Interesting, if it holds up. One of the big contradictions between quantum mechanics and general relativity is that the predictions for vacuum energy in the former are far greater than the values observed in the universe’s expansion (a small cosmological constant does a better job). If I get this correctly, this UBC PhD student takes the QM prediction seriously, but shows that the various contributions of vacuum energy are very chaotic (inhomogeneous is how he puts it) and tend to cancel out (phase differences?) except for a small positive remainder. Perhaps someone can state it a better form than I.

The published form is behind the usual scientific journal paywall, but the preprint can be found on ArXiv: https://arxiv.org/abs/1703.00543. (Unfortunately I lack the maths to really follow the paper.)

I certainly can’t follow all the math either, but as far as I can, it doesn’t actually work like that. In the typical model with constant vacuum energy, the scale of space – more or less their a_{t} – grows or shrinks based on field density, and there you would ask how close things come to cancelling.

What they get is entirely different. In their chaotic spacetime, a_{t} ends up following a sort of spring equation around zero. So the expansion and contraction actually do cancel, with each region alternately exploding and collapsing through an instantaneous singularity as it oscillates. It’s just supposed to be on a timescale where normal particles only see an average distance, and so still interact as if they were in normal (Minkowski) spacetime.

Then growth isn’t a question of residual expansion but of increasing amplitude. That has to do with cut-off frequencies, which I don’t really follow; but it seems something like the Casimir effect, where the vacuum field pushes on plates because certain frequencies don’t fit between them. Here everything is stable when the cut-offs approach infinity, but for lower ones there is resonance and the oscillations swing wider and wider, gently pushing our universe apart.

It at least sounds like an interesting idea to a non-physicist like me. Thanks for sharing it!

I was thinking of the Casimir effect myself - that I understand (to the extent that someone without the maths can…). My understanding of the Casimir effect was that the distance between plates precludes classes of virtual particles of longer wavelength than that distance (as you say, they don’t fit), leading to an imbalance of forces acting on the inner and outer faces of the plates.

That led me to think (rightly or wrongly) in terms of virtual particles as waves, with local occurrences at times reinforcing each other, at others cancelling each other, and everything in between, at the level of Planck time, with a resultant average field density leading to gradually accelerating expansion due to the resonance at lower frequencies/longer wavelengths. I’m guessing that an infinite cutoff without the resonance would probably lead to a static situation with regards to vacuum energy (not necessarily a static universe, you understand, but one not subject to accelerating expansion).

In this regard, it sort of sounds like an inverse Casimir effect. I frankly don’t understand the whys and wherefores of the low frequency resonance. Any ideas?