Is the Multiverse of Cantor Dust a Viable Solution to Olbers' Paradox?

[slatts]

At my Wikipedia-minus-math level of understanding, the problem with any resolution of "Olbers' Paradox" through a fractal distribution (such as the "Cantor set" depicted in the Wikipedia article of that name) of stars or star clusters, rather than the alternative of a beginning of our multiverse (or universe) in time, is such a distribution's fractal dimension of approximately 0.6, rather than the dimension of 2 or more that is reportedly favored by most cosmologists. It seems to me that the favored dimension implies some preferred size for the proportion of the multiverse taken by our observable region, which definitely does not seem to be supported by observation.

If this lack of support does leave such an alternative to any beginning open, a secondary problem might be the improbability of such fractally linear alignments of star clusters. (I'm assuming that they'd be even larger than the clusters of galaxies whose relations would reflect universal increases in the amounts of space between them.) In that case, might the pressure or other averaged effects of gravitational or other radiation on the evolution of such clusters,or of such components of them as the binary systems accounting for a large proportion of observed stars, perhaps account for such linear arrangements of star clusters over the periods of time during which they would form across larger regions of our local universe than the observable one, or would some anthropomorphic factor have to account for them?

 

[Chalnoth]

The expansion of the universe handles Olber's Paradox quite nicely: stars that are further away are redshifted, and so can never contribute as much to the temperature of the night sky as nearby stars.

 

[slatts]

Yes, I had thought so too, but the Wikipedia article "Homogeneity (physics)" claims that the redshifting is not sufficient to explain the weakening of the light that leaves the night sky dark, and claims that many "cosmologists think that the fact that the Universe is finite in time, that is that the Universe has not been around forever, is the solution to the paradox." (Although a request for its writer's citation for that claim has been outstanding since at least December, they have not otherwise been challenged for any lack of expertise.)

I can see how a beginning of everything would certainly resolve the paradox, but, aside from the fact that it would conflict with Ali and Das' recent paper "Cosmology from quantum potential" (whose math is way beyond me) reformulating the relativistic Raychaudhuri equation in quantum mechanical terms to arrive at "an infinite age of our universe", I can't quite grasp how spacetime would begin, except through one or more agents whose own beginnings could only be explained through an infinite regression. It seems more reasonable to assume some starting point for the examination of reality on a scale marking a limit beyond which it could be seen as impossible even with complete use of the potential in the means currently observable by us, but, since physicists at every level of competence and influence continue to use phrases like "space began" or "time began" rather than "currently divisible space began" or "currently divisible time began", I'm not sure whether I'm missing something almost mystically deep, or have become just too satiated with dramatic exaggerations from news and fiction to appreciate their inclusion in science.

I guess what I'm asking is, what is the principle that would identify a cutoff point in the finest scales of space and time beyond which we're going to have to leave things until we've expanded our observable region while maintaining its level of definition? Or maybe, to make the question more practical, would adding "currently divisible" immediately ahead of "space" or "time" or "universe" give the verbiage more of a resemblance to its numerical descriptions, when the context would otherwise leave it meaning "all of space" and/or "all of time"?

 

[Chalnoth]

In the end, it doesn't really matter. We have observed the very early universe, before there were any stars. We have observed the somewhat later universe, when the first galaxies were formed. We have a reasonably-clear picture of the entire span of time that is relevant for avoiding Olber's Paradox.

 

[slatts]

Well, I think you've understood that my real problem wasn't with Olbers' Paradox--it was with the notion of space (and, perhaps, time) having any origin. I'd looked at some popularizations of the paper by Ali & Das, but (I'm sorry to admit) hadn't read the two threads PF has already had about it. When I finally read 1-1/2 of them, just now, I was surprised to see that you'd addressed exactly that concern in an exchange with Bapowell on Feb. 11, by suggesting two ways around the phantasmagoric singularity: A quantum fluctuation from an empty universe with a small but positive cosmological constant, or a quantum tunneling event from a previous false-vacuum state. (Maybe you'd remembered that, in yet another thread, I'd asked PeterDonis whether Vilenkin's quantum tunneling from nothing could have actually been a tunneling from the past; if so, I'm flattered.) Please correct me if you think I'm going off the beam in associating a "previous false-vacuum state" tentatively with the pre-inflationary piece of what A & D are considering to be the universe's infinite age. Thanks very much for reducing my exasperation with half-baked uses of language by people who (fortunately) think a LOT better in mathematics than I do.