Historical research guide · 0745 · 2011
Vacuum Cherenkov effect in logarithmic nonlinear quantum theory
Konstantin G. Zloshchastiev
In one minute
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.
Connection
Chapter 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.
From the source
The 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
The 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
A 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
Because 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
The 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
The 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
The way in
https://doi.org/10.1016/j.physleta.2011.05.012How to cite it
Konstantin G. Zloshchastiev (2011) Vacuum Cherenkov effect in logarithmic nonlinear quantum theory doi:10.1016/j.physleta.2011.05.012