Physics & Cosmology: Dimensionless Void Pre Big Bang

[Rosen]

Is it within the realm of physics or cosmology to refer to a dimensionless void that may have preceded the big bang? If so, has there been any speculation or inquiry as to whether the uncertainty principle would have been in effect during such an era? Has anyone within physics attempted to describe such a void? I'm not entertaining metaphysical speculation with these questions. Thank you.

 

[jfizzix]

Physics as a science is only really equipped to extrapolate from what we can measure. In my experience (physics grad student) there's at least no common theories that show how spacetime might spontaneously change its number of dimensions. That being said, there are physical systems which behave as though they exist in two dimensions (electrons in graphene) or one dimension (electrons in nanowires).

Off the top of my head, if there are indeed curled up extra dimensions as string theorists say, one could conceive at least of somehow a dimension curling or unfurling over time, but this is just idle speculation about a topic I know precious little.

 

[Chronos]

AFAIK there is no mathematical description for a dimensionless void.

 

[Rosen]

Thank you for your responses. On reflection, I think my problem may be simply a matter of perspective. I know that there is no point of view outside the expanding universe (finite, but unbounded), despite the many diagrams illustrating such a perspective. That is there was no "dimensionless void" into which the cosmological inflation expanded, yet doesn't the term "expansion" imply some kind of potential/environment for growth? I was inquiring as to what models may have described such an area, and wondering if the uncertainty principle applied there. Great forum by the way. Thank you.

 

[94JZA80]

i don't think there exist any "evolution of the universe" models that attempt to define or describe an environment into which the universe expended over time...if there are, i don't know how seriously regarded these models are in the scientific community. i may be wrong though, and such models may be out there...i'm just unaware of them if they do exist.

also, i don't think there is such a thing as a "dimensionless void." by definition, a void is an empty space, or a space completely absent of matter and/or energy. the only dimensionless entity in our universe would be a point. and i think the simplest definition of a void would be an empty space between two points. in this case, the simplest "void" would be the absence of a line (or infinite set of points) between two endpoints. in 2 dimensions, a void would a surface (another infinite set of points) absent of any matter/energy, contained by 2 or more lines (you might be thinking that it takes at least 3 lines to constitute a "closed" area, but think outside of Euclidean geometry, i.e. think curved surfaces). in 3 dimensions, a void would be a volume absent of any matter/energy, contained by 2 or more surfaces. what I'm getting at here is that a void implies dimensions, and is not dimensionless.

finally, it would be impossible to tell if the uncertainty principle applies in such a void if it existed b/c a void is by definition empty of matter/energy. there would be no particles' positions or measure, and no particles' momentums to be uncertain about, or vice versa.

 

[bapowell]

I was inquiring as to what models may have described such an area, and wondering if the uncertainty principle applied there. Great forum by the way. Thank you.

By appealing to differential geometry, it is known that surfaces possesses certain properties (like curvature) independent of any embedding. For example, take the 2D surface of a sphere embedded in 3D space. We can readily visualize this manifold as the surface of a ball. Interestingly, the curvature of a sphere of radius r (K = 1/r^2) is independent of this embedding (i.e. does not depend on the nature of the higher-dimensional space). In fact, the embedding is not even necessary -- the curvature is intrinsic to the surface! (The 3D embedding space for the case of the ball helps us visualize this curvature, but it's there even in 2D space). Cosmological models are based on the differential manifolds of general relativity, and so there is no embedding in cosmology either. This means that cosmological models don't consider anything outside the universe -- the spacetime manifold representing the universe is the whole of the physical reality described by the theory.

 

[94JZA80]

In fact, the embedding is not even necessary -- the curvature is intrinsic to the surface!.

is this statement evidenced by the fact that the sum of the interior angles of the triangle formed by the Prime Meridian, the 90° line of longitude, and the equator = 270° (as opposed to 180° on a truly flat surface)?

TIA,
Eric

 

[bapowell]

is this statement evidenced by the fact that the sum of the interior angles of the triangle formed by the Prime Meridian, the 90° line of longitude, and the equator = 270° (as opposed to 180° on a truly flat surface)?

TIA,
Eric

Right. In particular, that you can make this determination by measuring the surface itself, irrespective of the space the Earth happens to be floating in.