Superfluid vacuum theory (SVT), sometimes known as theBEC vacuum theory, is an approach intheoretical physics andquantum mechanics where the fundamental physicalvacuum (non-removable background) is considered as asuperfluid or as aBose–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 developscientific models that unify quantum mechanics (which describes three of the four knownfundamental interactions) withgravity, making SVT a derivative ofquantum gravity and describes all known interactions in the Universe, at both microscopic and astronomic scales, as different manifestations of the same entity, superfluid vacuum.
The concept of aluminiferous aether as a medium sustainingelectromagnetic waves was discarded after the advent of thespecial 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 1951P.A.M. Dirac published two papers where he pointed out that we should take into account quantum fluctuations in the flow of the aether.[1][2]His arguments involve the application of theuncertainty 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 perfectvacuum state for which all aether velocities are equally probable.
Inspired by Dirac's ideas, K. P. Sinha, C. Sivaram andE. 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 macroscopicwave function.[3][4][5]They noted that particle-like small fluctuations of superfluid background obey theLorentz symmetry, even if the superfluid itself is non-relativistic.Nevertheless, they decided to treat the superfluid as therelativistic matter – by putting it into the stress–energy tensor of theEinstein field equations.This did not allow them to describe therelativistic gravity as a small fluctuation of the superfluid vacuum, as subsequent authors have noted[citation needed].
Since then, several theories have been proposed within the SVT framework. They differ in how the structure and properties of the backgroundsuperfluid must look.In absence of observational data which would rule out some of them, these theories are being pursued independently.
According to the approach, the background superfluid is assumed to be essentially non-relativistic whereas theLorentz 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 asrelativistic objects – unless theirenergy andmomentum are sufficiently high to make theLorentz-breaking corrections detectable.[6]If the energies and momenta are below the excitation threshold then thesuperfluid background behaves like theideal fluid, therefore, theMichelson–Morley-type experiments would observe nodrag force from such aether.[1][2]
Further, in the theory of relativity theGalilean symmetry (pertinent to ourmacroscopic non-relativistic world) arises as the approximate one – when particles' velocities are small compared tospeed 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.[7][8][9]
To summarize, the fluctuations of vacuum superfluid behave like relativistic objects at "small"[nb 1] momenta (a.k.a. the "phononic limit")
and like non-relativistic ones
at large momenta.The yet unknown nontrivial physics is believed to be located somewhere between these two regimes.
In the relativisticquantum field theory the physical vacuum is also assumed to be some sort of non-trivial medium to which one can associatecertain energy.This is because the concept of absolutely empty space (or "mathematical vacuum") contradicts the postulates ofquantum mechanics.According to QFT, even in absence of real particles the background is always filled by pairs of creating and annihilatingvirtual particles.However, a direct attempt to describe such medium leads to the so-calledultraviolet divergences.In some QFT models, such as quantum electrodynamics, these problems can be "solved" using therenormalization technique, namely, replacing the diverging physical values by their experimentally measured values.In other theories, such as thequantum general relativity, this trickdoes not work, and reliable perturbation theory cannot be constructed.
According to SVT, this is because in the high-energy ("ultraviolet") regime theLorentz 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 thecovariant field-theoretical actions by hand.
According togeneral relativity, gravitational interaction is described in terms ofspacetimecurvature using the mathematical formalism ofdifferential geometry.This was supported by numerous experiments and observations in the regime of low energies. However, the attempts to quantize general relativity led to varioussevere problems, therefore, the microscopic structure of gravity is still ill-defined.There may be a fundamental reason for this—thedegrees of freedom of general relativity are based on what may be only approximate andeffective. The question of whether general relativity is an effective theory has been raised for a long time.[10]
According to SVT, the curved spacetime arises as the small-amplitudecollective excitation mode of the non-relativistic background condensate.[6][11]The mathematical description of this is similar tofluid-gravity analogy which is being used also in theanalog gravity models.[12]Thus,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.
The notion of thecosmological 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.[13] Thus, in SVT this constant does not have any fundamental physical meaning, and related problems such as thevacuum catastrophe, simply do not occur in the first place.
 | This section'sfactual accuracy may be compromised due to out-of-date information. The reason given is: Gravitational waves were observed by LIGO in 2016. Additionally, the claims made here about GR are questionable. Relevant discussion may be found on thetalk page. Please help update this article to reflect recent events or newly available information.(January 2021) |
According togeneral relativity, the conventionalgravitational wave is:
Superfluid vacuum theory brings into question the possibility that a relativistic object possessing both of these properties exists in nature.[11]Indeed, according to the approach, the curved spacetime itself is the smallcollective excitation of the superfluid background, therefore, the property (1) means that thegraviton 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 aphonon, for instance).As a result, it may be not just a coincidence that in general relativity the gravitational field alone has no well-definedstress–energy tensor, only thepseudotensor one.[14]Therefore, the property (2) cannot be completely justified in a theory with exactLorentz symmetry which the general relativity is.Though, SVT does nota priori forbid an existence of the non-localizedwave-like excitations of the superfluid background which might be responsible for the astrophysical phenomena which are currently beingattributed to gravitational waves, such as theHulse–Taylor binary. However, such excitations cannot be correctly described within the framework of a fullyrelativistic theory.
| Parts of this article (those related to this section) need to beupdated. The reason given is: the Higgs boson was discovered in 2012. Please help update this article to reflect recent events or newly available information.(July 2020) |
TheHiggs boson is the spin-0 particle that has been introduced inelectroweak theory to give mass to theweak 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 theHiggs potential, which thus makes it yet another free parameter of theStandard Model.[15] Within the framework of theStandard Model (or its extensions) the theoretical estimates of this parameter's value are possible only indirectly and results differ from each other significantly.[16] Thus, the usage of the Higgs boson (or any other elementary particle with predefined mass) alone is not the most fundamental solution of themass generation problem but only its reformulationad infinitum. Another known issue of theGlashow–Weinberg–Salam model is the wrong sign of mass term in the (unbroken) Higgs sector for energies above thesymmetry-breaking scale.[nb 2]
While SVT does not explicitly forbid the existence of theelectroweak 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 insuperconductors orsuperfluids.[11][17]Although this idea is not entirely new, one could recall the relativisticColeman-Weinberg approach,[18]SVT gives the meaning to the symmetry-breaking relativisticscalar field as describing small fluctuations of background superfluid which can be interpreted as an elementary particle only under certain conditions.[19] In general, one allows two scenarios to happen:
Thus, the Higgs boson, even if it exists, would be a by-product of the fundamental mass generation phenomenon rather than its cause.[19]
Also, some versions of SVT favor awave equation based on the logarithmic potential rather than on thequartic one. The former potential has not only the Mexican-hat shape, necessary for thespontaneous symmetry breaking, but also someother features which make it more suitable for the vacuum's description.
In this model the physical vacuum is conjectured to be strongly-correlatedquantum Bose liquid whose ground-statewavefunction is described by thelogarithmic Schrödinger equation. It was shown that therelativistic gravitational interaction arises as the small-amplitudecollective excitation mode whereas relativisticelementary particles can be described by theparticle-like modes in the limit of low energies and momenta.[17]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.[11]
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 therelativistic one – they can reach thespeed of light limit at finite energy.[20]Among other predicted effects is thesuperluminal propagation and vacuumCherenkov radiation.[21]
Theory advocates the mass generation mechanism which is supposed to replace or alter theelectroweak 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 insuperconductors.[11][17] For instance, thephoton propagating in the averageinterstellar vacuum acquires a tiny mass which is estimated to be about 10−35electronvolt.One can also derive an effective potential for the Higgs sector which is different from the one used in theGlashow–Weinberg–Salam model, yet it yields the mass generation and it is free of the imaginary-mass problem[nb 2] appearing in theconventional Higgs potential.[19]
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