Re: Universe topology

"Michael S." <[EMAIL PROTECTED]> writes:

> What does it mean when people speak of the universe's topology? 

They are speaking of the possiblity that distant points within the universe
may be "indentified" in some regular fashion. For example, the universe
might have the topology of a "3-torus," wherein points on opposite faces 
of a hexahedral "unit cell" would be considered "identical." This would be
somewhat analogous to the situation you would be in if attempting to leave
your house by the front door simply brought you right back in through the
back door, trying to climb out onto the roof from the attic simply braought
you back in via the basement, etc. Alternatively, one might identify two of
the faces of the "unit cell" mapped via a 180 degree twist; this would imply 
that the Universe is a three-dimensional analog of a moebius strip or Klein
bottle. Other possible "unit cells" and identifications of faces would lead
to still different topologies.

In the most general case, one might imagine identifying points with each
other in an essentially arbitrary (but smooth) fashion, in which case the
Universe would be riddled with "wormholes" --- a so-called "spacetime foam."

It is still an open question whether it is possible for the topology of the
Universe to change with time, or whether its topology was "chiseled in stone"
at the beginning of Time.


> Does this topology imply any type of large scale variation in the
> universe's fundamental physical constants?

No. That is an entirely unrelated (and possibly undefinable) question.
(Undefinable, because it makes no sense to talk about dimensionful
quantities "varying" --- it only makes sense to talk about variations 
of dimensionless ratios.)  Whether or not the "physical constants" might
vary with position or time has nothing whatsoever to do with questions
of what sort of nontrivial topology the Universe might or might not have.


-- Gordon D. Pusch   

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