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.
