Superfluid analogies of cosmological phenomena

In a modern viewpoint relativistic quantum field theory is an emergent phenomenon arising in the low-energy corner of the physical fermionic vacuum – the medium, whose nature remains unknown. The same phenomenon occurs in condensed matter systems: In the extreme limit of low-energy condensed matter systems of special universality class acquire all the symmetries, which we know today in high-energy physics: Lorentz invariance, gauge invariance, general covariance, etc. The chiral fermions as well as gauge bosons and gravity field arise as fermionic and bosonic collective modes of the system. Inhomogeneous states of the condensed matter ground state – vacuum – induce nontrivial effective metrics of the space, where the free quasiparticles move along geodesics. This conceptual similarity between condensed matter and the quantum vacuum allows us to simulate many phenomena in high-energy physics and cosmology, including the axial anomaly, baryoproduction and magnetogenesis, event horizon and Hawking radiation, cosmological constant and rotating vacuum, etc., probing these phenomena in ultra-low-temperature superfluid helium, atomic Bose condensates and superconductors. Some of the experiments have been already conducted.     

The Planck Aether model for a unified theory of elementary particles

A dense assembly of an equal number of two kinds of Planck masses, one having positive and the other one negative kinetic energy, described by a nonrelativistic nonlinear Heisenberg equation with pointlike interactions, is proposed as a model for a unified theory of elementary particles. The dense assembly of Planck masses leads to a vortex field below the Planck scale having the form of a vortex lattice, which can propagate two types of waves, one having the property of Maxwell's electromagnetic and the other one the property of Einstein's gravitational waves. The waves have a cutoff at a wavelength equal to the vortex lattice constant about 10³ times larger than the Planck length, reproducing the GUT scale of elementary particle physics. The vortex lattice has a resonance energy leading to two kinds of quasiparticles, both of which have the property of Dirac spinors. Depending on the resonance energy, estimated to be 10⁷ times smaller than the Planck energy, the mass of one of these quasiparticles is about equal to the electron mass. The mass of the other particle is much smaller, making it a likely candidate for the much smaller neutrino mass. Larger spinor masses occur as internal excitations, with a maximum of four such excitations corresponding to a maximum of four particle families. Other vortex solutions may describe the quark-lepton symmetries of the standard model. All masses, with the exception of the Planck mass particles, are quasiparticles for which Lorentz invariance holds, with the Galilei invariance at the Planck scale dynamically broken into Lorentz invariance below this scale. The assumed equal number of Planck masses with positive and negative kinetic energy makes the cosmological constant exactly equal to zero.     

Lorentz invariance on trial in the weak decay of polarized atoms

The invariance of the laws of physics under Lorentz transformations is one of the most fundamental principles underlying our current understanding of nature. In theories trying to unify the Standard Model with quantum gravity, this invariance may be broken, and dedicated high-precision experiments at low energy could be used to reveal such suppressed signals from the Planck scale. We will test Lorentz invariance searching for a dependence of the decay rate of spin-polarized nuclei on the daily, yearly or deliberate re-orientation of the spin. Observation of such a dependence would imply a breakdown of Lorentz invariance.     

Derivation of quantum mechanics from the Boltzmann equation for the Planck aether

The Planck aether hypothesis assumes that space is densely filled with an equal number of locally interacting positive and negative Planck masses obeying an exactly nonrelativistic law of motion. The Planck masses can be described by a quantum mechanical two-component nonrelativistic operator field equation having the form of a two-component nonlinear Schrödinger equation, with a spectrum of quasiparticles obeying Lorentz invariance as a dynamic symmetry for energies small compared to the Planck energy. We show that quantum mechanics itself can be derived from the Newtonian mechanics of the Planck aether as an approximate solution of Boltzmann's equation for the locally interacting positive and negative Planck masses, and that the validity of the nonrelativistic Schrödinger equation depends on Lorentz invariance as a dynamic symmetry. We also show how the many-body Schrödinger wave function can be factorized into a product of quasiparticles of the Planck aether with separable quantum potentials. Finally, we present a possible explanation of wave function collapse as a kind of enhanced gravitational collapse in the presence of the negative Planck masses.     

Lorentz invariance on trial in the weak decay of polarized atoms

One of the most fundamental principles underlying our current understanding of nature is the invariance of the laws of physics under Lorentz transformations. Theories trying to unify the Standard Model with quantum gravity suggest that this invariance may be broken by the presence of Lorentz-violating background fields. Dedicated high-precision experiments at low energies could observe such suppressed signals from the Planck scale. At KVI, a test on Lorentz invariance of the weak interaction is performed searching for a dependence of the decay rate of spin-polarized nuclei on the orientation of their spin with respect to a fixed absolute galactical reference frame. An observation of such a dependence would imply a violation of Lorentz invariance.     

Lorentz invariance violation and generalized uncertainty principle

There are several theoretical indications that the quantum gravity approaches may have predictions for a minimal measurable length, and a maximal observable momentum and throughout a generalization for Heisenberg uncertainty principle. The generalized uncertainty principle (GUP) is based on a momentum-dependent modification in the standard dispersion relation which is conjectured to violate the principle of Lorentz invariance. From the resulting Hamiltonian, the velocity and time of flight of relativistic distant particles at Planck energy can be derived. A first comparison is made with recent observations for Hubble parameter in redshift-dependence in early-type galaxies. We find that LIV has two types of contributions to the time of flight delay Δt comparable with that observations. Although the wrong OPERA measurement on faster-than-light muon neutrino anomaly, Δt, and the relative change in the speed of muon neutrino Δv in dependence on redshift z turn to be wrong, we utilize its main features to estimate Δv. Accordingly, the results could not be interpreted as LIV. A third comparison is made with the ultra high-energy cosmic rays (UHECR). It is found that an essential ingredient of the approach combining string theory, loop quantum gravity, black hole physics and doubly spacial relativity and the one assuming a perturbative departure from exact Lorentz invariance. Fixing the sensitivity factor and its energy dependence are essential inputs for a reliable confronting of our calculations to UHECR. The sensitivity factor is related to the special time of flight delay and the time structure of the signal. Furthermore, the upper and lower bounds to the parameter, a that characterizes the generalized uncertainly principle, have to be fixed in related physical systems such as the gamma rays bursts.     

Lorentz invariance and quantum gravity: an additional fine-tuning problem?

Trying to combine standard quantum field theories with gravity leads to a breakdown of the usual structure of space time at around the Planck length, 1.6x10(-35) m, with possible violations of Lorentz invariance. Calculations of preferred-frame effects in quantum gravity have further motivated high precision searches for Lorentz violation. Here, we explain that combining known elementary particle interactions with a Planck-scale preferred frame gives rise to Lorentz violation at the percent level, some 20 orders of magnitude higher than earlier estimates, unless the bare parameters of the theory are unnaturally strongly fine tuned. Therefore an important task is not just the improvement of the precision of searches for violations of Lorentz invariance, but also the search for theoretical mechanisms for automatically preserving Lorentz invariance.     

Remarks on possible CPT violations

We argue that it is certainly unusual, but not entirely anathema to present theoretical thinking that a breakdown of CPT invariance (and even Lorentz symmetry) might occur at some scale, be it the Planck mass or even the grand unification point. We discuss how the sensitivity of existing tests of CPT invariance can be greatly improved in neutrino oscillations irrespective of whether CP is conserved or not. Also the source of a possible CPT breakdown can be further analyzed in such experiments.     

Naturalness in an emergent analogue spacetime

Effective field theories (EFTs) have been widely used as a framework in order to place constraints on the Planck suppressed Lorentz violations predicted by various models of quantum gravity. There are, however, technical problems in the EFT framework when it comes to ensuring that small Lorentz violations remain small--this is the essence of the "naturalness" problem. Herein we present an "emergent" spacetime model, based on the "analogue gravity" program, by investigating a specific condensed-matter system. Specifically, we consider the class of two-component BECs subject to laser-induced transitions between the components, and we show that this model is an example for Lorentz invariance violation due to ultraviolet physics. Furthermore, our model explicitly avoids the naturalness problem, and makes specific suggestions regarding how to construct a physically reasonable quantum gravity phenomenology.     

Radiative effects and dimension 5 operators arising from quantum gravity

We examine radiative corrections arising from Lorentz violating dimension five operators presumably associated with Planck scale physics as recently considered by Myers and Pospelov. We find that observational data result in bounds on the dimensionless parameters of the order 10^–15. These represent the most stringent bounds on Lorentz violation to date.     

ESSAY: The Cosmological Constant Problem in Brane-Worlds and Gravitational Lorentz Violations

Brane worlds are theories with extra spatial dimensions in which ordinary matter is localized on a (3+1) dimensional submanifold. Such theories could have interesting consequences for particle physics and gravitational physics. In this essay we concentrate on the cosmological constant (CC) problem in the context of brane worlds. We show how extra-dimensional scenarios may violate Lorentz invariance in the gravity sector of the effective 4D theory, while particle physics remains unaffected. In such theories the usual no-go theorems for adjustment of the CC do not apply, and we indicate a possible explanation of the smallness of the CC. Lorentz violating effects would manifest themselves in gravitational waves travelling with a speed different from light, which can be searched for in gravitational wave experiments.     

Atomic collapse,Lorentz boosts,Klein scattering,and other quantum-relativistic phenomena in graphene

Electrons in graphene, which behave as massless relativistic Dirac particles, provide a new perspective on the relation between condensed matter and high-energy physics. We discuss atomic collapse, a phenomenon in which discrete energy levels of superheavy atoms are transformed into resonant states. Charge impurities in graphene provide a convenient condensed matter system in which this effect can be explored. Relativistic dynamics also manifests itself in graphene p–n junctions. We show how the transport problem in the presence of a magnetic field can be solved with the help of a Lorentz transformation, and use it to investigate magnetotransport in p–n junctions. Finally, we review a recent proposal to use Fabry–Pérot resonances in p–n–p structures as a vehicle to investigate Klein scattering, another hallmark phenomenon of relativistic dynamics.     

Relativistic Quantum Mechanics as a Consequence of the Planck Mass Plasma Conjecture

The Planck mass plasma conjecture is the hypothesis that the vacuum of space is a kind of plasma composed of positive and negative Planck mass particles interacting by the Planck force over a Planck length, repulsive for equal and attractive for unequal Planck masses. The hypothesis permits to derive quantum mechanics and Lorentz invariance as asymptotic approximations for energies small compared to the Planck energy. Besides a spectrum of elementary particles greatly resembling the particles of the standard model, the hypothesis gives a value of the fine structure constant at the energy where the strong, the weak, and electromagnetic interaction become equal.     

Scheme dependence of quantum gravity on de Sitter background

We extend our investigation of the IR effects on the local dynamics of matter fields in quantum gravity. Specifically we clarify how the IR effects depend on the change of the quantization scheme: different parametrization of the metric and the matter field redefinition. Conformal invariance implies effective Lorentz invariance of the matter system in de Sitter space. An arbitrary choice of the parametrization of the metric and the matter field redefinition does not preserve the effective Lorentz invariance of the local dynamics. As for the effect of different parametrization of the metric alone, the effective Lorentz symmetry breaking term can be eliminated by shifting the background metric. In contrast, we cannot compensate the matter field redefinition dependence by such a way. The effective Lorentz invariance can be retained only when we adopt the specific matter field redefinitions where all dimensionless couplings become scale invariant at the classical level. This scheme is also singled out by unitarity as the kinetic terms are canonically normalized.     

Landau theory of relativistic Fermi liquids

A relativistic extension of the Landau Fermi liquid theory, applicable to the study of high density matter, is developed. Consequences of Lorentz invariance in the theory are explored. The formalism is illustrated by a study of relativistic Fermi systems weakly interacting via scalar and vector meson exchange. Second order exchange energies for both massless scalar and massless vector interactions are calculated in terms of Landau parameters on the Fermi surface. Zero sound and “color-plasma oscillations” are studied in quark matter with SU(3) color gluon coupling.     

Lorentz and CPT tests with spin-polarized solids

Experiments using macroscopic samples of spin-polarized matter offer exceptional sensitivity to Lorentz and CPT violation in the electron sector. Data from existing experiments with a spin-polarized torsion pendulum provide sensitivity in this sector rivaling that of all other existing experiments and could reveal spontaneous violation of Lorentz symmetry at the Planck scale.     

Are the invariance principles really truly Lorentz-covariant?

It is shown that some sections of the invariance (or symmetry) principles, such as the space reversal symmetry (or parityP) and time reversal symmetryT (of elementary particle and condensed matter physics, etc.), are not really truly Lorentz covariant and hence are dependent on the chosen inertial frame; while the world parity or the proper parityW (i.e., the spacetime reversal symmetryPT) is a truly Lorentz covariant concept, the same for all inertial observers. The basic reason for this is that in theMinkowskian space-time continuum frames of special relativity (in contrast to the space and time frames) one cannot change either space or time keeping the other one fixed and also maintain the causality requirements that all world space mappings should be timelike. Indeed, I find that the Dirac-Wigner and Lee-Yang, etc. sense of Lorentz invarianceis not in full compliance with the Einstein-Minkowskirequirements of the Lorentz covariance (in conjunction with the causality requirements) of all physical laws (i.e., the worldspaceMach principle).     

Spinor Relativity

Spinor relativity is a unified field theory, which derives gravitational and electromagnetic fields as well as a spinor field from the geometry of an eight-dimensional complex and ‘chiral’ manifold. The structure of the theory is analogous to that of general relativity: it is based on a metric with invariance group GL(ℂ²), which combines the Lorentz group with electromagnetic U(1), and the dynamics is determined by an action, which is an integral of a curvature scalar and does not contain coupling constants. The theory is related to physics on spacetime by the assumption of a symmetry-breaking ground state such that a four-dimensional submanifold with classical properties arises. In the vicinity of the ground state, the scale of which is of Planck order, the equation system of spinor relativity reduces to the usual Einstein and Maxwell equations describing gravitational and electromagnetic fields coupled to a Dirac spinor field, which satisfies a non-linear equation; an additional equation relates the electromagnetic field to the polarization of the ground state condensate.     

Gauge dependence in MBPT amplitudes

We generally discuss both electrodynamic and quantum mechanical gauge invariance. Many-body perturbation theory (MBPT) is widely used in various fields of physics and has been used to define mechanisms for collision dynamics for the interaction of matter with both photons and with charged particles. It is shown that individual MBPT amplitudes for photoionization do not obey gauge invariance, but that MBPT amplitudes summed to within a given order do satisfy gauge invariance. Explicit gauge transformations between length (L), velocity (V), and acceleration (A) forms of the dipole matrix element used for interactions of matter with photons are given.