On Fri, Jan 17, 2020 at 9:58 AM Bruno Marchal <[email protected]> wrote:
> >> 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 space*TIME *(not to be confused with space) to >> calculate a distance in space*TIME* 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. * > Yes, you can use that to represent a curved path in 4D (one of time 3 of space) Minkowski Space where Special Relativity lives, but as you say that doesn't really get to the fundamental issue because Minkowski Space is flat and Special Relativity says nothing about gravity, for that you need General Relativity and GR doesn't live in Minkowski Space. In General Relativity curved Spacetime is what gravity is, and in GR if there is any curvature in the Spacetime of the universe, and we know there is because we know that gravity exists, then, unless vacuum energy also exists and is fine tuned to one very precise value, the universe can not be stable, it must be either expanding or contracting. There are thermodynamic reasons to think it can't be contracting so it must be expanding. And that is why no physicist would say that Carroll's statement "*the manifestation of spacetime curvature is simply the fact that space is expanding*" was controversial . 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]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CAJPayv3XNWk4TXLcLNKr0RL%3DQWP-cFKrJ2TngG0N3uUrYVPsTg%40mail.gmail.com.
