Upon the initial cosmological singularity

[Loren Booda]

What perspective can one take concerning the origin of the universe in the big bang model? Can a collapsed observer occupy the singularity itself, or is there a higher dimensional "superspace" (John Archibald Wheeler) one shares apart from it? Might an observer possesses properties beyond those of ordinary space-time, to enable cosmogony outside the confines of a point?

 

[Garth]

What perspective can one take concerning the origin of the universe in the big bang model? Can a collapsed observer occupy the singularity itself, or is there a higher dimensional "superspace" (John Archibald Wheeler) one shares apart from it? Might an observer possesses properties beyond those of ordinary space-time, to enable cosmogony outside the confines of a point?

There once was a man who said,
“God
Must think it exceedingly odd
If He finds that this tree
Continues to be
When there’s no one about in the Quad.”

“Dear Sir:
Your astonishment’s odd:
I am always about in the Quad
And that’s why the tree
Will continue to be,
Since observed by,
Yours faithfully,
God.”
“God in the Quad”—a précis of the thinking of Bishop George Berkeley (Irish Philosopher 1685-1753) by Ronald Knox.

(I know this might be moved to the philosophy section - but Berkeley's thinking that 'objective existence is dependent on an observer' is pertinent to the QM cosmological question.)

Garth

 

[Loren Booda]

Give this thread another try; I think you'll find it worthwhile. Please review the initial post.

How do you model yourself: inside or outside the primordial point whence time's arrow derived its dawn and direction?

 

[selfAdjoint]

Loren, I am not at all sure the initial singularity is really there, in a suffuciient sense to support philosophical argument. Various approaches to quantum cosmology seem to predict no singularity and some kind of bounce, perhaps a pre-big-bang existence of some sort. And Hawking famously asserted his no-boundary condition, which looks at a mere "cooordinate singulatiry (like what happens to longitude at the poles, no real geometry change there, but the coordinate system blows up. There's a topological theorem that any coordinate system on a sphere has to blow up somewhere).

But if we want to assume a big-bang cosmology for purposes of argument then I would say that within such assumption it is wrong (breaks covariance) to think about the singularity apart from the whole cosmological manifold. In other words it's the whole existence and shape of spacetime, with causality acting within it, that you have to account for and describe, not some mere pointy end of it. This I believe is what Wheeler was getting at, the observer sees it all. And I don't think it requires an embedding in higher space to do this. I know it's hard for non mathematicians to understand this, but the universe can be observed in and of itself, with its self-defining geometry, without any higher dimensional perspective. In fact this is one of the exciting things about Riemannian and pseudo-Riemannian geometry, that they do self-define themselves; from the metric you can get the connection or you can use the connection in the tangent bundle to define the metric, either way it's without any reference to stuff outside the manifold.

 

[Loren Booda]

selfAdjoint,

Your response deserves much study. It certainly shows me how far removed from physics I have become. One observation that I might surmise from the cosmological spacetime manifold is the constraint that both it and its curvature must be continuous.

What do you think of a big bang singularity governing direction, not only spacetime origin, of time?

 

[selfAdjoint]

What do you think of a big bang singularity governing direction, not only spacetime origin, of time?

I personally would rather say that the expansion, that is the four-dimensional shape of the spacetime manifold, determines both the direction of time (i.e. the direction in which it gets bigger) and the singularity, as a distinguished point on the manifold.