View source for Physics:Superfluid vacuum theory

{{Short description|Theory of fundamental physics}}
{{Beyond the Standard Model|expanded=Theories}}
'''Superfluid vacuum theory''' ('''SVT'''), sometimes known as the '''BEC vacuum theory''', is an approach in [[Physics:Theoretical physics|theoretical physics]] and [[Physics:Quantum mechanics|quantum mechanics]] where the fundamental physical [[Physics:Vacuum|vacuum]] (non-removable background) is considered as a superfluid or as a [[Physics:Bose–Einstein condensate|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 research is to develop scientific models that unify quantum mechanics (which describes three of the four known [[Physics:Fundamental interaction|fundamental interaction]]s) with [[Physics:Gravity|gravity]], making SVT a candidate for the theory of [[Physics:Quantum gravity|quantum gravity]] and describes 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 [[Physics:Luminiferous aether|luminiferous aether]] as a medium sustaining [[Physics:Electromagnetic waves|electromagnetic waves]] was discarded after the advent of the [[Physics:Special relativity|special theory of relativity]], as the presence of the concept alongside special relativity results in several contradictions; in particular, aether having a definite velocity at each spacetime 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. |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 |bibcode = 1951Natur.168..906D |s2cid=4288946 }}</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|doi=10.1038/169702b0|bibcode = 1952Natur.169..702D |s2cid=4279193|doi-access=free}}</ref>
His arguments involve the application of the [[Physics:Uncertainty principle|uncertainty principle]] to the velocity of aether at any spacetime 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 [[Physics:Vacuum state|vacuum state]] for which all aether velocities are equally probable.

Inspired by Dirac's 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|wave function]].<ref>{{cite journal | last1=Sinha | first1=K. P. | last2=Sivaram | first2=C. | last3=Sudarshan | first3=E. C. G. | title=Aether as a superfluid state of particle-antiparticle pairs | journal=Foundations of Physics | publisher=Springer Nature | volume=6 | issue=1 | year=1976 | issn=0015-9018 | doi=10.1007/bf00708664 | pages=65–70| bibcode=1976FoPh....6...65S | s2cid=119731867 }}</ref><ref>{{cite journal | last1=Sinha | first1=K. P. | last2=Sivaram | first2=C. | last3=Sudarshan | first3=E. C. G. | title=The superfluid vacuum state, time-varying cosmological constant, and nonsingular cosmological models | journal=Foundations of Physics | publisher=Springer Nature | volume=6 | issue=6 | year=1976 | issn=0015-9018 | doi=10.1007/bf00708950 | pages=717–726| bibcode=1976FoPh....6..717S | s2cid=122996788 }}</ref><ref>{{cite journal | last1=Sinha | first1=K. P. | last2=Sudarshan | first2=E. C. G. | title=The superfluid as a source of all interactions | journal=Foundations of Physics | publisher=Springer Nature | volume=8 | issue=11–12 | year=1978 | issn=0015-9018 | doi=10.1007/bf00715056 | pages=823–831| bibcode=1978FoPh....8..823S | s2cid=123412015 }}</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 [[Physics:Theory of relativity|relativistic]] matter – by putting it into the stress–energy tensor of the [[Physics:Einstein field equations|Einstein field equations]].
This did not allow them to describe the [[Physics:General relativity|relativistic gravity]] as a small fluctuation of the superfluid vacuum, as subsequent authors have noted {{Citation needed|date=September 2020}}.

Since then, several theories have been proposed within the SVT framework. They differ in how the structure and properties of the background superfluid must look.
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 [[Physics:Theory of relativity|relativistic]] objects – unless their [[Physics:Energy|energy]] and [[Physics:Momentum|momentum]] are sufficiently high to make the 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 [[Physics:Macroscopic|macroscopic]] non-relativistic world) arises as the approximate one – when particles' velocities are small compared to [[Physics:Speed of light|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 [[Physics:Quantum field theory|quantum field theory]] the physical vacuum is also assumed to be some sort of non-trivial medium to which one can associate [[Physics:Vacuum energy|certain energy]].
This is because the concept of absolutely empty space (or "mathematical vacuum") contradicts the postulates of [[Physics:Quantum mechanics|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 [[Physics:Renormalization|renormalization]] technique, namely, replacing the diverging physical values by their experimentally measured values.
In other theories, such as the [[Physics:Canonical quantum gravity|quantum general relativity]], this trick 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 spacetime===
According to [[Physics:General relativity|general relativity]], gravitational interaction is described in terms of [[Physics:Spacetime|spacetime]] [[Curvature|curvature]] using the mathematical formalism of [[Differential geometry|differential 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 [[Physics: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 [[Chemistry:Degrees of freedom (physics and chemistry)|degrees of freedom]] of general relativity are based on what may be only approximate and [[Physics: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 spacetime arises as the small-amplitude collective excitation mode of the non-relativistic background condensate.<ref name=volovik03/><ref name="zlo0912">{{cite journal | last=Zloshchastiev | first=K.G. |title=Spontaneous symmetry breaking and mass generation as built-in phenomena in logarithmic nonlinear quantum theory| journal=Acta Physica Polonica B | volume=42 | issue=2 | year=2011 | pages=261–292 | issn=0587-4254 | doi=10.5506/aphyspolb.42.261 |arxiv=0912.4139| bibcode=2011AcPPB..42..261Z | s2cid=118152708 }}</ref>
The mathematical description of this is similar to [[Physics: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, [[Physics: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 [[Astronomy:Cosmological constant|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 the vacuum itself.<ref>{{cite journal | last=VOLOVIK | first=G. E. | title=Vacuum Energy: Myths and Reality | journal=International Journal of Modern Physics D | volume=15 | issue=12 | year=2006 | issn=0218-2718 | doi=10.1142/s0218271806009431 | pages=1987–2010|arxiv=gr-qc/0604062| bibcode=2006IJMPD..15.1987V | s2cid=11256434 }}</ref> Thus, in SVT this constant does not have any fundamental physical meaning, and related problems such as the vacuum catastrophe, simply do not occur in the first place.

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

Superfluid vacuum theory brings into question the possibility that a relativistic object possessing both of these properties exists 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 [[Physics:Graviton|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 [[Physics:Phonon|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|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|wave]]-like excitations of the superfluid background which might be responsible for the astrophysical phenomena which are currently being [[Astronomy:Gravitational wave#Astrophysics and gravitational waves|attributed]] to gravitational waves, such as the [[Astronomy:Hulse–Taylor binary|Hulse–Taylor binary]]. However, such excitations cannot be correctly described within the framework of a fully [[Physics:Theory of relativity|relativistic]] theory.

===Mass generation and Higgs boson===
The [[Physics:Higgs boson|Higgs boson]] is the spin-0 particle that has been introduced in [[Physics:Electroweak interaction|electroweak theory]] to give mass to the [[Physics:W and Z bosons|weak bosons]]. The origin of mass of the Higgs boson itself is not explained by electroweak theory. Instead, this mass is introduced as a free parameter by means of the [[Physics:Quartic interaction|Higgs potential]], which thus makes it yet another free parameter of the [[Physics:Standard Model|Standard Model]].<ref>{{cite journal | last1=Bednyakov | first1=V. A. | last2=Giokaris | first2=N. D. | last3=Bednyakov | first3=A. V. | title=On the Higgs mass generation mechanism in the Standard Model | journal=Physics of Particles and Nuclei | volume=39 | issue=1 | year=2008 | issn=1063-7796 | doi=10.1134/s1063779608010024 | pages=13–36|arxiv=hep-ph/0703280| s2cid=258710188 }}</ref> Within the framework of the [[Physics:Standard Model|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>{{cite journal | last1=Schrempp | first1=B | last2=Wimmer | first2=M | title=Top quark and Higgs boson masses: Interplay between infrared and ultraviolet physics | journal=Progress in Particle and Nuclear Physics | volume=37 | year=1996 | issn=0146-6410 | doi=10.1016/0146-6410(96)00059-2 | pages=1–90|arxiv=hep-ph/9606386| bibcode=1996PrPNP..37....1S | s2cid=118976123 }}</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 [[Physics:Mass|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 [[Physics:Electroweak scale|symmetry-breaking scale]].<ref group=nb name="higgs">If one expands the [[Physics: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 [[Physics:Quartic interaction|squared mass]] of a scalar particle.</ref>
 
While SVT does not explicitly forbid the existence of the [[Physics: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 [[Physics:Superconductor|superconductor]]s or superfluids.<ref name=zlo0912/><ref name="az2011">{{cite journal | last1=Avdeenkov | first1=Alexander V | last2=Zloshchastiev | first2=Konstantin G | title=Quantum Bose liquids with logarithmic nonlinearity: self-sustainability and emergence of spatial extent | journal=Journal of Physics B: Atomic, Molecular and Optical Physics | publisher=IOP Publishing | volume=44 | issue=19 | date=2011-09-13 | issn=0953-4075 | doi=10.1088/0953-4075/44/19/195303 | page=195303|arxiv=1108.0847| bibcode=2011JPhB...44s5303A | s2cid=119248001 }}</ref>
Although this idea is not entirely new, one could recall the relativistic [[Physics:Coleman–Weinberg potential|Coleman-Weinberg approach]],<ref>{{cite journal | last1=Coleman | first1=Sidney | last2=Weinberg | first2=Erick | title=Radiative Corrections as the Origin of Spontaneous Symmetry Breaking | journal=Physical Review D | publisher=American Physical Society (APS) | volume=7 | issue=6 | date=1973-03-15 | issn=0556-2821 | doi=10.1103/physrevd.7.1888 | pages=1888–1910| arxiv=hep-th/0507214 | bibcode=1973PhRvD...7.1888C | s2cid=6898114 }}</ref>
SVT gives the meaning to the symmetry-breaking relativistic [[Scalar field|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 |s2cid= 91178852 }}</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 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 [[Physics:Logarithmic Schrödinger equation|wave equation based on the logarithmic potential]] rather than on the [[Physics:Quartic interaction|quartic]] one. The former potential has not only the Mexican-hat shape, necessary for the [[Physics:Spontaneous symmetry breaking|spontaneous symmetry breaking]], but also some 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 [[Physics:Bose–Einstein condensate|quantum Bose liquid]] whose ground-state [[Wave function|wavefunction]] is described by the [[Physics:Logarithmic Schrödinger equation|logarithmic Schrödinger equation]]. It was shown that the [[Physics:General relativity|relativistic gravitational interaction]] arises as the small-amplitude collective excitation mode whereas relativistic elementary particles can be described by the 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 [[Physics:Theory of relativity|relativistic]] one – they can reach the [[Physics:Speed of light#Upper limit on speeds|speed of light limit]] at finite energy.<ref>{{cite journal | last=Zloshchastiev | first=K. G. | title=Logarithmic nonlinearity in theories of quantum gravity: Origin of time and observational consequences | journal=Gravitation and Cosmology | volume=16 | issue=4 | year=2010 | issn=0202-2893 | doi=10.1134/s0202289310040067 | pages=288–297|arxiv=0906.4282| bibcode=2010GrCo...16..288Z | s2cid=119187916 }}</ref>
Among other predicted effects is the superluminal propagation and vacuum [[Physics:Cherenkov radiation|Cherenkov radiation]].<ref>{{cite journal | last=Zloshchastiev | first=Konstantin G. | title=Vacuum Cherenkov effect in logarithmic nonlinear quantum theory | journal=Physics Letters A | volume=375 | issue=24 | year=2011 | issn=0375-9601 | doi=10.1016/j.physleta.2011.05.012 | pages=2305–2308|arxiv=1003.0657| bibcode=2011PhLA..375.2305Z | s2cid=118152360 }}</ref>

Theory advocates the mass generation mechanism which is supposed to replace or alter the [[Physics: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 [[Physics:Superconductor|superconductor]]s.<ref name=zlo0912/><ref name=az2011/> For instance, the [[Physics:Photon|photon]] propagating in the average interstellar vacuum acquires a tiny mass which is estimated to be about 10<sup>−35</sup> [[Physics:Electronvolt|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 [[Physics:Quartic interaction|conventional Higgs potential]].<ref name=dz01/>

==See also==
*Analog gravity
*[[Physics:Acoustic metric|Acoustic metric]]
*Casimir vacuum
*[[Physics:Dilaton#The dilaton in quantum gravity|Dilatonic quantum gravity]]
*[[Physics:Hawking radiation|Hawking radiation]]
*[[Induced gravity]]
*[[Physics:Logarithmic Schrödinger equation|Logarithmic Schrödinger equation]]
*[[Physics:Hořava–Lifshitz gravity|Hořava–Lifshitz gravity]]
*[[Astronomy:Sonic black hole|Sonic black hole]]
*[[Physics:Vacuum energy|Vacuum energy]]
*[[Physics:Hydrodynamic quantum analogs|Hydrodynamic quantum analogs]]
*[[Physics:Fluid solution|Fluid solution]]
*[[Physics:Vacuum solution (general relativity)|Vacuum solution (general relativity)]]

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

==References==
{{reflist}}

{{Theories of gravitation}}
{{quantum gravity}}
{{Standard model of physics}}

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