Vacuum Wave Research Articles

The dispersion relation for matter waves in a two-phase vacuum

The cosmological constant Λ of general relativity is a natural consequence of embedding Einstein's theory in a five-dimensional (5D) theory of the type needed for unification. The exact 5D solution for Λ<0 shows waves in ordinary three-dimensional (3D) space with properties similar to those of de Broglie or matter waves. Here the dispersion relation is derived for matter waves in a toy two-phase model, where regions with Λ<0 and Λ>0 average on the large scale to Λ≃0, thus providing in principle a resolution of the cosmological-constant problem. A striking result of the analysis is that the dispersion relation is bimodal, with a well-defined window of high-frequency transmission which effectively defines the speed of light.

Russian

The article analyzes the main content, functions and cognition possibilities of the three main methods of constructing physical theories: a thought experiment, mathematical hypothesis and the method of symmetries. The author follows the understanding of scientific theory as a special kind of scientific knowledge that is qualitatively different from both the sensory and empirical levels of scientific knowledge. He believes that the different levels of scientific knowledge are of particular ontology and a special object of his description. The subject of scientific theories, including physical, is a special kind of reality. This is a theoretical reality that is constructed by scientists from the objects and relations of empirical reality using such method as idealization. The main task of a scientific theory is finding and formulation of scientific laws that exist between ideal objects of theory and govern their relationships with each other. Accordingly, the special subject of scientific theory and there are special methods of construction of scientific and theoretical knowledge as knowledge of ideal objects. On the example of physical science and its history shows that during the formation and development of physical theories was invented three main methods of constructing physical theories. This is a thought experiment, mathematical hypothesis and the method of symmetries. All of these methods actually appeared only in the New Time, the time of formation of classical physics. The Creator of all three methods can rightly be called a city of Galilee. The method of thought experiment, he had received the law of inertia, the method of mathematical hypothesis - the law of free fall, and the method of symmetries was proof of the invariance of the laws of mechanics for different inertial reference frames. On the work of another physicist theorist Maxwell it is shown that the method of thought experiment, he proved the existence of a bias current, and the possibility of propagation of electromagnetic waves in vacuum. Using the method of mathematical hypotheses Maxwell formulated the basic mathematical equations of the electromagnetic theory. However, he failed to prove using the method of symmetry is the invariance of the laws of electrodynamics in different inertial reference frames. This problem was partially solved by G. Lorentz, and finally A. Einstein, Creator of the theory of relativity. They are actively used all three main methods of constructing a physical theory. Especially actively and fruitfully A. Einstein used a thought experiment method and the method of symmetries. And one of the founders of quantum mechanics, W. Heisenberg actively used the other main method of constructing physical theories - the method of mathematical hypotheses. In the middle of the twentieth century was finally realized the fundamental role of the method of symmetries in the

Propagation of gravitational waves in the nonperturbative spinor vacuum

The propagation of gravitational waves on the background of a nonperturbative vacuum of a spinor field is considered. It is shown that there are several distinctive features in comparison with the propagation of plane gravitational waves through empty space: there exists the fixed phase difference between the $h_{yy,zz}$ and $h_{yz}$ components of the wave; the phase and group velocities of gravitational waves are not equal to the velocity of light; the group velocity is always less than the velocity of light; under some conditions the gravitational waves are either damped or absent; for given frequency, there exist two waves with different wave vectors. We also discuss the possibility of experimental verification of the obtained effects as a tool to investigate nonperurbative quantum field theories.

TRAPPING ELECTROMAGNETIC SOLITONS IN CYLINDERS

Electromagnetic waves in vacuum or dielectrics can be confined in unbounded cylinders in such a way that they turn around the main axis. For particular choices of the cylinder's section, interesting stationary configurations may be assumed. By refining some results obtained in previous papers, additional more complex situations are examined here. For such peculiar guided waves an explicit expression is given in terms of Bessel's functions. Possible applications are in the development of whispering gallery resonators.

Numerical study of the Yang-Mills vacuum wave functional inD=3+1dimensions

Ratios of the true Yang-Mills vacuum wave functional, evaluated on any two field configurations out of a finite set of configurations, can be obtained from lattice Monte Carlo simulations. The method was applied some years ago to test various proposals for the vacuum wave functional in $2+1$ dimensions. In this article we use the same method to test our own proposal for the Yang-Mills ground state in $3+1$ dimensions, using two different types of test configurations: Abelian plane waves and non-Abelian constant field configurations. Our proposed vacuum state has the property of ``dimensional reduction'' at large scales, meaning that the (squared) vacuum state, evaluated on long-wavelength, large scale fluctuations, has the form of the Boltzmann weight for Yang-Mills theory in $D=3$ Euclidean dimensions. Our numerical results support this conjectured behavior. We also investigate the form of the ground state evaluated on shorter wavelength configurations.

The Hamiltonian Approach to Yang-Mills (2+1): An Update and Corrections to String Tension

Yang-Mills theories in 2+1 (or 3) dimensions are interesting as nontrivial gauge theories in their own right and as effective theories of QCD at high temperatures. I shall review the basics of our Hamiltonian approach to this theory, emphasizing symmetries with a short update on its status. We will show that the calculation of the vacuum wave function for Yang-Mills theory in 2+1 dimensions is in the lowest order of a systematic expansion. Expectation values of observables can be calculated using an effective interacting chiral boson theory, which also leads to a natural expansion as a double series in the coupling constant (to be interpreted within a resummed perturbation series) and a particular kinematical factor. The calculation of the first set of corrections in this expansion shows that the string tension is modified by about −0.3% to −2.8% compared to the lowest order value. This is in good agreement with lattice estimates.

Yang-Mills vacuum wave functional in three dimensions at weak coupling

We compute the Yang-Mills vacuum wave functional in three dimensions at weak coupling with O(e^2) precision. We use two different methods to solve the Schroedinger functional equation. One of them generalizes to O(e^2) the method followed by Hatfield at O(e). The other uses the weak coupling version of the gauge invariant formulation of the Schroedinger equation and the ground state wave functional followed by Karabali, Nair, and Yelnikov. We compare both results and discuss the differences between them.

Parametric excitation of traveling waves in a circular non-dispersive medium

This paper discusses a special type of propagating waves created by parametric excitation in a circular taught string. The string, being a non-dispersive medium propagates deformations in a similar manner to electromagnetic waves in vacuum, both have simple wavelength–frequency relationship that play an important role here. Nonlinear equations are derived under the assumption of finite deformations, whose solution produces a square-wave like, limited-amplitude, traveling wave. Closed-form expressions are obtained for the parametric excitation characteristics of the nonlinear system and the steady-state traveling waves are described by a generalized eigenvalue problem. The latter relates the nonlinear elongation of the neutral axis to the participating wavelengths forming the propagating wave. Detailed numerical simulations are provided to validate the solution and to illustrate graphically the waveforms. It is shown that propagating sinusoidal parametric excitation gives rise to various square-wave like deformation shapes which a unique phenomenon is arising in non-dispersive media.

The regularization and determination of the Yang–Mills vacuum wave functional in three dimensions at [formula omitted

We complete the computation of the Yang–Mills vacuum wave functional in three dimensions at weak coupling with O(e2) precision. We use two different methods to solve the functional Schrödinger equation. One of them generalizes to O(e2) the method followed by Hatfield at O(e)[1]. The other uses the weak coupling version of the gauge invariant formulation of the Schrödinger equation and the ground-state wave functional followed by Karabali, Nair, and Yelnikov [2]. These methods need to be carefully regularized to yield correct results. This is done in this paper with full detail.

Wheeler-DeWitt equation in3+1dimensions

Physical properties of the quantum gravitational vacuum state are explored by solving a lattice version of the Wheeler--DeWitt equation. The constraint of diffeomorphism invariance is strong enough to uniquely determine part of the structure of the vacuum wave functional in the limit of infinitely fine triangulations of the three-sphere. In the large fluctuation regime, the nature of the wave function solution is such that a physically acceptable ground state emerges, with a finite nonperturbative correlation length naturally cutting off any infrared divergences. The location of the critical point in Newton's constant ${G}_{c}$, separating the weak from the strong coupling phase, is obtained, and it is inferred from the general structure of the wave functional that fluctuations in the curvatures become unbounded at this point. Investigations of the vacuum wave functional further suggest that for weak enough coupling, $G<{G}_{c}$, a pathological ground state with no continuum limit appears, where configurations with small curvature have vanishingly small probability. One would then be lead to the conclusion that the weak coupling, perturbative ground state of quantum gravity is nonperturbatively unstable and that gravitational screening cannot be physically realized in the lattice theory. The results we find tend to be in general agreement with the Euclidean lattice gravity results and would suggest that the Lorentzian and Euclidean lattice formulations of gravity ultimately describe the same underlying nonperturbative physics.

Nonclassicality in Raman scattering: Quantum entanglement, squeezing of vacuum fluctuations, sub-shot noise and joint photon–phonon number and integrated-intensity distributions

A completely quantum description of Raman process is used to investigate the nonclassical properties of the modes in the stimulated, spontaneous and partially spontaneous Raman process. Both coherent scattering (where all the initial modes are coherent) and chaotic scattering (where initial phonon mode is chaotic and all the other modes are coherent) are studied. Nonclassical character of Raman process is observed by means of intermodal entanglement, single mode and intermodal squeezing of vacuum fluctuations, sub-shot noise and wave variances. Joint photon-phonon number and integrated-intensity distributions are then used to illustrate the observed nonclassicalities. Conditional and difference number distributions are also provided to illustrate the nonclassical character. The mutual relation between the obtained nonclassicalities and their variations dependent on phases, rescalled time and ratio of coupling constants are also reported.

Vacuum waves

An exact solution of the five-dimensional field equations is studied which describes waves in the classical Einstein vacuum. While the solution is essentially 5D in nature, the waves exist in ordinary 3D space. They should not be confused with standard gravitational waves, since their phase velocity can exceed that of light. They resemble de Broglie waves, and may give insight to wave-particle duality.

Dynamical Quarkonia Suppression from Complex Potentials

I address the effect that a temperature dependent potential has on the suppression of heavy quarkonia states in deconfined hadronic matter. I focus on a simple medium: a homogenous, fixed temperature and deconfined system with a finite lifetime (QGP-brick). Assuming that all the interactions of a heavy quark anti-quark (Q – Q̄) pair with the medium can be recast into an in-medium potential, I solve the time dependent Schrödinger equation to evolve the density matrix which describes the hard pair production and its connection to the final distribution of hadrons after the medium disappears. For those temperatures in which bound states survive in the medium, I find a non-trivial dependence of the production of excited quarkonia states on the in-medium levels, due to the mixing of vacuum and in-medium wave functions. This mixing leads, in particular, to the enhancement of the relative abundance of 2S to 1S states for the case in which the in-medium ground state of the Q – Q̄ system is dissolved.

Dynamical quarkonia suppression in a QGP-brick

I address the effect that a temperature dependent potential has on the suppression of heavy quarkonia states in deconfined hadronic matter. I focus on a simple medium: a homogenous, fixed temperature and deconfined system with a finite lifetime (QGP-brick). Assuming that all the interactions of a heavy quark anti-quark ($Q-\bar Q$) pair with the medium can be recast into an in-medium potential, I solve the time dependent Schr\"odinger equation to evolve the density matrix which describes the hard pair production and its connection to the final distribution of hadrons after the medium disappears. For those temperatures in which bound states survive in the medium, I find a non-trivial dependence of the production of excited quarkonia states on the in-medium levels, due to the mixing of vacuum and in-medium wave functions. This mixing leads, in particular, to the enhancement of the relative abundance of 2S to 1S states for those systems in which the in-medium ground state of the $Q-\bar Q$ system is dissolved or close to threshold. I also explore quarkonia production in a non-homogeneous expanding medium and find that the finite formation time effects arising from the low binding energies of in-medium states lead to the insensitivity of the heavy mesons yield to the hottest part of the system evolution.

Relative Transformation of Matter Motion Based on theArbitrary Wave Velocity

Albert Einstein proposed the special relativity under the condition that using light wave as the signal and the propagation velocity of light wave in vacuum is a constant. According to the special relativity, Albert Einstein concluded that the rest mass of photon is zero and the velocity of any matter could not exceed that of light. These conclusions are doubted by many experimental phenomenons. In this paper, the wave that could carry arbitrary signals was used to transfer information. Assuming the velocity of the wave is a constant, the parameters of matter motion was calculated with the Lorentz transform. The results show that rest mass of photon may be not zero, when the wave with a velocity exceeding that of light is used as the propagation carrier. And also, obtain the conclusion that the powerful gravitation would change the density distribution of photon in the universe. The light wave will change the direction of propagation according to the density distribution of photon. As a result, the route of light propagation will change too. Photons will be attracted into the black hole continually by its limitless attraction force. In addition, wave propagating though photons could not escape the gravitation of the black hole.

Potential of the effective Polyakov line action from the underlying lattice gauge theory

I adapt a numerical method, previously applied to investigate the Yang-Mills vacuum wave functional, to the problem of extracting the effective Polyakov line action from $\mathrm{SU}(N)$ lattice gauge theories, with or without matter fields. The method can be used to find the variation of the effective Polyakov line action along any trajectory in field configuration space; this information is sufficient to determine the potential term in the action and strongly constrains the possible form of the kinetic term. The technique is illustrated for both pure and gauge Higgs SU(2) lattice gauge theory at finite temperature. A surprise, in the pure gauge theory, is that the potential of the corresponding Polyakov line action contains a nonanalytic (yet center-symmetric) term proportional to $|P{|}^{3}$, where $P$ is the trace of the Polyakov line at a given point, in addition to the expected analytic terms proportional to even powers of $P$.

Universal phase relation between longitudinal and transverse fields observed in focused terahertz beams

We directly observe longitudinal electromagnetic fields in focused freely propagating terahertz (THz) beams of radial and linear polarization. Employing electro-optic detection, which is phase sensitive, allows one to selectively detect longitudinal and transverse field components. A phase shift of π/2 between the transverse and longitudinal field components is revealed. This phase shift is of universal nature, as it does not depend on the mode, frequency and focusing conditions. We show that the universal phase relation is a direct consequence of the divergence-free nature of electromagnetic waves in vacuum. In the experiments, we observe the phase shift of π/2 for all frequency components of single-cycle THz radiation pulses of both radial and linear polarization. Additionally, we show that the longitudinal field of a radially polarized THz beam has a smaller spot size as compared with the transverse field of a linearly polarized beam that is focused under the same conditions. For field-sensitive measurements this property can be exploited even for moderate focusing conditions. Furthermore, the phase-sensitive detection of longitudinal electromagnetic fields opens up new possibilities to study their interaction with electronic excitations in semiconductor nanostructures.

Electromagnetic shock wave in nonlinear vacuum: exact solution

An analytical approach to the theory of electromagnetic waves in nonlinear vacuum is developed. The evolution of the pulse is governed by a system of nonlinear wave vector equations. An exact solution with its own angular momentum in the form of a shock wave is obtained.

SUPERLUMINAL NEUTRINOS FROM SPECIAL RELATIVITY WITH DE SITTER SPACETIME SYMMETRY

We explore the recent OPERA experiment of superluminal neutrinos in the framework of special relativity with de Sitter spacetime symmetry (dS-SR). According to Einstein, a photon is treated as a massless particle in the framework of special relativity. In special relativity (SR) we have the universal parameter c, the photon velocity c photon and the phase velocity of a light wave in vacuum c wave = λν. Due to the null experiments of Michelson–Morley we have c = c wave . The parameter c photon is determined by the Noether charges corresponding to the spacetime symmetries of SR. In Einstein's special relativity (E-SR) we have c = c photon . In dS-SR, i.e. the special relativity with SO(4, 1) de Sitter spacetime symmetry, we have c photon > c. In this paper, the OPERA datum are examined in the framework of dS-SR. We show that OPERA anomaly is in agreement with the prediction of dS-SR with R≃1.95×1012 l.y. Based on the p-E relation of dS-SR, we also prove that the Cohen and Glashow's argument of possible superluminal neutrino's Cherenkov-like radiation is forbidden. We conclude that OPERA and ICARUS results are consistent and they are explained in the dS-SR framework.

Temporal Wilson loop in the Hamiltonian approach in Coulomb gauge

We investigate the temporal Wilson loop using the Hamiltonian approach to Yang-Mills theory. In simple cases such as the Abelian theory or the non-Abelian theory in (1+1) dimensions, the known results can be reproduced using unitary transformations to take care of time evolution. We show how Coulomb gauge can be used for an alternative solution if the exact ground state wave functional is known. In the most interesting case of Yang-Mills theory in (3+1) dimensions, the vacuum wave functional is not known, but recent variational approaches in Coulomb gauge give a decent approximation. We use this formulation to compute the temporal Wilson loop and find that the Wilson and Coulomb string tension agree within our approximation scheme. Possible improvements of these findings are briefly discussed.