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{{Beyond the Standard Model|expanded=Theories}}

'''Superfluid vacuum theory''' (SVT), sometimes known as the '''[[Bose-Einstein condensate|BEC]] vacuum theory''', is an approach in [[theoretical physics]] and [[quantum mechanics]] where the fundamental physical [[vacuum]] (non-removable background) is viewed as [[superfluid]] or as a [[Bose-Einstein condensate]] (BEC).

The microscopic structure of this physical vacuum is currently unknown and is a subject of intensive studies in SVT. An ultimate goal of this approach is to develop [[scientific model]]s that unify quantum mechanics (describing three of the four known [[fundamental interaction]]s) with [[gravity]], making SVT a candidate for the theory of [[quantum gravity]] and describing all known interactions in the [[Universe]], at both microscopic and astronomic scales, as different manifestations of the same entity, superfluid vacuum.

==History==
The concept of a [[luminiferous aether]] as a medium sustaining [[electromagnetic waves]] was discarded after the advent of the [[Special relativity|special theory of relativity]].
The [[Luminiferous aether|aether]], as conceived in classical physics leads to several contradictions; in particular, aether having a definite velocity at each
space-time point will exhibit a preferred direction. This conflicts with the
relativistic requirement that all directions within a light cone are
equivalent.
However, as early as in 1951 [[P.A.M. Dirac]] published two papers where he pointed out that we should take into account quantum fluctuations in the flow of the aether.<ref name="dir51">{{cite journal |last1=Dirac |first1=P.A.M. |last2= |first2= |date=24 November 1951 |title=Is there an Æther? |journal=Letters to Nature |volume=168 |issue=4282 |pages=906–907 |publisher=Nature |doi=10.1038/168906a0 |url=http://www.nature.com/nature/journal/v168/n4282/abs/168906a0.html |accessdate=16 October 2012|bibcode = 1951Natur.168..906D }}</ref><ref name="dir52">{{cite journal|last=Dirac|first=P. A. M.|title=Is there an Æther?|journal=Nature|date=26 April 1952|volume=169|issue=4304|pages=702–702|doi=10.1038/169702b0}}</ref>
His arguments involve
the application of the [[uncertainty principle]] to the velocity of aether at any
space-time point, implying that the velocity will not be a well-defined
quantity. In fact, it will be distributed over various possible values. At best,
one could represent the aether by a wave function representing the perfect
[[vacuum state]] for which all aether velocities are equally probable.
These works can be regarded as the birth point of the theory.

Inspired by the Dirac ideas, K.P. Sinha, C. Sivaram and E.C.G. Sudarshan published in 1975 a series of papers that suggested
a new model for the aether according to which it is a superfluid
state of fermion and anti-fermion pairs, describable by a macroscopic [[wave function]].<ref>K.P. Sinha, C. Sivaram, E.C.G. Sudarshan, Found. Phys. 6, 65 (1976).</ref><ref>K.P. Sinha, C. Sivaram, E.C.G. Sudarshan, Found. Phys. 6, 717 (1976).</ref><ref>K.P. Sinha and E.C.G. Sudarshan, Found. Phys. 8, 823 (1978).</ref>
They noted that particle-like small fluctuations of superfluid background obey the [[Lorentz symmetry]], even if the superfluid itself is non-relativistic.
Nevertheless, they decided to treat the superfluid as the [[Theory of relativity|relativistic]] matter - by putting it into the stress-energy tensor of the [[Einstein field equations]].
This did not allow them to describe the [[General relativity|relativistic gravity]] as a small fluctuation of the superfluid vacuum, as subsequent authors have noted.

As an alternative to the better known string theories, a very different theory by [[Friedwardt Winterberg]] proposes instead, that the vacuum is a kind of superfluid plasma compound of positive and negative Planck masses, called a Planck mass plasma.<ref>{{cite journal|last=Winterberg|first=Friedwardt|title=Substratum Approach to a Unified Theory of Elementary Particles|journal=Z.f. Naturforsch.-Physical Sciences.|year=1988|volume=43a}}</ref><ref>{{cite journal|last=Winterberg|first=Friedwardt|title=Planck Mass Plasma Vacuum Conjecture|journal=Z. Naturforsch|year=2003|volume=58a|pages=231-267}}</ref>{{cn|date=November 2013}}

Since then, several theories have been proposed within the SVT framework.
They share the main idea{{which|date=December 2013}} but differ in how the structure and properties of the background [[superfluid]] must look like.
In absence of observational data which would rule out some of them, these theories are being pursued independently.

==Relation to other concepts and theories==
===Lorentz and Galilean symmetries===
According to the approach, the background superfluid is assumed to be essentially non-relativistic whereas the [[Lorentz symmetry]] is not an exact symmetry of Nature but rather the approximate description valid only for small fluctuations.
An observer who resides inside such vacuum and is capable of creating or measuring the small fluctuations would observe them as [[Theory of relativity|relativistic]] objects - unless their [[energy]] and [[momentum]] are sufficiently high to make the [[Lorentz violation|Lorentz-breaking]] corrections detectable.<ref name="volovik03">G. E. Volovik, ''The Universe in a helium droplet'', Int. Ser. Monogr. Phys. '''117''' (2003) 1-507.</ref>
If the energies and momenta are below the excitation threshold then the [[superfluid]] background behaves like the [[ideal fluid]], therefore, the [[Michelson-Morley]]-type experiments would observe no [[drag force]] from such aether.<ref name=dir51/><ref name=dir52/>

Further, in the [[theory of relativity]] the [[Galilean symmetry]] (pertinent to our [[macroscopic]] non-relativistic world) arises as the approximate one -
when particles' velocities are small compared to [[speed of light]] in vacuum.
In SVT one does not need to go through [[Lorentz symmetry]] to obtain
the Galilean one - the dispersion relations of most non-relativistic
superfluids are known to obey the non-relativistic behavior
at large momenta.<ref>N.N. Bogoliubov, Izv. Acad. Nauk USSR 11, 77 (1947).</ref><ref>N.N. Bogoliubov, J. Phys. 11, 23 (1947)</ref><ref>V.L. Ginzburg, L.D. Landau, Zh. Eksp. Teor. Fiz. 20, 1064 (1950).</ref>

To summarize, the fluctuations of vacuum superfluid behave like relativistic objects at "small"<ref group=nb>The term "small" refers here to the linearized limit, in practice the values of these momenta may not be small at all.</ref> momenta (a.k.a. the "[[phononic limit]]")
:<math>E^2 \propto |\vec p|^2</math>
and like non-relativistic ones
:<math>E \propto |\vec p|^2</math>
at large momenta.
The yet unknown nontrivial physics is believed to be located somewhere between these two regimes.

===Relativistic quantum field theory===
In the relativistic [[quantum field theory]] the physical vacuum is also assumed to be some sort of non-trivial medium to which one can associate [[Vacuum energy|certain energy]].
This is because the concept of absolutely empty space (or "mathematical vacuum") contradicts to the postulates of [[quantum mechanics]].
According to QFT, even in absence of real particles the background is always filled by pairs of creating and annihilating [[virtual particles]].
However, a direct attempt to describe such medium leads to the so-called [[ultraviolet divergences]].
In some QFT models, such as quantum electrodynamics, these problems can be "solved" using the [[renormalization]] technique, namely, replacing the diverging physical values by their experimentally measured values.
In other theories, such as the [[Canonical quantum gravity|quantum general relativity]], this trick [[Nonrenormalizable|does not work]], and reliable perturbation theory cannot be constructed.

According to SVT, this is because in the high-energy ("ultraviolet") regime the [[Lorentz symmetry]] starts failing so dependent theories cannot be regarded valid for all scales of energies and momenta.
Correspondingly,
while the Lorentz-symmetric quantum field models are obviously a good approximation below the vacuum-energy threshold, in its close vicinity the
relativistic description becomes more
and more "effective" and less and less natural since
one will need to adjust the expressions for the [[Covariance|covariant]] field-theoretical actions by hand.

===Curved space-time===
According to [[general relativity]], the gravitational interaction is described in terms of [[space-time]] [[curvature]] using the mathematical formalism of [[Riemannian geometry]].
This was supported by numerous experiments and observations in the regime of low energies. However, the attempts to quantize [[general relativity]] led to various [[Quantum_gravity#Nonrenormalizability_of_gravity|severe problems]], therefore, the microscopic structure of gravity is still ill-defined.
There may be a fundamental reason for this--the [[Degrees of freedom (physics and chemistry)|degrees of freedom]] of [[general relativity]] are based on
may be only approximate and [[Effective field theory|effective]]. The question of whether general relativity is an effective theory has been raised for a long
time.<ref>A.D. Sakharov, Sov. Phys. Dokl. 12, 1040 (1968). This paper was reprinted in Gen. Rel. Grav. 32, 365 (2000) and commented in: M. Visser, Mod. Phys. Lett. A 17, 977 (2002).</ref>

According to SVT, the curved space-time arises as the small-amplitude [[collective excitation]] mode of the non-relativistic background condensate.<ref name=volovik03/><ref name="zlo0912">K. G. Zloshchastiev, ''Spontaneous symmetry breaking and mass generation as built-in phenomena in logarithmic nonlinear quantum theory'', Acta Phys. Polon. B '''42''' (2011) 261-292 [http://arxiv.org/abs/0912.4139 ArXiv:0912.4139].</ref>
The mathematical description of this is similar to
[[Acoustic metric|fluid-gravity analogy]] which is being used also in the [[analog gravity]] models.<ref>M. Novello, M. Visser, G. Volovik, ''Artificial Black Holes'', World Scientific, River Edge, USA, 2002, p391.</ref>
Thus, [[General relativity|relativistic gravity]] is essentially a long-wavelength theory of the collective modes whose amplitude is small compared to the background one.
Outside this requirement the curved-space description of gravity in terms of the [[Riemannian geometry]] becomes incomplete or ill-defined.

===Cosmological constant===
The notion of the [[cosmological constant]] makes sense
in a relativistic theory only, therefore, within the SVT framework this constant can refer at most to the energy of small fluctuations
of the vacuum above a background value but not to the energy of vacuum
itself.<ref>G.E. Volovik, Int. J. Mod. Phys. D15, 1987 (2006) [http://arxiv.org/abs/gr-qc/0604062 ArXiv: gr-qc/0604062].</ref> Thus, in SVT this constant does not have
any fundamental physical meaning and the related problems, such as the [[vacuum catastrophe]], simply do not
occur in first place.

===Gravitational waves and gravitons===
According to [[general relativity]], the conventional [[gravitational wave]] is:
# the small fluctuation of curved spacetime which
# has been separated from its source and propagates independently.

Theory of superfluid vacuum brings into question that the relativistic object possessing both of these properties may exist in Nature.<ref name=zlo0912/>
Indeed, according to the approach, the curved spacetime itself is the small [[collective excitation]] of the superfluid background, therefore,
the property (1) means that the [[graviton]] would be in fact the "small fluctuation of the small fluctuation" which does not look like a physically robust concept
(as if somebody tried to introduce small fluctuations inside a [[phonon]], for instance).
As a result, it may be not just a coincidence that in [[general relativity]] the gravitational field alone has no well-defined [[stress-energy tensor]],
only the [[Stress-energy-momentum pseudotensor|pseudotensor]] one.<ref name="LL">L.D. Landau and E.M. Lifshitz, ''The Classical Theory of Fields'', (1951), Pergamon Press, chapter 11.96.</ref>
Therefore, the property (2) cannot be completely justified in a theory with exact [[Lorentz symmetry]] which the general relativity is.
Though, SVT does not ''a priori'' forbid an existence of the non-localized [[wave]]-like excitations of the superfluid background
which might be responsible for the astrophysical phenomena
which are currently being [[Gravitational_wave#Astrophysics_and_gravitational_waves|attributed]] to gravitational waves, such as the [[Hulse-Taylor binary]]. However, such excitations cannot be correctly described within the framework of a fully [[Theory of relativity|relativistic]] theory.

===Mass generation and Higgs boson===
The [[Higgs boson]] is the spin-0 particle which has been introduced in the [[Electroweak interaction|electroweak theory]] to give the mass to the [[W and Z bosons|weak bosons]]. The origin of mass of the Higgs boson itself is not explained by the electroweak theory. Instead, this mass introduced as a free parameter by means of the [[Quartic interaction|Higgs potential]] which thus makes it yet another free parameter of the [[Standard Model]].<ref>V. A. Bednyakov, N. D. Giokaris and A. V. Bednyakov, Phys. Part. Nucl. '''39''' (2008) 13-36 [http://arxiv.org/abs/hep-ph/0703280 ArXiv:hep-ph/0703280].</ref> Within a framework of the [[Standard Model]] (or its extensions) the theoretical estimates of this parameter's value are possible only indirectly and results differ from each other significantly.<ref>B. Schrempp and M. Wimmer, Prog. Part. Nucl. Phys. '''37''' (1996) 1-90 [http://arxiv.org/abs/hep-ph/9606386 ArXiv:hep-ph/9606386].</ref> Thus, the usage of the [[Higgs boson]] (or any other elementary particle with predefined mass) alone is not the most fundamental solution of the [[mass]] generation problem but only its reformulation ''ad infinitum''.
Another known issue of the [[Glashow-Weinberg-Salam model]] is the wrong sign of mass term in the (unbroken) Higgs sector for
energies above the [[electroweak scale|symmetry-breaking scale]].<ref group=nb name="higgs">If one expands the [[Scalar_field_theory#.CF.864_theory|Higgs potential]] then the coefficient at the quadratic term appears to be [[negative number|negative]]. This coefficient has a physical meaning of [[Quartic interaction|squared mass]] of a scalar particle.</ref>

While SVT does not explicitly forbid the existence of the [[Electroweak symmetry breaking|electroweak Higgs particle]], it has its own idea of the fundamental mass generation mechanism - elementary particles acquire mass due to the interaction with the vacuum condensate, similarly to the gap generation mechanism in [[superconductor]]s or [[superfluid]]s.<ref name=zlo0912/><ref name="az2011">A. V. Avdeenkov and K. G. Zloshchastiev, ''Quantum Bose liquids with logarithmic nonlinearity: Self-sustainability and emergence of spatial extent'', J. Phys. B: At. Mol. Opt. Phys. '''44''' (2011) 195303. [http://arxiv.org/abs/1108.0847 ArXiv:1108.0847].</ref>
Although this idea is not entirely new,
one could recall the relativistic [[Coleman–Weinberg potential|Coleman-Weinberg approach]],<ref>S.R. Coleman and E.J. Weinberg, Phys. Rev. D7, 1888 (1973).</ref>
SVT gives the meaning to the symmetry-breaking relativistic [[scalar field]] as describing small fluctuations of background superfluid
which can be interpreted as an elementary particle only under certain conditions.<ref name="dz01">{{cite journal|author=V. Dzhunushaliev and K.G. Zloshchastiev|journal= Cent. Eur. J. Phys. |volume=11|pages= 325–335 |year=2013|arxiv=1204.6380|doi=10.2478/s11534-012-0159-z|title=Singularity-free model of electric charge in physical vacuum: Non-zero spatial extent and mass generation|issue=3|bibcode = 2013CEJPh..11..325D }}</ref>In general, one allows two scenarios to happen:
* Higgs boson exists: in this case SVT provides the mass generation mechanism which underlies the electroweak one and explains the origin of mass of the Higgs boson itself;
* Higgs boson does not exist: then the [[W and Z bosons|weak bosons]] acquire mass by directly interacting with the vacuum condensate.

Thus, the [[Higgs boson]], even if it exists, would be a by-product of the fundamental mass generation phenomenon rather than its cause.<ref name=dz01/>

Also, some versions of SVT favor a [[Logarithmic Schrödinger equation|wave equation based on the logarithmic potential]] rather than on the [[Quartic interaction|quartic]] one. The former potential has not only the Mexican-hat shape, necessary for the [[spontaneous symmetry breaking]], but also some [[Superfluid_vacuum#Logarithmic_BEC_vacuum_theory|other features]] which make it more suitable
for the vacuum's description.

==Logarithmic BEC vacuum theory==
In this model
the physical vacuum is conjectured to be strongly-correlated [[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 whereas relativistic [[elementary particles]] can be described by the [[Quasi-particle|particle-like modes]] in the limit of low energies and momenta.<ref name=az2011/>
The essential difference of this theory from others is that in the logarithmic superfluid the maximal velocity of fluctuations is constant in the leading (classical) order.
This allows to fully recover the relativity postulates in the "phononic" (linearized) limit.<ref name=zlo0912/>

The proposed theory has many observational consequences.
They are based on the fact that at high energies and momenta the behavior of the particle-like modes eventually 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.<ref>K. G. Zloshchastiev, ''Logarithmic nonlinearity in theories of quantum gravity: Origin of time and observational consequences'', Grav. Cosmol. '''16''' (2010) 288-297 [http://arxiv.org/abs/0906.4282 ArXiv:0906.4282].</ref>
Among other predicted effects is the [[superluminal]] propagation and vacuum [[Cherenkov radiation]].<ref>K. G. Zloshchastiev, ''Vacuum Cherenkov effect in logarithmic nonlinear quantum theory'', Phys. Lett. A '''375''' (2011) 2305-2308 [http://arxiv.org/abs/1003.0657 ArXiv:1003.0657].</ref>

Theory advocates the mass generation mechanism which is supposed to replace or alter the [[Electroweak symmetry breaking|electroweak Higgs]] one.
It was shown that masses of elementary particles can arise as a result of interaction with the superfluid vacuum, similarly to the gap generation mechanism in [[superconductor]]s.<ref name=zlo0912/><ref name=az2011/> For instance, the [[photon]] propagating in the average [[interstellar space|interstellar]] vacuum acquires a tiny mass which is estimated to be about 10<sup>−35</sup> [[electronvolt]].
One can also derive an effective potential for the Higgs sector which is different from the one used in the [[Glashow-Weinberg-Salam model]], yet it yields the mass generation and it is free of the imaginary-mass problem<ref group=nb name=higgs/> appearing in the [[Quartic interaction|conventional Higgs potential]].<ref name=dz01/>

==See also==
*[[Analog gravity]]
*[[Acoustic metric]]
*[[Bose-Einstein condensate]]
*[[Casimir vacuum]]
*[[Hawking radiation]]
*[[Induced gravity]]
*[[Planck scale]]
*[[Planck units]]
*[[Hořava–Lifshitz gravity]]
*[[Quantum gravity]]
*[[Quantum realm]]
*[[Macrocosm and microcosm]]
*[[Sonic black hole]]
*[[Vacuum energy]]

==Notes==
{{Reflist|group=nb}}

==References==
{{reflist}}

{{Theories of gravitation}}
{{quantum gravity}}

{{DEFAULTSORT:Superfluid vacuum theory}}
[[Category:Theoretical physics]]
[[Category:Physics beyond the Standard Model]]

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