fast enough that there > would be measurable disagreements about fit), it would be a fatal flaw for > the theory of relativity if any situation whatsoever led to conflicting > predictions about local events, regardless of whether it was realized. > > Jesse > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to everything-list+unsubscr...@googlegroups.com. > To view this discussion visit > https://groups.google.com/d/msgid/everything-list/b528d833-c135-4c26-b438-d27a47bfc25dn%40googlegroups.com > <https://groups.google.com/d/msgid/everything-list/b528d833-c135-4c26-b438-d27a47bfc25dn%40googlegroups.com?utm_medium=email&utm_source=footer> > . > -- You received this message because you are subscribed to the Google Groups "Everything List" group. 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