On Friday, January 17, 2020 at 6:03:46 PM UTC-7, Lawrence Crowell wrote: > > On Friday, January 17, 2020 at 5:08:14 PM UTC-6, John Clark wrote: >> >> On Fri, Jan 17, 2020 at 5:03 PM Alan Grayson <[email protected]> wrote: >> >> >> 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 . >>>> >>> >>> > *The question is, what does he mean? Is space expanding BECAUSE of >>> curvature? If so it's expanding because of gravity, since you wrote that >>> gravity and curvature are equivalent. But since gravity is attractive (as >>> far as we know), how could it be responsible for expansion (as >>> distinguished from contraction)? AG * >>> >> >> If the universe consisted of a cloud of particles that were not moving >> with respect to each other the gravitational attraction between the >> particles would indeed cause the universe to contract, but the particles >> ARE moving with respect to each other, so what will happen? It depends on >> how they are moving, but General Relativity can tell you one thing, unless >> you invoke a very fine tuned vacuum energy (aka the Cosmological Constant) >> that cloud of particles will NOT remain the same size, it will either >> expand or contract. We learn from observation that it's expanding which is >> consistent with thermodynamic reasoning. >> >> John K Clark >> > > > Sometimes a picture works best. Below is a diagram that represents how > space can be flat in a curved spacetime that expands space. > > LC > > [image: vsl.gif] > *Earlier you agreed that a flat universe has infinite spatial extent. Do you agree that IF the universe was spatially small after one Planck duration had elapsed, it could never have infinite extent now or in the future because the rate of expansion must be finite? If you agree that the universe was small after one Planck duration but still think it's flat, the infinite spatial extent must have occurred instantaneously, at the BB. But wouldn't that be a singularity since it implies a physical process resulting in infinite spatial extent occurred in a zero duration of time, which is impossible. AG*
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