Superfluid vacuum theory (SVT), sometimes
known as the 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
models that unify quantum mechanics (describing
three of the four known fundamental interactions)
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
theory of relativity.
The 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.
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.
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 relativistic matter - by putting it
into the stress–energy tensor of the Einstein
field equations.
This did not allow them to describe the relativistic
gravity as a small fluctuation of the superfluid
vacuum, as subsequent authors have noted.
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 relativistic
objects - unless their energy and momentum
are sufficiently high to make the Lorentz-breaking
corrections detectable.
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.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.To summarize, the
fluctuations of vacuum superfluid behave like
relativistic objects at "small" momenta (a.k.a.
the "phononic limit")
E
2
∝
|
p
→
|
2
{\displaystyle E^{2}\propto |{\vec {p}}|^{2}}
and like non-relativistic ones
E
∝
|
p
→
|
2
{\displaystyle E\propto |{\vec {p}}|^{2}}
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 certain energy.
This is because the concept of absolutely
empty space (or "mathematical vacuum") contradicts
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 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 covariant field-theoretical
actions by hand.
=== Curved space-time ===
According to general relativity, 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 severe problems,
therefore, the microscopic structure of gravity
is still ill-defined.
There may be a fundamental reason for this—the
degrees of freedom of general relativity are
based on may be only approximate and effective.
The question of whether general relativity
is an effective theory has been raised for
a long time.According to SVT, the curved space-time
arises as the small-amplitude collective excitation
mode of the non-relativistic background condensate.
The mathematical description of this is similar
to fluid-gravity analogy which is being used
also in the analog gravity models.
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.
=== 
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 the vacuum itself. 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 general relativity, the conventional
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.
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 pseudotensor one.
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 attributed to gravitational
waves, such as the Hulse–Taylor binary.
However, such excitations cannot be correctly
described within the framework of a fully
relativistic theory.
=== Mass generation and Higgs boson ===
The Higgs boson is the spin-0 particle that
has been introduced in electroweak theory
to give mass to the 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 Higgs potential, which thus makes it
yet another free parameter of the Standard
Model. Within the 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. 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 symmetry-breaking scale.While
SVT does not explicitly forbid the existence
of the 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 superconductors or superfluids.
Although this idea is not entirely new, one
could recall the relativistic Coleman-Weinberg
approach,
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. 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.Also, some versions
of SVT favor a wave equation based on the
logarithmic potential rather than on the quartic
one. The former potential has not only the
Mexican-hat shape, necessary for the 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 quantum Bose liquid
whose ground-state wavefunction is described
by the logarithmic Schrödinger equation.
It was shown that the 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.
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.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
relativistic one - they can reach the speed
of light limit at finite energy.
Among other predicted effects is the superluminal
propagation and vacuum Cherenkov radiation.Theory
advocates the mass generation mechanism which
is supposed to replace or alter the 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 superconductors. For
instance, the photon propagating in the average
interstellar vacuum acquires a tiny mass which
is estimated to be about 10−35 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 appearing
in the conventional Higgs potential.
== 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
Sonic black hole
Vacuum energy
De Broglie–Bohm theory
Hydrodynamic quantum analogs
== Notes
