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] > * Can you elaborate further? Not clear what this diagram demonstrates. AG* >
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