Search Results (11)

The microscopic origin of the de Sitter entropy remains a central puzzle in quantum gravity that is related to the cosmological constant problem. Within the paradigm of $\mathcal{H}$olographic $\mathcal{N}$aturalness, we propose that this entropy is carried by a vast number of light, coherent degrees of freedom—called “hairons”—which emerge as the moduli of gravitational instantons on orbifolds. Starting from the Euclidean de Sitter instanton ($S^4$), we construct a new class of orbifold gravitational instantons, $S^4/{\mathbb{Z}}_N$, where N corresponds to the de Sitter entropy. We demonstrate that the dimension of the moduli space of these instantons scales linearly with N, and we identify these moduli with the hairon fields. A ${\mathbb{Z}}_N$ symmetry, derived from Wilson loops in the instanton background, ensures the distinguishability of these modes, leading to the correct entropy count. The hairons acquire a mass of the order of the Hubble scale and exhibit negligible mutual interactions, suggesting that the de Sitter vacuum is a coherent state, or Bose–Einstein condensate, of these fundamental excitations. Then, we present a novel framework which unifies neutrino mass generation with the cosmological constant through gravitational topology and holography. The small neutrino mass scale emerges naturally from first principles, without requiring new physics beyond the Standard Model and Gravity. The gravitational Chern–Simons structure and its anomaly with neutrinos force a topological Higgs mechanism, leading to neutrino condensation via $S^4/{\mathbb{Z}}_N$ gravitational instantons. The number of topological degrees of freedom $N\sim M_{\mathrm{P}}^2/\mathrm{\Lambda }\sim {10}^{120}$ provides both the holographic counting of the de Sitter entropy and a $1/N$information see-saw mechanism for neutrino masses. Our framework makes the following predictions: (i) a neutrino superfluid condensation forming Cooper pairs below meV energies, as a viable candidate for cold dark matter; (ii) a possible resolution of the strong CP problem through a QCD composite axion state; (iii) time-varying neutrino masses which track the evolution of dark energy; and (iv) several distinctive signatures in astroparticle physics, ultra-high-energy cosmic rays and high magnetic field experiments. Full article

We conjecture that during the time period preceding the inflationary epoch, the background matter was initially a condensate formed from a many-body system of indistinguishable particles whose states were in a quantum superposition. This resulted in the occurrence of a statistical ensemble of spacetimes, thus causing the probabilistic uncertainty in the spacetime geometry of the pre-inflationary multiverse. Then, at a certain moment in time, a measurement event occurred, which broke the linear superposition and reduced the primordial geometrical multiverse to a single state. This process can be described as a quantum Shannon information transfer, which induces logarithmic nonlinearity in the evolution equations of the background system. The latter, therefore, transformed into a logarithmic quantum liquid of a superfluid type and formed the physical vacuum. This measurement also generated the primary mass energy necessary for the Universe’s further evolution into the inflationary epoch, followed by the contemporary “dark energy” era. Full article

We propose that the observed value of the cosmological constant may be explained by a fundamental uncertainty in the spacetime metric, which arises when combining the principle that mass and energy curve spacetime with the quantum uncertainty associated with particle localization. Since the position of a quantum particle cannot be sharply defined, the gravitational influence of such particles leads to intrinsic ambiguity in the formation of spacetime geometry. Recent experimental studies suggest that gravitational effects persist down to length scales of approximately ${10}^{-5}$ m, while quantum coherence and macroscopic quantum phenomena such as Bose–Einstein condensation and superfluidity also manifest at similar scales. Motivated by these findings, we identify a length scale of spacetime uncertainty, $L_Z\sim 2.2\times {10}^{-5}$ m, which corresponds to the geometric mean of the Planck length and the radius of the observable universe. We argue that this intermediate scale may act as an effective cutoff in vacuum energy calculations. Furthermore, we explore the interpretation of dark energy as a Bose–Einstein distribution with a characteristic reduced wavelength matching this uncertainty scale. This approach provides a potential bridge between cosmological and quantum regimes and offers a phenomenologically motivated perspective on the cosmological constant problem. Full article

The laminar constant-velocity superflow of a physical vacuum modelled by logarithmic quantum Bose liquid is considered. We demonstrate that this three-dimensional non-relativistic quantum flow generates a four-dimensional relativistic quinton system, which comprises the dilaton and quintom (a combination of the quintessence and tachyonic phantom fields); all three fields are thus shown to be projections of the dynamical evolution of superfluid vacuum density and its fluctuations onto the measuring apparatus of a relativistic observer. The unified model describes the transition from the inflationary period in the early universe to the contemporary accelerating expansion of the universe, commonly referred to as the “dark energy” period. The quintessence and tachyonic scalar components of the derived model turn out to be non-minimally coupled, which is a hitherto unexplored generalization of cosmological phantom models. Full article

A review of recent advances in spacetime optics is given, with special emphasis on time refraction. This is a basic optical process, occurring at a temporal discontinuity or temporal boundary, which is able to produce various different effects, such as frequency shifts, energy amplification, time reflection, and photon emission. If, instead of a single discontinuity, we have two reverse temporal boundaries, we can form a temporal beam splitter, where temporal interferences can occur. It will also be shown that, in the presence of an axis of symmetry, such as a magnetic field, the temporal beam splitter can induce a rotation of the initial polarization state, similar to a Faraday rotation. Recent work on time crystals, superluminal fronts, and superfluid light will be reviewed. Time gates based on spacetime optical effects will be discussed. We also mention recent work on optical metamaterials. Finally, the quantum properties of time refraction, which imply the emission of photon from vacuum, are considered, while similar problems in high-energy QED associated with electron–positron pairs are briefly mentioned. Full article

We consider the discrete $Z_4$ symmetry $\widehat{\mathbf{i}}$, which takes place in the scenario of quantum gravity where the gravitational tetrads emerge as the order parameter—the vacuum expectation value of the bilinear combination of fermionic operators. Under this symmetry operation, $\widehat{\mathbf{i}}$, the emerging tetrads are multiplied by the imaginary unit, $\widehat{\mathbf{i}}{e}_{\mu }^a=-i{e}_{\mu }^a$. The existence of such symmetry and the spontaneous breaking of this symmetry are also supported by the consideration of the symmetry breaking scheme in the topological superfluid ³He-B. The order parameter in ³He-B is also the bilinear combination of the fermionic operators. This order parameter is the analog of the tetrad field, but it has complex values. The $\widehat{\mathbf{i}}$-symmetry operation changes the phase of the complex order parameter by $\pi /2$, which corresponds to the $Z_4$ discrete symmetry in quantum gravity. We also considered the alternative scenario of the breaking of this $Z_4$ symmetry, in which the $\widehat{\mathbf{i}}$-operation changes sign of the scalar curvature, $\widehat{\mathbf{i}}\mathcal{R}=-\mathcal{R}$, and thus the Einstein–Hilbert action violates the $\widehat{\mathbf{i}}$-symmetry. In the alternative scenario of symmetry breaking, the gravitational coupling $K=1/16\pi G$ plays the role of the order parameter, which changes sign under $\widehat{\mathbf{i}}$-transformation. Full article

Within the frameworks of the logarithmic superfluid model of physical vacuum, we demonstrate the emergence of four-dimensional curved spacetime from the dynamics of quantum Bose liquid in three-dimensional Euclidean space. We derive the metric tensor of this spacetime and study its special cases and limits, such as the linear-phase flow and linearized gravity limit. We show that the value of speed of light, which is a fundamental parameter in a theory of relativity, is a derived notion in superfluid vacuum theory: its value is a combination of the Planck constant and original parameters of the background superfluid. As for the gravitational potential, then it can be defined in terms of the quantum information entropy of the background superfluid. Thus, relativistic gravity and curved spacetime are shown to result from the dynamics of quantum excitations of the background superfluid being projected onto the measurement apparatus of a relativistic observer. Full article

In a basis of the space-time coordinate frame four quaternions discovered by Hamilton can be used. For subsequent reproduction of the coordinate frame these four quaternions are expanded to four 4 × 4 matrices with real-valued matrix coefficients −0 and 1. This group set is isomorphic to the SU(2) group. Such a matrix basis introduces extra six degrees of freedom of matter motion in space-time. There are three rotations about three space axes and three boosts along these axes. Next one declares the differential generating operators acting on the energy-momentum density tensor written in the above quaternion basis. The subsequent actions of this operator together with its transposed one on the above tensor lead to the emergence of the gravitomagnetic equations that are like the Maxwell equations. Wave equations extracted from the gravitomagnetic ones describe the propagation of energy density waves and their vortices through space. The Dirac equations and their reduction to two equations with real-valued functions, the quantum Hamilton-Jacobi equations and the continuity equations, are considered. The Klein-Gordon equations arising on the mass shell hints to the alternation of the paired fermion fields and boson ones. As an example, a Feynman diagram of an electron–positron time crystal is illustrated. Full article

Herein is a review of the essentials of Modified Newtonian Dynamics (MOND) versus dark matter models based on Superfluids for modeling galactic rotation curves. We review the successes and issues of both approaches. We then mention a recent alternative based on the Superfluid Vacuum Theory (SVT) with a nonlinear logarithmic Schrödinger equation (LogSE) which reconciles both approaches, retains the essential success of MOND and the Superfluid nature but does not necessitate the hypothesis of processes including dark matter. We conclude with the implications of this SVT alternative on quantum theory itself. Full article

Quaternions are a natural framework of 4D space-time, where the unit element relates to time, and three others relate to 3D space. We define a quaternion set of differential torsion operators (shifts with rotations) that act to the energy-momentum tensor written on the same quaternion basis. It results in the equations of gravity-torsion (gravitomagnetic) fields that are similar to Maxwell’s equations. These equations are parent equations, generating the following equations: (a) equations of the transverse gravity-torsion waves; (b) the vorticity equation describing vortices orbital speed of which grows monotonically in the vortex core but far from it, it goes to a permanent level; (c) the modified Navier–Stokes equation leading to the Schrödinger equation in the nonrelativistic limit and to the Dirac equation in the relativistic limit. The Ginsburg–Landau theory of superfluidity resulting from the Schrödinger equation shows the emergence of coupled proton-antiproton pairs forming the Bose–Einstein condensate. In the final part of the article, we describe Samokhvalov’s experiment with rotating nonelectric, nonferromagnetic massive disks in a vacuum. It demonstrates an unknown force transferring the rotational moment from the driving disk to a driven one. It can be a manifestation of the dark matter. For studying this phenomenon, we propose a neutron interference experiment that is like the Aharonov–Bohm one. Full article

We derive an effective gravitational potential, induced by the quantum wavefunction of a physical vacuum of a self-gravitating configuration, while the vacuum itself is viewed as the superfluid described by the logarithmic quantum wave equation. We determine that gravity has a multiple-scale pattern, to such an extent that one can distinguish sub-Newtonian, Newtonian, galactic, extragalactic and cosmological terms. The last of these dominates at the largest length scale of the model, where superfluid vacuum induces an asymptotically Friedmann–Lemaître–Robertson–Walker-type spacetime, which provides an explanation for the accelerating expansion of the Universe. The model describes different types of expansion mechanisms, which could explain the discrepancy between measurements of the Hubble constant using different methods. On a galactic scale, our model explains the non-Keplerian behaviour of galactic rotation curves, and also why their profiles can vary depending on the galaxy. It also makes a number of predictions about the behaviour of gravity at larger galactic and extragalactic scales. We demonstrate how the behaviour of rotation curves varies with distance from a gravitating center, growing from an inner galactic scale towards a metagalactic scale: A squared orbital velocity’s profile crosses over from Keplerian to flat, and then to non-flat. The asymptotic non-flat regime is thus expected to be seen in the outer regions of large spiral galaxies. Full article