I meant ds^2 = -dt^2 + dx^2 + dy^2 + dz^2 On Friday, September 6, 2024 at 1:53:52 PM UTC-6 Brent Meeker wrote:
> You mean this one? > > [image: Schwarzschild Metric] > > Brent > > > > > On 9/6/2024 5:34 AM, Alan Grayson wrote: > > I think we can use the usual metric in relativity, ds^2, with the minus > sign in from of dt^2. AG > > On Friday, September 6, 2024 at 6:26:14 AM UTC-6 smitra wrote: > >> Yes, but then a vector space without a norm. No inner product is >> defined, so from a pure math point of view, you are free to define any >> arbitrary inner product that satisfies the axioms for it. Alan the >> physicist will prefer that inner product that is dictated by the >> relevant physics, so this has to take the form of the indefinite Lorentz >> inner product in a locally free-falling coordinate system. This means >> that you must also consider the metric, so the distance between >> infinitesimally separated points. So, labels are arbitrary and hey are >> then meaningless, unless you also specify what the distance is between a >> point at [ct, x, y, z] and at [c(t+dt), x+dx, y+dy, z+dz]. >> >> Saibal >> >> >> >> On 06-09-2024 10:03, Alan Grayson wrote: >> > Do the 4-tuple labels on spacetime, (ct, x, y, z), form a vector >> > space? I was told on good authority that the answer is negative, but >> > now I have grave doubts of that conclusion. 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 on the web visit >> > >> https://groups.google.com/d/msgid/everything-list/fa891f6c-5195-4078-b8d7-0844b1aa6e5an%40googlegroups.com >> >> > [1]. >> > >> > >> > Links: >> > ------ >> > [1] >> > >> https://groups.google.com/d/msgid/everything-list/fa891f6c-5195-4078-b8d7-0844b1aa6e5an%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 on the web visit > https://groups.google.com/d/msgid/everything-list/6b491fb6-3210-4b86-8c56-a1cdd2b79586n%40googlegroups.com > > <https://groups.google.com/d/msgid/everything-list/6b491fb6-3210-4b86-8c56-a1cdd2b79586n%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 on the web visit https://groups.google.com/d/msgid/everything-list/23d56990-7b44-4270-99a1-d52a9e45bfbfn%40googlegroups.com.
