On Friday, December 20, 2024 at 7:36:49 PM UTC-7 Jesse Mazer wrote:
On Fri, Dec 20, 2024 at 7:21 PM Alan Grayson <[email protected]> wrote: On Friday, December 20, 2024 at 5:09:12 PM UTC-7 Alan Grayson wrote: On Friday, December 20, 2024 at 5:11:00 AM UTC-7 Alan Grayson wrote: Worldline problem; solution is x(t) = 7 + 12 * t, which is a straight line, with positive slope of 12. Do I get a gold star? AG No gold star. What I wrote is wrong. It doesn't have the line crossing the x-axis at x=7. Correction coming. AG In further consideration, it's OK. My equation does cross x-axis at x=7, when t=0. AG Yep, that's right. And if we had a second object whose worldline was described by some different equation like x(t) = 9 + 3*t, and we asked the question "where is each object located at t=8 ?", then in terms of a graph we could solve this by drawing a horizontal line that crossed the 8 mark on the vertical time axis, and seeing where it intersects the two lines x(t) = 7 + 12*t and x(t) = 9 + 3*t -- in other words, where a 1D line of simultaneity intersects the worldlines. That's the same basic idea in relativity, except that in relativity a given frame will have its simultaneity lines tilted at an angle when it's plotted in the coordinates of a different frame. Jesse You claimed that local events are frame invariant under the LT. So if we consider the endpoints of the car, and each event is frame invariant, then presumably the events, having the same time in the garage frame, will have the same time in the car frame, and thus must be simultaneous. But the claim is they're NOT simultaneous and somehow this solve the apparent paradox. I still don't get it. AG On Friday, December 20, 2024 at 4:14:30 AM UTC-7 Alan Grayson wrote: Please define what you mean by local events, with some examples. And Yes, I agree that coordinate systems are arbitrary. And Yes, I can do the assigned problem for defining a worldline, but I need to think about it a little more. And finally, Yes again. I am quite able to admit when I am mistaken. TY, AG -- 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 [email protected]. To view this discussion visit https://groups.google.com/d/msgid/everything-list/4787aab8-a11a-4061-9b13-d8523e425875n%40googlegroups.com <https://groups.google.com/d/msgid/everything-list/4787aab8-a11a-4061-9b13-d8523e425875n%40googlegroups.com?utm_medium=email&utm_source=footer> . -- 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 [email protected]. To view this discussion visit https://groups.google.com/d/msgid/everything-list/a0570ea5-13e8-4dcd-8c4d-df44420c541dn%40googlegroups.com.
