Superfluid vacuum
Encyclopedia
Superfluid vacuum theory (SVT), sometimes dubbed as the theory of BEC vacuum, is an approach in theoretical physics
and quantum mechanics
where the physical vacuum
(fundamental non-removable background) is viewed as a superfluid
or BEC.
The microscopical structure of the vacuum is currently largely unknown and is a subject of intensive studies in SVT.
The ultimate goal of the approach is to develop scientific models that unify quantum mechanics (describing three of the four known fundamental interaction
s) with gravity. This makes SVT a candidate for the theory of quantum gravity
. It is hoped that development of such theory would unify into a single consistent model all fundamental interactions,
and to describe all known interactions in the Universe
, at both microscopic and astronomic scales, as different manifestations of the same entity, superfluid vacuum.
as a medium sustaining electromagnetic waves was discarded after the advent of the special theory of relativity
.
The aether
, as conceived in classical physics, does indeed lead to several
contradictions; in particular, aether having a definite velocity at each
space-time point will exhibit a preferred direction. This is in
conflict with the
relativistic requirement that all directions within the light cone are
equivalent.
However, as early as in 1951 P.A.M. Dirac published two papers where 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.
Although these works didn't gain much popularity, they 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 antifermion pairs, describable by a macroscopic wave function.
They correctly noticed that particle-like small fluctuations of superfluid background do 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 equations, etcetera.
This did not allow them to make an important step - describe the relativistic gravity
as one of the small fluctuations of the superfluid vacuum as well.
This was done by other authors subsequently.
Since then, several theories have been proposed within the SVT framework.
They share the main idea but 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.
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.
Also,
the Lorentz-symmetric models are obviously a good approximation in that case.
However, in the close vicinity of the threshold the
relativistic description begins to fail: of course, as one approaches higher and
higher energy scales one can still employ
the relativistic
description as an effective one but the price will be that it will become more
and more "effective" and less and less natural since
one will need to adjust the form of the covariant field-theoretical action by hand.
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, vacuum superfluid describes relativistic objects at "small"The term "small" refers here to the linearized limit, in practice the values of these momenta may not be small at all. momenta (a.k.a. the "phonon
ic" limit)
and non-relativistic ones
at large momenta.
The most interesting nontrivial physics is believed to be located somewhere between these two regimes.
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 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 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 begins to fail, as mentioned above, so theories based on it cannot be regarded as valid for all scales of energies and momenta.
, the gravitational interaction is described in terms of space-time curvature
using the mathematical formalism of the 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 microscopical structure of gravity is still ill-defined.
There may be a fundamental reason for it - the degrees of freedom
the general relativity
is based on
may not be the correct ones but only approximate and effective
. The question whether the general relativity is an effective theory
has been raised long
time ago.
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.
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. 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.
, the conventional gravitational wave
is:
Theory of superfluid vacuum brings into question that the relativistic object possessing both of these properties may exist 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.
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
rather than an elementary particle. This may result in inability to detect the Higgs boson as an elementary particle of the electroweak-scale mass.
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.
was originally designed as a set of the Lorentz-covariant quantum gravity models whose renormalizability was ensured by assuming superconformal
symmetry and higher-dimensionality as fundamental properties of space-time.
The theory postulates that some extended objects are more fundamental than point particles.
String theory is known to suffer from various problems, not to mention that its non-perturbative formulation
is still pending.
According to SVT, theory of quantum gravity, as many other physical theories we know, does not have to be renormalizable nor valid at all scales.
Instead, SVT models have the ultraviolet cutoff scale which is determined by the vacuum energy
and corresponding length scale - such that all practical computations will necessarily contain this finite cutoff. Besides, as long as the Lorentz symmetry is only an approximate one in SVT, the main motivation behind introducing the exact fundamental supersymmetry
fades away too.
As for the extendedness issue then the theory's goal is to have the nonzero-size feature derived from quantum-mechanical principles rather than mathematically postulated from the beginning - as to be able to answer the "naive" physical questions such as, for example, what is the microscopical structure of the "material" an extended object, be it string or brane or anything else, is "made of".
Otherwise such extended object can be regarded only as an approximate, effective description of a real phenomenon.
the physical vacuum is conjectured to be the 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 momenta.
The essential difference of this theory from others is that in the logarithmic superfluid the maximal velocity of the phonon-like 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 very high velocities the behavior of the particle-like modes 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
.
The theory also proposes the mass generation mechanism which may replace or supplement 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
.
Theoretical physics
Theoretical physics is a branch of physics which employs mathematical models and abstractions of physics to rationalize, explain and predict natural phenomena...
and quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
where the physical vacuum
Vacuum
In everyday usage, vacuum is a volume of space that is essentially empty of matter, such that its gaseous pressure is much less than atmospheric pressure. The word comes from the Latin term for "empty". A perfect vacuum would be one with no particles in it at all, which is impossible to achieve in...
(fundamental non-removable background) is viewed as a superfluid
Superfluid
Superfluidity is a state of matter in which the matter behaves like a fluid without viscosity and with extremely high thermal conductivity. The substance, which appears to be a normal liquid, will flow without friction past any surface, which allows it to continue to circulate over obstructions and...
or BEC.
The microscopical structure of the vacuum is currently largely unknown and is a subject of intensive studies in SVT.
The ultimate goal of the approach is to develop scientific models that unify quantum mechanics (describing three of the four known fundamental interaction
Fundamental interaction
In particle physics, fundamental interactions are the ways that elementary particles interact with one another...
s) with gravity. This makes SVT a candidate for the theory of quantum gravity
Quantum gravity
Quantum gravity is the field of theoretical physics which attempts to develop scientific models that unify quantum mechanics with general relativity...
. It is hoped that development of such theory would unify into a single consistent model all fundamental interactions,
and to describe all known interactions in the Universe
Universe
The Universe is commonly defined as the totality of everything that exists, including all matter and energy, the planets, stars, galaxies, and the contents of intergalactic space. Definitions and usage vary and similar terms include the cosmos, the world and nature...
, at both microscopic and astronomic scales, as different manifestations of the same entity, superfluid vacuum.
History
The concept of a luminiferous aetherLuminiferous aether
In the late 19th century, luminiferous aether or ether, meaning light-bearing aether, was the term used to describe a medium for the propagation of light....
as a medium sustaining electromagnetic waves was discarded after the advent of the special theory of relativity
Special relativity
Special relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...
.
The aether
Aether
-Metaphysics and mythology:* Aether , the material that fills the region of the universe above the terrestrial sphere* Aether was the personification of the "upper sky", space and heaven, in Greek mythology-Science and engineering:...
, as conceived in classical physics, does indeed lead to several
contradictions; in particular, aether having a definite velocity at each
space-time point will exhibit a preferred direction. This is in
conflict with the
relativistic requirement that all directions within the light cone are
equivalent.
However, as early as in 1951 P.A.M. Dirac published two papers where 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
Uncertainty principle
In quantum mechanics, the Heisenberg uncertainty principle states a fundamental limit on the accuracy with which certain pairs of physical properties of a particle, such as position and momentum, can be simultaneously known...
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
Vacuum state
In quantum field theory, the vacuum state is the quantum state with the lowest possible energy. Generally, it contains no physical particles...
for which all aether velocities are equally probable.
Although these works didn't gain much popularity, they 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 antifermion pairs, describable by a macroscopic wave function.
They correctly noticed that particle-like small fluctuations of superfluid background do obey the Lorentz symmetry even if the superfluid itself is non-relativistic.
Nevertheless, they decided to treat the superfluid as the relativistic
Theory of relativity
The theory of relativity, or simply relativity, encompasses two theories of Albert Einstein: special relativity and general relativity. However, the word relativity is sometimes used in reference to Galilean invariance....
matter - by putting it into the stress-energy tensor of the Einstein equations, etcetera.
This did not allow them to make an important step - describe the relativistic gravity
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...
as one of the small fluctuations of the superfluid vacuum as well.
This was done by other authors subsequently.
Since then, several theories have been proposed within the SVT framework.
They share the main idea but differ in how the structure and properties of the background superfluid
Superfluid
Superfluidity is a state of matter in which the matter behaves like a fluid without viscosity and with extremely high thermal conductivity. The substance, which appears to be a normal liquid, will flow without friction past any surface, which allows it to continue to circulate over obstructions and...
must look.
In absence of observational data which would rule out some of them, these theories are being pursued independently.
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
Theory of relativity
The theory of relativity, or simply relativity, encompasses two theories of Albert Einstein: special relativity and general relativity. However, the word relativity is sometimes used in reference to Galilean invariance....
objects - unless their energy
Energy
In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...
and momentum
Momentum
In classical mechanics, linear momentum or translational momentum is the product of the mass and velocity of an object...
are sufficiently high to make the Lorentz-breaking corrections detectable.
If the energies and momenta are below the excitation threshold then the superfluid
Superfluid
Superfluidity is a state of matter in which the matter behaves like a fluid without viscosity and with extremely high thermal conductivity. The substance, which appears to be a normal liquid, will flow without friction past any surface, which allows it to continue to circulate over obstructions and...
background behaves like the ideal fluid, therefore, the Michelson-Morley-type experiments would observe no drag force from such aether.
Also,
the Lorentz-symmetric models are obviously a good approximation in that case.
However, in the close vicinity of the threshold the
relativistic description begins to fail: of course, as one approaches higher and
higher energy scales one can still employ
the relativistic
description as an effective one but the price will be that it will become more
and more "effective" and less and less natural since
one will need to adjust the form of the covariant field-theoretical action by hand.
Further, in the theory of relativity
Theory of relativity
The theory of relativity, or simply relativity, encompasses two theories of Albert Einstein: special relativity and general relativity. However, the word relativity is sometimes used in reference to Galilean invariance....
the Galilean symmetry (pertinent to our macroscopic
Macroscopic
The macroscopic scale is the length scale on which objects or processes are of a size which is measurable and observable by the naked eye.When applied to phenomena and abstract objects, the macroscopic scale describes existence in the world as we perceive it, often in contrast to experiences or...
non-relativistic world) arises as the approximate one -
when particles' velocities are small compared to speed of light
Speed of light
The speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...
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, vacuum superfluid describes relativistic objects at "small"The term "small" refers here to the linearized limit, in practice the values of these momenta may not be small at all. momenta (a.k.a. the "phonon
Phonon
In physics, a phonon is a collective excitation in a periodic, elastic arrangement of atoms or molecules in condensed matter, such as solids and some liquids...
ic" limit)
and non-relativistic ones
at large momenta.
The most interesting nontrivial physics is believed to be located somewhere between these two regimes.
Relativistic quantum field theory
In the relativistic quantum field theoryQuantum field theory
Quantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically parametrized by an infinite number of dynamical degrees of freedom, that is, fields and many-body systems. It is the natural and quantitative language of particle physics and...
the physical vacuum is also assumed to be some sort of non-trivial medium to which one can associate certain energy
Vacuum energy
Vacuum energy is an underlying background energy that exists in space even when the space is devoid of matter . The concept of vacuum energy has been deduced from the concept of virtual particles, which is itself derived from the energy-time uncertainty principle...
.
This is because the concept of absolutely empty space (or "mathematical vacuum") contradicts to the postulates of quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
.
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
Renormalization
In quantum field theory, the statistical mechanics of fields, and the theory of self-similar geometric structures, renormalization is any of a collection of techniques used to treat infinities arising in calculated quantities....
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 begins to fail, as mentioned above, so theories based on it cannot be regarded as valid for all scales of energies and momenta.
Curved space-time
According to general relativityGeneral relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...
, the gravitational interaction is described in terms of space-time curvature
Curvature
In mathematics, curvature refers to any of a number of loosely related concepts in different areas of geometry. Intuitively, curvature is the amount by which a geometric object deviates from being flat, or straight in the case of a line, but this is defined in different ways depending on the context...
using the mathematical formalism of the Riemannian geometry
Riemannian geometry
Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, smooth manifolds with a Riemannian metric, i.e. with an inner product on the tangent space at each point which varies smoothly from point to point. This gives, in particular, local notions of angle, length...
.
This was supported by numerous experiments and observations in the regime of low energies.
However, the attempts to quantize general relativity
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...
led to various severe problems, therefore, the microscopical structure of gravity is still ill-defined.
There may be a fundamental reason for it - the degrees of freedom
Degrees of freedom
Degrees of freedom can mean:* Degrees of freedom , independent displacements and/or rotations that specify the orientation of the body or system...
the general relativity
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...
is based on
may not be the correct ones but only approximate and effective
Effective field theory
In physics, an effective field theory is, as any effective theory, an approximate theory, that includes appropriate degrees of freedom to describe physical phenomena occurring at a chosen length scale, while ignoring substructure and degrees of freedom at shorter distances .-The renormalization...
. The question whether the general relativity is an effective theory
has been raised long
time ago.
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
Acoustic metric
In mathematical physics, a metric describes the arrangement of relative distances within a surface or volume, usually measured by signals passing through the region – essentially describing the intrinsic geometry of the region. An acoustic metric will describe the signal-carrying properties...
which is being used also in the analog gravity models.
Thus, relativistic gravity
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...
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
Riemannian geometry
Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, smooth manifolds with a Riemannian metric, i.e. with an inner product on the tangent space at each point which varies smoothly from point to point. This gives, in particular, local notions of angle, length...
becomes incomplete or ill-defined.
Cosmological constant
The notion of the cosmological constantCosmological constant
In physical cosmology, the cosmological constant was proposed by Albert Einstein as a modification of his original theory of general relativity to achieve a stationary universe...
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. Thus, in SVT this constant does not have
any fundamental physical meaning and the related problems, such as the vacuum catastrophe
Vacuum catastrophe
In cosmology the vacuum catastrophe refers to the disagreement of 107 orders of magnitude between the upper bound upon the vacuum energy density as inferred from data obtained from the Voyager spacecraft of less than 1014 GeV/m3 and the zero-point energy of 10121 GeV/m3 calculated using quantum...
, simply do not
occur in first place.
Gravitational waves and gravitons
According to general relativityGeneral relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...
, the conventional gravitational wave
Gravitational wave
In physics, gravitational waves are theoretical ripples in the curvature of spacetime which propagates as a wave, traveling outward from the source. Predicted to exist by Albert Einstein in 1916 on the basis of his theory of general relativity, gravitational waves theoretically transport energy as...
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.
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
Graviton
In physics, the graviton is a hypothetical elementary particle that mediates the force of gravitation in the framework of quantum field theory. If it exists, the graviton must be massless and must have a spin of 2...
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
Phonon
In physics, a phonon is a collective excitation in a periodic, elastic arrangement of atoms or molecules in condensed matter, such as solids and some liquids...
, for instance).
As a result, it may be not just a coincidence that in general relativity
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...
the gravitational field alone has no well-defined stress-energy tensor
Stress-energy tensor
The stress–energy tensor is a tensor quantity in physics that describes the density and flux of energy and momentum in spacetime, generalizing the stress tensor of Newtonian physics. It is an attribute of matter, radiation, and non-gravitational force fields...
,
only the pseudotensor
Stress-energy-momentum pseudotensor
In the theory of general relativity, a stress–energy–momentum pseudotensor, such as the Landau–Lifshitz pseudotensor, is an extension of the non-gravitational stress–energy tensor which incorporates the energy-momentum of gravity. It allows the energy-momentum of a system of gravitating matter to...
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
Wave
In physics, a wave is a disturbance that travels through space and time, accompanied by the transfer of energy.Waves travel and the wave motion transfers energy from one point to another, often with no permanent displacement of the particles of the medium—that is, with little or no associated mass...
-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 of relativity
The theory of relativity, or simply relativity, encompasses two theories of Albert Einstein: special relativity and general relativity. However, the word relativity is sometimes used in reference to Galilean invariance....
theory.
Mass generation and Higgs boson
While SVT does not explicitly forbid the existence of the electroweak Higgs particle, it has its own idea of the mass generation mechanism - elementary particles acquire mass due to the interaction with the vacuum condensate, similarly to the gap generation mechanism in superconductors.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
Scalar field
In mathematics and physics, a scalar field associates a scalar value to every point in a space. The scalar may either be a mathematical number, or a physical quantity. Scalar fields are required to be coordinate-independent, meaning that any two observers using the same units will agree on the...
as describing small fluctuations of background superfluid
rather than an elementary particle. This may result in inability to detect the Higgs boson as an elementary particle of the electroweak-scale mass.
Also, some versions of SVT favor a wave equation based on the logarithmic potential
Logarithmic Schrödinger equation
In theoretical physics, the logarithmic Schrödinger equation is one of the nonlinear modifications of Schrödinger's equation...
rather than on the quartic one. The former potential has not only the Mexican-hat shape, necessary for the spontaneous symmetry breaking
Spontaneous symmetry breaking
Spontaneous symmetry breaking is the process by which a system described in a theoretically symmetrical way ends up in an apparently asymmetric state....
, but also some other features which make it more suitable
for the vacuum's description.
String theory and supersymmetry
Superstring theorySuperstring theory
Superstring theory is an attempt to explain all of the particles and fundamental forces of nature in one theory by modelling them as vibrations of tiny supersymmetric strings...
was originally designed as a set of the Lorentz-covariant quantum gravity models whose renormalizability was ensured by assuming superconformal
Superconformal algebra
In theoretical physics, the superconformal algebra is a graded Lie algebra or superalgebra that combines the conformal algebra and supersymmetry. It generates the superconformal group in some cases .In two dimensions, the superconformal algebra is infinite-dimensional...
symmetry and higher-dimensionality as fundamental properties of space-time.
The theory postulates that some extended objects are more fundamental than point particles.
String theory is known to suffer from various problems, not to mention that its non-perturbative formulation
M-theory
In theoretical physics, M-theory is an extension of string theory in which 11 dimensions are identified. Because the dimensionality exceeds that of superstring theories in 10 dimensions, proponents believe that the 11-dimensional theory unites all five string theories...
is still pending.
According to SVT, theory of quantum gravity, as many other physical theories we know, does not have to be renormalizable nor valid at all scales.
Instead, SVT models have the ultraviolet cutoff scale which is determined by the vacuum energy
Vacuum energy
Vacuum energy is an underlying background energy that exists in space even when the space is devoid of matter . The concept of vacuum energy has been deduced from the concept of virtual particles, which is itself derived from the energy-time uncertainty principle...
and corresponding length scale - such that all practical computations will necessarily contain this finite cutoff. Besides, as long as the Lorentz symmetry is only an approximate one in SVT, the main motivation behind introducing the exact fundamental supersymmetry
Supersymmetry
In particle physics, supersymmetry is a symmetry that relates elementary particles of one spin to other particles that differ by half a unit of spin and are known as superpartners...
fades away too.
As for the extendedness issue then the theory's goal is to have the nonzero-size feature derived from quantum-mechanical principles rather than mathematically postulated from the beginning - as to be able to answer the "naive" physical questions such as, for example, what is the microscopical structure of the "material" an extended object, be it string or brane or anything else, is "made of".
Otherwise such extended object can be regarded only as an approximate, effective description of a real phenomenon.
Logarithmic BEC vacuum theory
In this theorythe physical vacuum is conjectured to be the strongly-correlated quantum Bose liquid whose ground-state wavefunction is described by the logarithmic Schrödinger equation
Logarithmic Schrödinger equation
In theoretical physics, the logarithmic Schrödinger equation is one of the nonlinear modifications of Schrödinger's equation...
. It was shown that the relativistic gravitational interaction
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...
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 momenta.
The essential difference of this theory from others is that in the logarithmic superfluid the maximal velocity of the phonon-like 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 very high velocities the behavior of the particle-like modes becomes distinct from the relativistic
Theory of relativity
The theory of relativity, or simply relativity, encompasses two theories of Albert Einstein: special relativity and general relativity. However, the word relativity is sometimes used in reference to Galilean invariance....
one - they can reach the speed of light limit at finite energy.
Among other predicted effects is the superluminal propagation and vacuum Cherenkov radiation
Cherenkov radiation
Cherenkov radiation is electromagnetic radiation emitted when a charged particle passes through a dielectric medium at a speed greater than the phase velocity of light in that medium...
.
The theory also proposes the mass generation mechanism which may replace or supplement 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
Photon
In physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...
propagating in the average interstellar vacuum acquires a tiny mass which is estimated to be about 10−35 electronvolt
Electronvolt
In physics, the electron volt is a unit of energy equal to approximately joule . By definition, it is equal to the amount of kinetic energy gained by a single unbound electron when it accelerates through an electric potential difference of one volt...
.
See also
- Analog gravity
- Acoustic metricAcoustic metricIn mathematical physics, a metric describes the arrangement of relative distances within a surface or volume, usually measured by signals passing through the region – essentially describing the intrinsic geometry of the region. An acoustic metric will describe the signal-carrying properties...
- Bose-Einstein condensate
- Casimir vacuum
- Hawking radiationHawking radiationHawking radiation is a thermal radiation with a black body spectrum predicted to be emitted by black holes due to quantum effects. It is named after the physicist Stephen Hawking, who provided a theoretical argument for its existence in 1974, and sometimes also after the physicist Jacob Bekenstein...
- Induced gravityInduced gravityInduced gravity is an idea in quantum gravity that space-time background emerges asa mean field approximation of underlying microscopic degrees of freedom, similar to the fluid mechanics approximation of Bose–Einstein condensates...
- Planck scalePlanck scaleIn particle physics and physical cosmology, the Planck scale is an energy scale around 1.22 × 1019 GeV at which quantum effects of gravity become strong...
- Planck unitsPlanck unitsIn physics, Planck units are physical units of measurement defined exclusively in terms of five universal physical constants listed below, in such a manner that these five physical constants take on the numerical value of 1 when expressed in terms of these units. Planck units elegantly simplify...
- Hořava–Lifshitz gravity
- Quantum gravityQuantum gravityQuantum gravity is the field of theoretical physics which attempts to develop scientific models that unify quantum mechanics with general relativity...
- Quantum realmQuantum realmQuantum realm is a term of art in physics referring to scales where quantum mechanical effects become important . Typically, this means distances of 100 nanometers or less. Not coincidentally, this is the same scale as nanotechnology....
- Macrocosm and microcosmMacrocosm and microcosmMacrocosm and microcosm is an ancient Greek Neo-Platonic schema of seeing the same patterns reproduced in all levels of the cosmos, from the largest scale all the way down to the smallest scale...
- Sonic black holeSonic black holeA sonic black hole is a phenomenon in which phonons are unable to escape from a fluid that is flowing more quickly than the local speed of sound. They are called sonic, or acoustic, black holes because these trapped phonons are analogous to light in astrophysical black holes...
- Vacuum energyVacuum energyVacuum energy is an underlying background energy that exists in space even when the space is devoid of matter . The concept of vacuum energy has been deduced from the concept of virtual particles, which is itself derived from the energy-time uncertainty principle...