On Fri, Dec 20, 2024 at 9:48 PM Alan Grayson <[email protected]> wrote:
> > > 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. > How do you figure? No, only the set of things happening at any *single* point in spacetime (like clock readings and ruler markers and other events like two worldlines crossing) will be frame-invariant, and I already said when I talk about "local events" I am talking about single points in spacetime. Any time you are talking about relationships between *different* points in spacetime, whether temporal relations like simultaneity/non-simultaneity or spatial relations like distance, that is *not* a claim about local events at a single point in spacetime, and so not frame-invariant. Jesse > 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 > <https://groups.google.com/d/msgid/everything-list/a0570ea5-13e8-4dcd-8c4d-df44420c541dn%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/CAPCWU3%2BY3UrRO3m4GLmrfd2DJqeWdQQXphe1JO44PNiPHCAhmg%40mail.gmail.com.
