General Relativity and countability

In short form, general relativity tells us how countable is SpaceTime.

The metric captures all the geometric and causal structure of spacetime, being used to define notions such as distance, volume, curvature, angle, future and past.

Mainly, what makes space and time countable unit.

Metric signature can be defined as the dimensions of a maximal positive, negative and null subspace.

What are the sizes of the boxes that can be positioned in this space. The grocery business sends cases of eggs to the retail outlet, which are then delivered in dozens to the customer. It has dimension 2. So, if you rob the egg delivery guy anywhere along the road, you get cases of eggs. Same for the retail customer, you get dozens. That is; make the tightest loop around the egg business gets you a dozen eggs or a case of eggs.

So Einstein goes into the business of delivering momentum*position. Against what back ground does he do this? The basic unit of the vacuum naturally. It becomes the cosmological constant, does the vacuum have a smallest unit?

The existence of a cosmological constant is thus equivalent to the existence of a non-zero vacuum energy.

Anything with a redundancy is energy, and the vacuum can only measure redundancy up to a limit. 

Einstein, computes the amount of momentum*position in a closed system that makes Newton's gravitational constant true. Or, in our metaphor, how much flow of eggs is needed to keep the truck full and the customers moving thru the check out line.

It is all about countability, and this is all about Pauli separability. And those are balanced against the residual noise of the vacuum.

What is the residual energy of the vacuum?

A positive vacuum energy density resulting from a cosmological constant implies a negative pressure, and vice versa. If the energy density is positive, the associated negative pressure will drive an accelerated expansion of the universe, as observed.

Is the vacuum asymmetric, or evenly balanced? Is it flat, a hump, or a well? Nature is not that complicated, and the gravitational constant is not the final word.

What is really going on is simple quantum mechanics, how many orders of quants are supported given the density of redundancy, the asymmetry of the vacuum. The SpaceTime units are the Pauli paths left over when all the redundancy has been packaged, up to the vacuum limit of countability..