Editing Faster-than-light (section)

===Superfluid theories of physical vacuum===
{{Main|Superfluid vacuum theory}}

In this approach, the physical [[vacuum]] is viewed as a quantum [[superfluid]] which is essentially non-relativistic, whereas [[Lorentz symmetry]] is not an exact symmetry of nature but rather the approximate description valid only for the small fluctuations of the superfluid background.<ref name="volovik03">{{cite journal |last1=Volovik |first1=G. E. |year=2003 |title=The Universe in a helium droplet |journal=International Series of Monographs on Physics |volume=117 |pages=1–507}}</ref> Within the framework of the approach, a theory was proposed in which the physical vacuum is conjectured to be a [[Bose–Einstein condensate|quantum Bose liquid]] whose ground-state [[wave function|wavefunction]] is described by the [[logarithmic Schrödinger equation]]. It was shown that the [[general relativity|relativistic gravitational interaction]] arises as the small-amplitude [[collective excitation]] mode<ref>{{cite journal |title=Spontaneous symmetry breaking and mass generation as built-in phenomena in logarithmic nonlinear quantum theory |last1=Zloshchastiev |first1=Konstantin G. |year=2011 |doi=10.5506/APhysPolB.42.261 |journal=Acta Physica Polonica B |volume=42 |issue=2 |pages=261–292 |arxiv=0912.4139 |bibcode= 2011AcPPB..42..261Z|s2cid=118152708 }}</ref> whereas relativistic [[elementary particle]]s can be described by the [[quasiparticle|particle-like modes]] in the limit of low momenta.<ref>{{cite journal |arxiv=1108.0847 |bibcode=2011JPhB...44s5303A |doi=10.1088/0953-4075/44/19/195303 |title=Quantum Bose liquids with logarithmic nonlinearity: Self-sustainability and emergence of spatial extent |year=2011 |last1=Avdeenkov |first1=Alexander V. |last2=Zloshchastiev |first2=Konstantin G. |journal=Journal of Physics B: Atomic, Molecular and Optical Physics |volume=44 |issue=19 |page=195303|s2cid=119248001 }}</ref> The important fact is that at very high velocities the behavior of the particle-like modes becomes distinct from the [[theory of relativity|relativistic]] one – they can reach the [[speed of light#Upper limit on speeds|speed of light limit]] at finite energy; also, faster-than-light propagation is possible without requiring moving objects to have [[imaginary mass]].<ref>{{cite journal |arxiv=0906.4282 |bibcode=2010AIPC.1206..112Z |doi=10.1063/1.3292518 |title=Logarithmic nonlinearity in theories of quantum gravity: Origin of time and observational consequences |journal=American Institute of Physics Conference Series |volume=1206 |pages=288–297 |series=AIP Conference Proceedings |year=2010 |last1=Zloshchastiev |first1=Konstantin G. |last2=Chakrabarti |first2=Sandip K. |last3=Zhuk |first3=Alexander I. |last4=Bisnovatyi-Kogan |first4=Gennady S.}}</ref><ref>{{cite journal |arxiv=1003.0657 |bibcode=2011PhLA..375.2305Z |doi=10.1016/j.physleta.2011.05.012 |title=Vacuum Cherenkov effect in logarithmic nonlinear quantum theory |year=2011 |last1=Zloshchastiev |first1=Konstantin G. |journal=Physics Letters A |volume=375 |issue=24 |pages=2305–2308|s2cid=118152360 }}</ref>