I've been trying to get a better grasp of the vacuum catastrophe problem, that is vacuum energy as calculated in QFT vs the observed value in cosmology differs by 120 orders of magnitude. The issue fundamentally arises from the fact that if we try to calculate the absolute value of the zero point energy of any quantum field the result is necessarily divergent (infinity) as we add all the possible modes of vibrations (frequencies) of the field, which are infinite. It is then speculated that there exist a cutoff frequency which would prevent adding infinite quantities, but to me it seems rather arbitrary this cutoff corresponds to the Planck lenght, which is simply a number where seemingly unphysical stuff happens when we cram two electrons too close together. Using this reasoning we get the wildly wrong (according to measurements) 10^110 value.

If we instead try to fit the measured value in the equations (from astronomical observations of the Hubble constant), we get a corresponding cut off lenght of around 1 mm.

Now this result has mostly been deemed unphysical as well, but for reasons that are not really convincing to me, like the cutoff corresponding to the natural quantization of spacetime can't be 1 mm, but it doesn't seem to be necessarily related to that. It could stem from a totally different property of fields. To my understanding this cutoff doesn't prevent lower wavelength vibrations, it just prevents them at the fundamental level of the field (unexcited fields).

I'd be glad if anyone could link or just explain this issue better, and why they think 1 mm cutoff is/is not a valid solution.

I tried looking this stuff up online, but i couldn't really find many papers that tackled this issue (explaining a possible 1 mm cutoff), and many of those i found were rather hard to digest.

Something I will link though is these two studies, that hopefully will make it more clear where I'm trying to point the discussion: one that refutes first low energies cutoffs, then tries to generalize to any possible cutoff, using the common explanation of the Casimir effect as stemming from a quantum vacuum effect. The second study elegantly explains how a quantum vacuum interpretation of this effect is not legitimate mathematically, hence invalidating many assumptions of the first paper.

This paper discusses why a cut off of any kind in vacuum energy would produce different effects from those observed in the Casimir experiment (IF vacuum energy is responsible for the effect)


This paper explains why the Casimir effect is better understood with Van Der Waals forces rather than vacuum fluctuations:


  • $\begingroup$ @Chiral_Anomaly Yes I believe my terminology was a bit iffy. It is my understanding that the paper eliminated contributions from shorter lenght scales than 1 mm (hence also ruling out Lc>1mm) based on forces measured in the Casimir effect, of course assuming the effect is caused by vacuum modes suppressions, which the second paper goes in detail why this might not be entirely correct. $\endgroup$
    – Leureka
    Aug 27 at 20:15

I'm not an expert, but...

I think that the second paper that you linked is correct, but it doesn't solve the problem in the first (also correct) paper, because the same considerations that apply to electromagnetism also apply to gravity.

In other words, it is more correct to treat the Casimir force as a loop correction to the electromagnetic interaction between the plates, but it's also more correct to treat the "vacuum catastrophe" as a loop correction to gravitional interactions between objects (since one can't observe the vacuum as such, only, e.g., bending of light). Gravity is universal, so if loops above the cutoff affect electromagnetic interactions (which experimentally seems to be the case) then it's not clear how you could prevent them from also affecting gravity.

  • $\begingroup$ I'm not sure? What does this have to do with dark energy and the expansion of the universe? $\endgroup$
    – Leureka
    Aug 28 at 8:31
  • $\begingroup$ I linked the first paper just because it's one of the few discussing the 1 mm problem, I didn't really want to focus on the study of attraction between plates. How can the vacuum energy density stem from corrections to gravitational interactions? ED is just the sum of the base energy of all quantum fields. Not to mention gravity is not treated as a quantum field. $\endgroup$
    – Leureka
    Aug 28 at 8:40

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