Correction: ds^2 = -(cdt)^2 + dx^2 + dy^2 + dz^2 On Friday, September 6, 2024 at 2:03:08 PM UTC-6 Alan Grayson wrote:
> 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/f4c96f73-eab8-4074-b2fb-5a310aa64f8en%40googlegroups.com.
