> On 16 Jan 2020, at 22:01, John Clark <[email protected]> wrote: > > On Thu, Jan 16, 2020 at 1:25 PM Alan Grayson <[email protected] > <mailto:[email protected]>> wrote: > > >> as Sean Carroll says "the manifestation of spacetime curvature is simply > >> the fact that space is expanding". > > > If curvature is caused by energy and momentum in space-time, Carroll's > > statement doesn't make sense. AG > > Has it ever occured to you that if a professor of physics at one of the best > universities in the world makes a statement about physics that makes no sense > to you it might not be because he is talking nonsense but because you don't > understand something? It makes no sense to you because you assume spatial > curvature and spacetime curvature mean the same thing. But you're wrong, they > don't. And they don't because the time dimension behaves in a fundamentally > different way than any of the 3 spatial dimensions do; more specifically if > you want to use Pythagoras theorem in spaceTIME (not to be confused with > space) to calculate a distance in spaceTIME then you have to stick in a minus > sign that Euclid and Pythagoras knew nothing about.
Of course, as I guess you now, by using an imaginary time (defining t’ = it), we can come back to the Pythagorean theorem, without the minus sign, and restore Euclideanity. That leads to something called Euclidian Relativity. I do often that for pedagogical purpose. Not sure if this is really fundamental. Bruno > > John K Clark > > -- > 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] > <mailto:[email protected]>. > To view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/CAJPayv2Yp%3DY4tgw0eozCpwsNanSDMepaCw05iHHk6GK3Y17Fug%40mail.gmail.com > > <https://groups.google.com/d/msgid/everything-list/CAJPayv2Yp%3DY4tgw0eozCpwsNanSDMepaCw05iHHk6GK3Y17Fug%40mail.gmail.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/7E5FD19C-D0DD-4B60-B585-757164A5C76D%40ulb.ac.be.
