Vacuum Cherenkov effect in logarithmic nonlinear quantum theory
Konstantin G. Zloshchastiev
Abstract and summary · read the original at the source
In one page
Konstantin Zloshchastiev takes the superfluid picture of the vacuum seriously and asks a mechanical question about it: if empty space is a medium, what happens when a particle outruns light inside that medium? In water or glass the answer is the Cherenkov effect, the cone of blue light trailing a fast particle. In Zloshchastiev’s vacuum — described by the logarithmic nonlinear wave equation that also describes a Bose-Einstein condensate — the medium has its own refractive index and its own natural frequency, set by the vacuum’s proper energy scale, so the same cone can form in empty space. He works out what an observer would actually see: the opening angle of the cone, the duration of the flash, which is finite only because the vacuum disperses, the spectrum, and the energy carried off. The yield grows as the square of the vacuum energy scale, and that same scale supplies a natural ultraviolet cutoff rather than one inserted by hand.
Why it matters hereChapter 5 treats the vacuum as a quantum fluid, and this paper shows what follows the moment you take that literally: a fluid has a refractive index, a dispersion curve and a natural frequency, so it can be shocked, and the shock radiates. Chapter 2 gains a concrete observational handle on the vacuum’s energy scale, because the radiated power depends on it as a square. The theory underneath is on this site at /library/stm-094d44f853, and the same author’s superfluid-vacuum cosmology at /library/stm-4a4bcf1126.
What it claims
01The physical vacuum is treated as a non-removable background Bose liquid or Bose-Einstein condensate, in which Lorentz symmetry is an emergent low-energy phenomenon and the Standard-Model particles and gravity are small fluctuations of the background superfluid — the logarithmic nonlinearity being the one extension of quantum mechanics that keeps both the additivity of energy for uncorrelated systems and the Planck relation for stationary states.Section 1, Introduction; the two conserved properties argued in the paragraph before Equation 2
Published and peer-reviewed02The vacuum carries an effective refractive index of Cauchy form, with a constant of refraction and a natural vacuum frequency equal to the vacuum’s proper energy divided by the reduced Planck constant, so both particles and electromagnetic waves propagating through it are affected — and the speed-of-light barrier becomes finite rather than infinite, reachable by a particle of high but finite energy.Section 2, Deformed dispersion relations; Equations 1, 2 and 3
Published and peer-reviewed03A charge moving faster than light in that medium emits a Cherenkov cone whose angle is given by the cosine equal to one over the product of the particle’s reduced speed and the vacuum refractive index, plus a small correction that splits into two contributions — one because the Cherenkov wave feels the vacuum and one because the emitting particle does.Section 3, Cherenkov cone angle; Equations 5 to 7
Published and peer-reviewed04Because the vacuum is dispersive rather than a perfect medium, the shock front has thickness and the flash an observer tuned to a frequency band would see has finite duration, computed here in terms of the vacuum frequency, the distance from the particle’s track and the two band edges.Section 4, Flash duration; Equation 8
Published and peer-reviewed05The radiation yield follows a Frank-Tamm spectral distribution whose ultraviolet cutoff is not postulated but supplied by the theory itself, at the vacuum energy scale, and the energy radiated per unit path is proportional to the square of that scale — 3 times ten to the tenth, times the constant of refraction, times the square of the charge number, times the square of the vacuum energy, in GeV per centimetre. The author’s reading is that such shocks would be a very efficient, fast and powerful way of draining and releasing energy, the vacuum being a fluid of minimum dissipation.Section 5, Energy and spectral distribution; Equations 11 and 12; concluding paragraph of Section 6
Published and peer-reviewed06The vacuum energy scale is not yet known: the author brackets it between ten thousand GeV, from current non-observability data, and the Planck energy of ten to the nineteenth GeV, which puts the radiated power somewhere in a very wide band, and names the places to look — supernovae and hypernovae, active galactic nuclei, gamma-ray bursts and radio objects with continuous optical spectra. He also notes that the results should hold for any Lorentz-invariance-violating theory that describes the vacuum as an effectively continuous medium in the long-wavelength approximation.Section 5, the bounds and the estimate at Equation 13; Section 7, Conclusion
What to watch
Read it · abstract
Abstract
We describe the radiation phenomena which can take place in the physical vacuum such as Cherenkov-type shock waves. Their macroscopical characteristics — cone angle, flash duration, radiation yield and spectral distribution — are computed. It turns out that the radiation yield is proportional to the square of the proper energy scale of the vacuum which serves also as the vacuum instability threshold and the natural ultraviolet cutoff. While the analysis is mainly based on the theory engaging the logarithmic nonlinear quantum wave equation, some of the obtained results must be valid for any Lorentz-invariance-violating theory describing the vacuum by (effectively) continuous medium in the long-wavelength approximation.
Konstantin G. Zloshchastiev, Department of Physics and Center for Theoretical Physics, University of the Witwatersrand, Johannesburg. Published as Physics Letters A 375 (2011) 2305–2308; preprint arXiv:1003.0657.
(Abstract only — see the rights note above for why the full text is not reproduced here. The complete Letter, with the derivations of the cone angle, the flash duration, the Frank-Tamm yield and the luminal boom wave, is at the source. The theory it builds on is on this site at /library/stm-094d44f853, and the author’s 2025 superfluid-vacuum cosmology at /library/stm-4a4bcf1126.)
The way in
https://doi.org/10.1016/j.physleta.2011.05.012LICENCE. Published as Physics Letters A 375 (2011) 2305–2308; Elsevier declares only its text-and-data-mining user licence for the record, and the preprint, arXiv:1003.0657v3 of 31 May 2011, carries the arXiv.org perpetual non-exclusive distribution licence. No Creative Commons statement appears in the text or on the arXiv record, so this page holds the summary, the claims and the author’s own abstract and sends the reader to the source. The claims below are read from the preprint text, written at the Department of Physics and Center for Theoretical Physics, University of the Witwatersrand, Johannesburg. The theory this paper builds on has its own sheet at /library/stm-094d44f853, and the author’s 2025 cosmology in the same framework is at /library/stm-4a4bcf1126.
How to cite it
Konstantin G. Zloshchastiev (2011) Vacuum Cherenkov effect in logarithmic nonlinear quantum theory. doi:10.1016/j.physleta.2011.05.012
Where it sits in the curriculum
The vacuum as a quantum fluidWhat the vacuum isThe unified picture