no beginning no end

[AntonioLao]

In a Möbius universe there can be no beginning and no end. The topology is that of a one-sided surface and cannot be closed like a sphere to form an enclosed volume of inside and outside. A 3D Möbius strip is called a Klein bottle. A 1D Möbius strip can be topologically equivalent to a Hopf link. Transverse motion is always toward the same edge since a Möbius strip can at most only have one edge. Lateral motion cannot be detected but can be referenced relatively to another point on the surface. Expansion on the Möbius surface can be detected as points pointing in the same direction. However, since Möbius strip is non-orientable, an expansion center is not defined and does not exist.

All these topological properties of the Möbius strip satisfy both principle of general relativity as well as quantum mechanical suppositions of non-Abelian Yang-Mills gauge invariance. Physical dimensionality is determined by the directions of trivectors. By a principle of directional invariance there are four unique trivectors and their complements. The complement of left-future-top is right-future-top, the complement of left-future-bottom is right-future-bottom, the complement of left-past-top is right-past-top, and the complement of left-past-bottom is right-past-bottom. A trivector can be determined to complete one cycle around the universe if and if it is transformed spontaneously into it complement. To transform back into itself, each trivector must complete two and exactly two cycles around the Möbius universe. But since lateral motion is relative, a maximum speed is set at light speed. So, until lateral motion exceeds lightspeed, no trivector can ever complete one cycle around the Möbius universe and it has no beginning and no end.

[Bogie]

There are other topologies that accommodate no beginning and no end, and yet can display expansion throughout the entire Hubble viewing volume. One is Euclidean and it is quite simple to grasp relative to the topology you describe, i.e. a one-sided surface that cannot be closed like a sphere to form an enclosed volume of inside and outside.

Since you describe how expansion of the Mobius universe could be factual and can be referenced relatively to another point on the surface, is it your premise that the simpler Euclidean space cannot display expansion without a delectable center of expansion or cannot have "no beginning and no end"? (Excuse the double negatives )

Remember that the local expansion may not be the same thing as expansion of the universe.

[AntonioLao]

simpler Euclidean space cannot display expansion without

Without a metric tensor Euclidean space cannot expand nor contract. This metric tensor is infinitesimal in its design and structure. It's effective only within its local infinitesimal neighborhood. It's a local gauge invariance. Every point of the vector field is associated with a unique metric tensor and each tensor is a center of action.

[Bogie]

Without a metric tensor Euclidean space cannot expand nor contract. This metric tensor is infinitesimal in its design and structure. It's effective only within its local infinitesimal neighborhood. It's a local gauge invariance. Every point of the vector field is associated with a unique metric tensor and each tensor is a center of action.

Space does not expand, it displays the separation of objects within it. I am saying that in terms of 3D motion which I say takes place in a Euclidean coordinate system, all galaxies and clusters can appear to be moving away from each other in such a way that there is no detectable center of expansion. Said another way, it would appear that any point within the expansion could be considered the center even if factually there was one exact center.

[AntonioLao]

Space does not expand

It expands by a given metric tensor. Objects are made of local tensors called spinors. The spinor prevent contraction but the tensor causes expansion.For any spinor there is no center.