Lorentz Frame Research Articles

On the three-dimensional sound fields from a moving monopole source above a non-locally reacting ground.

This study derives an accurate analytic solution for sound fields due to a moving point monopole source above a non-locally reacting ground. Based on the property of the invariant phase function, the acoustic pressure and normal particle velocity are matched across the air/ground interface in the frequency-wave number domain. Expressions for the integral form of the sound fields in three different frames are used to analyze and compare the original physical frame in the reception time geometry, the Lorentz frame, and the emission time frame. For ease of interpretation, the final form of the asymptotic solution is expressed in the geometry of the emission time frame. The accuracy of the asymptotic solution is validated using the direct numerical integration technique. The three-dimensional point source solution derived from the current study is compared with that of the two-dimensional line source solution. Explicit comparisons of the cylindrical and spherical wave reflection coefficients are available, allowing a better understanding of the impact of the ground wave term in the vicinity of a non-locally reflecting plane. Finally, contour plots are presented that demonstrate the need to employ the asymptotic formula for the non-locally reacting ground instead of approximating it with a locally reacting property.

Born’s rule for arbitrary Cauchy surfaces

Suppose that particle detectors are placed along a Cauchy surface $\Sigma$ in Minkowski space-time, and consider a quantum theory with fixed or variable number of particles (i.e., using Fock space or a subspace thereof). It is straightforward to guess what Born's rule should look like for this setting: The probability distribution of the detected configuration on $\Sigma$ has density $|\psi_\Sigma|^2$, where $\psi_\Sigma$ is a suitable wave function on $\Sigma$, and the operation $|\cdot|^2$ is suitably interpreted. We call this statement the "curved Born rule." Since in any one Lorentz frame, the appropriate measurement postulates referring to constant-$t$ hyperplanes should determine the probabilities of the outcomes of any conceivable experiment, they should also imply the curved Born rule. This is what we are concerned with here: deriving Born's rule for $\Sigma$ from Born's rule in one Lorentz frame (along with a collapse rule). We describe two ways of defining an idealized detection process, and prove for one of them that the probability distribution coincides with $|\psi_\Sigma|^2$. For this result, we need two hypotheses on the time evolution: that there is no interaction faster than light, and that there is no propagation faster than light. The wave function $\psi_\Sigma$ can be obtained from the Tomonaga--Schwinger equation, or from a multi-time wave function by inserting configurations on $\Sigma$. Thus, our result establishes in particular how multi-time wave functions are related to detection probabilities.

On the sound field from a source moving above non-locally reacting grounds

This paper investigates the sound fields generated by a source moving horizontally at a constant speed above a non-locally reacting flat ground. The present study offers an extension of an earlier study that focused on sound fields owing to a moving source above a locally reacting ground. However, a locally reacting ground model may not be sufficient for many acoustic “soft” grounds such as snow-covered ground or a layer of sound-absorbing materials. An integral representation for the sound fields is obtained by means of a Lorentz transform. Further analysis using the steepest descent method is then applied and leads to a uniform asymptotic approximation for the total sound fields. The explicit connection between the Lorentz frame and the physical space is explored. This allows for a closed-form analytical expression written in the emission time frame for arbitrary spatial locations of a moving source and stationary receiver. The asymptotic solution is validated by comparing it with a direct numerical solution of the time-domain linearized Euler equations. The analytical solution, which is referred to as the Dopplerized Weyl-van der Pol (D-WVDP) formula, generalizes the earlier theoretical results to allow for the source motion and non-locally reacting ground surfaces. An approximation scheme can further be identified, and its range of validity is discussed.

Boosted Kerr black holes in general relativity

A solution of Einstein's vacuum field equation is derived that describes a general boosted Kerr black hole relative to a Lorentz frame at future null infinity. The metric contains five independent parameters -- mass $m$, rotation $\omega$, boost parameter $v/c$ and the boost direction defined by $(n_1,n_2,n_3)$ satisfying $(n_1)^2+(n_2)^2+(n_3)^2=1$ -- and reduces to the Kerr black hole when the boost parameter is zero and $n_1=1$. The solution describes the most general configuration that an astrophysical black hole must have. The black hole rotates about the $z$-axis with angular momentum proportional to $m \omega$ and the geometry has just one Killing vector $\partial/\partial{u}$, where $u$ is the retarded time coordinate. The boost turns the ergosphere asymmetric, with dominant lobes in the direction opposite to the boost. The event and Cauchy horizons, defined for the case $\omega < m$, are specified respectively by the radii $r_{\pm}=m \pm \sqrt{m^2-\omega^2}$. The horizons are topologically spherical and the singularity has the topology of a circle on planes that are orthogonal to the boost direction. We argue that this black hole geometry is the natural set to describe the remnants of the recently observed gravitational wave events $GW150914$, $GW151226$, $GW170814$ and $GW170817$\cite{gw1,gw2,gw3,gw4}. In the conclusions we discuss possible astrophysical processes in the asymmetric ergosphere and the electromagnetic dynamical effects that may result from the rotating black hole moving at relativistic speeds together with the precession of the boost axis about the rotation axis of the black hole.

Completely New Gravitational Physics: The Ingenious Outside-Inside Centrifuge Mechanism of Gravity Clarified

The present work implements the idea that gravity is not a fundamental force and that the observed gravitational dynamics is the result of inertial motions within a Keplerian velocity field of the Higgs Quantum Space (HQS), giving mass and ruling the inertial motions of matter-energy. The Higgs theory introduces profound changes in the current view about the nature of empty space. It introduces the idea that a real quantum fluid medium, filling up the whole of space, gives mass to the elementary particles by the Higgs mechanism, an effect analogous to the Meissner effect, giving mass to the photons within superconductors. This HQS necessarily governs the inertial motion of matter-energy and is the locally ultimate reference for rest and for motions. The HQS materializes the local Lorentz frames (LFs), turning them into local proper LFs, intrinsically stationary with respect to the local moving HQS. This HQS also necessarily is responsible for the gravitational dynamics; because it is mass that creates the gravitational fields. The observed absence of the gravitational slowing of the GPS clocks by the solar field and the absence of light anisotropy with respect to the moving earth are both obvious signatures of the true physical mechanism of gravity. These observations demonstrate that the HQS is circulating round the sun and round earth according to Keplerian velocity fields (GM/r)1/2, closely consistent respectively with the planetary motions and the orbital motion of the Moon. In this Keplerian velocity field the planets are closely stationary with respect to the local HQS and carried by the moving HQS round the sun without the need of a central force field. The Keplerian velocity field of the HQS is the only possible imaginable mechanism able to give rise to the ingenious outside-inside centrifuge mechanism of gravity that creates a central field of centrifugal forces toward the gravitational center on all matter bodies not moving strictly along direct circular equatorial orbits. The Keplerian velocity field of the HQS is shown to appropriately create all the observed effects of the gravitational fields on matter, on light and on clocks.

Classical Relativistic Extension of Kanai’s Frictional Lagrangian

Working in an arbitrary Lorentz frame, we address the question of formulating the covariant variational principle for classical, single-particle, dissipative, relativistic mechanics. First, within a Minkowskian geometry, the basic properties of the proper time τ and the covariant velocity uμ are recapitulated. Next, using a scalar function ψ(x) and its negative derivatives ϕμ’s, we construct a covariant Lagrangian Λ that generalizes the famous Bateman-Caldirola-Kanai Lagrangian of nonrelativistic frictional mechanics. Finally, we propose a deterministic model for ψ (involving the drag coefficient A) whose explicit solution leads to relativistic damped Rayleigh motion in the rest frame of the medium.

Disentangling covariant Wigner functions for chiral fermions

We develop a general formalism for the quantum kinetics of chiral fermions in a background electromagnetic field based on a semiclassical expansion of covariant Wigner functions in the Planck constant $\hbar$. We demonstrate to any order of $\hbar$ that only the time-component of the Wigner function is independent while other components are explicit derivative. We further demonstrate to any order of $\hbar$ that a system of quantum kinetic equations for multiple-components of Wigner functions can be reduced to one chiral kinetic equation involving only the single-component distribution function. These are remarkable properties of the quantum kinetics of chiral fermions and will significantly simplify the description and simulation of chiral effects in heavy ion collisions and Dirac/Weyl semimetals. We present the unintegrated chiral kinetic equations in four-momenta up to $O(\hbar ^2)$ and the integrated ones in three-momenta up to $O(\hbar)$. We find that some singular terms emerge in the integration over the time component of the four-momentum, which result in a new source term contributing to the chiral anomaly, in contrast to the well-known scenario of the Berry phase term. Finally we rewrite our results in any Lorentz frame with a reference four-velocity and show how the non-trivial transformation of the distribution function in different frames emerges in a natural way.

Complete and consistent chiral transport from Wigner function formalism

Recently there has been significant interest in understanding the macroscopic quantum transport in a many-body system of chiral fermions. A natural framework for describing such a system which is generally out of equilibrium, is the transport equation for its phase space distribution function. In this paper, we obtain a complete solution of the covariant chiral transport for massless fermions, by starting from the general Wigner function formalism and carrying out a complete and consistent semiclassical expansion up to $\hat{\mathbf{O}}(\hbar)$ order. In particular, we clarify certain subtle and confusing issues surrounding the Lorentz non-invariance and frame dependence associated with the 3D chiral kinetic theory. We prove that such frame dependence is uniquely and completely fixed by an unambiguous definition of the $\hat{\mathbf{O}}(\hbar)$ correction to the distribution function in each reference frame.

Medium generated gap in gravity and a 3D gauge theory

It is well known that a physical medium that sets a Lorentz frame generates a Lorentz-breaking gap for a graviton. We examine such generated "mass" terms in the presence of a fluid medium whose ground state spontaneously breaks spatial translation invariance in $d = D+1$ spacetime dimensions, and for a solid in $D = 2$ spatial dimensions. By requiring energy positivity and subluminal propagation, certain constraints are placed on the equation of state of the medium. In the case of $D = 2$ spatial dimensions, classical gravity can be recast as a Chern-Simons gauge theory and motivated by this we recast the massive theory of gravity in AdS$_3$ as a massive Chern-Simons gauge theory with an unusual mass term. We find that in the flat space limit the Chern-Simons theory has a novel gauge invariance that mixes the kinetic and mass terms, and enables the massive theory with a non-compact internal group to be free of ghosts and tachyons.

A 5D, polarised, Bethe–Heitler event generator for [formula omitted] conversion

We describe a new version of the 5D, exact, polarised, Bethe–Heitler event generator of γ-ray conversions to e+e−, developed in the context of the HARPO project, that is able to simulate successive events with different photon energies and on different atomic targets without any substantial CPU overhead. The strong correlation between kinematic variables in the region where the five dimensional cross section diverges is mitigated by performing each step of the conversion in the appropriate Lorentz frame. We extend the verification range down to 1 keV above threshold and up to 1 EeV. This work could pave the way to the precise simulation of the high-performance γ-ray telescopes and polarimeters of the post-Fermi-LAT area.

Lorentz-diffeomorphism edge modes in 3d gravity

The proper definition of subsystems in gauge theory and gravity requires an extension of the local phase space by including edge mode fields. Their role is on the one hand to restore gauge invariance with respect to gauge transformations supported on the boundary, and on the other hand to parametrize the largest set of boundary symmetries which can arise if both the gauge parameters and the dynamical fields are unconstrained at the boundary. In this work we construct the extended phase space for three-dimensional gravity in first order connection and triad variables. There, the edge mode fields consist of a choice of coordinate frame on the boundary and a choice of Lorentz frame on the bundle, which together constitute the Lorentz-diffeomorphism edge modes. After constructing the extended symplectic structure and proving its gauge invariance, we study the boundary symmetries and the integrability of their generators. We find that the infinite-dimensional algebra of boundary symmetries with first order variables is the same as that with metric variables, and explain how this can be traced back to the expressions for the diffeomorphism Noether charge in both formulations. This concludes the study of extended phase spaces and edge modes in three-dimensional gravity, which was done previously by the author in the BF and Chern-Simons formulations.

Einstein’s Theory of Relativity in the Scenario of the Higgs Quantum Space Dynamics

This work is concerned about the true physical mechanism of gravity. The Higgs theory introduces important changes in Einstein’s view about the nature of empty space, about the meaning of motions and about the nature of the gravitational physics. The Higgs Quantum Space (HQS) is a real quantum fluid spatial medium, giving inertial mass to the elementary particles by the Higgs mechanism. Therefore, the HQS rules the inertial motion of matter-energy and is the local ultimate reference for rest and for motions. In this new scenario, velocity with respect to the local HQS and not relative velocity is the origin of all the effects of motion. The HQS also necessarily is responsible for the gravitational fields because it is mass that creates the gravitational fields. The observed absence of the gravitational slowing of the GPS clocks by the solar field and the absence of light anisotropy with respect to earth are both the obvious signature of the true physical mechanism of gravity in action. These observations show that the HQS is moving itself round the sun according to a Keplerian velocity field, consistent with the planetary motions, which will be shown to accurately create, besides the observed gravitational dynamics, all the observed effects of the gravitational fields on light and on clocks. Current theories explain the absence of the solar gravitational slowing of the GPS clocks with base in the principle of equivalence. In the language of the present work, the HQS materializes the local Lorentz frames (LFs), turning them into local proper LFs, intrinsically stationary with respect to the local moving HQS. In its motions, the HQS carries these local proper LFs with it round the sun, so that the planets of the solar system are stationary with respect to them, which directly predicts the absence of the gravitational slowing of the GPS clocks by the solar field, the absence of light anisotropy with respect to earth and all the other effects of the gravitational fields observed on earth.

Higgs Quantum Space Dynamics and the Nature of the Gravitational Fields

This work discusses the implications of the Higgs theory on Einstein’s General Relativity, showing that these implications accurately lead to all the experimental observations. The Higgs theory introduces the Higgs field breaking the electroweak symmetry and filling up the universe with the Higgs quantum condensate. This Higgs Quantum Space (HQS) gives inertial mass to elementary particles by the Higgs mechanism and hence necessarily is the local ultimate reference for rest and for motions. Velocity with respect to the local HQS and not relative velocity is the origin of all the effects of motion on matter-energy. Within this scenario, the observed absence of the gravitational slowing of the GPS clocks by the solar field, as well as the absence of light anisotropy with respect to earth, demonstrates that earth and also the other planets of the solar system are very nearly stationary with respect to the local HQS. This can make a sense only if the HQS is itself moving round the sun according to a Keplerian velocity field, consistent with the planetary motions. The current theories explain the absence of the solar gravitational slowing of the GPS clocks with base in the principle of equivalence. Accordingly, the local Lorentz frame (LF), moving with earth round the sun, cancels the spacetime curvature and reproduces locally the environment of special relativity. In this local environment, earth and the GPS clocks are stationary and therefore display proper time. In the scenario of the present HQS dynamics, the local HQS materializes the local LFs, turning them into local proper LFs, stationary with respect to the local HQS. In its motion, the HQS carries these local proper LFs with it round the sun. The orbiting earth is stationary with respect to the local moving HQS and necessarily too with respect to these local proper LFs, thereby canceling the effects of the gravitational field and perfectly implementing the principle of equivalence. The present work shows moreover that this Keplerian velocity field of the HQS accurately creates the observed gravitational dynamics and all the effects of the gravitational fields on matter, on light and on clocks.

Asymmetry observables for measuring spin correlations in top-quark pair production

Spin correlations between top-quark and anti-top-quark in pair production are sensitive to physics beyond the standard model. A complete set of observables, that can be used to measure all independent parameters of the production spin density matrix, is necessary to search for anomalous interactions in the production dynamics. In this letter, we provide a set of asymmetry observables for measuring all the density matrix elements. These observables are defined regardless of the production mechanism, and can be specified in any desired reference frame, particularly the laboratory frame in which the first evidence of spin correlation was observed experimentally. Our method can be used to find an optimal Lorentz frame in which the sensitivity to the density matrices is high for given production process and experimental environment, or to test possible correlations among the matrix elements.

Do non-relativistic neutrinos oscillate?

We study the question of whether oscillations between non-relativistic neutrinos or between relativistic and non-relativistic neutrinos are possible. The issues of neutrino production and propagation coherence and their impact on the above question are discussed in detail. It is demonstrated that no neutrino oscillations can occur when neutrinos that are non-relativistic in the laboratory frame are involved, except in a strongly mass-degenerate case. We also discuss how this analysis depends on the choice of the Lorentz frame. Our results are for the most part in agreement with Hinchliffe’s rule.

A new formulation of Lee-Wick quantum field theory

The Lee-Wick models are higher-derivative theories that are claimed to be unitary thanks to a peculiar cancelation mechanism. In this paper, we provide a new formulation of the models, to clarify several aspects that have remained quite mysterious, so far. Specifically, we define them as nonanalytically Wick rotated Euclidean theories. The complex energy plane is divided into disconnected regions, which can be related to one another by a well-defined, albeit nonanalytic procedure. Working in a generic Lorentz frame, the models are intrinsically equipped with the right recipe to treat the pinchings of the Lee-Wick poles, with no need of external ad hoc prescriptions. We describe these features in detail by calculating the one-loop bubble diagram and explaining how the key properties generalize to more complicated diagrams. The physical results of our formulation are different from those of the previous ones. The unusual behaviors of the physical amplitudes lead to interesting phenomenological predictions.

A boosted Kerr black hole solution and the structure of a general astrophysical black hole

A solution of Einstein's vacuum field equations that describes a boosted Kerr black hole relative to an asymptotic Lorentz frame at the future null infinity is derived. The solution has three parameters (mass, rotation and boost) and corresponds to the most general configuration that an astrophysical black hole must have; it reduces to the Kerr solution when the boost parameter is zero. In this solution the ergosphere is north-south asymmetric, with dominant lobes in the direction opposite to the boost. However the event horizon, the Cauchy horizon and the ring singularity, which are the core of the black hole structure, do not alter, being independent of the boost parameter. Possible consequences for astrophysical processes connected with Penrose processes in the asymmetric ergosphere are discussed.

Gauge invariant gluon spin operator for spinless nonlinear wave solutions

We consider nonlinear wave type solutions with intrinsic mass scale parameter and zero spin in a pure SU(2) quantum chromodynamics (QCD). A new stationary solution which can be treated as a system of static Wu–Yang monopole dressed in off-diagonal gluon field is proposed. A remarkable feature of such a solution is that it possesses a finite energy density everywhere. All considered nonlinear wave type solutions have common features: presence of the mass scale parameter, nonvanishing projection of the color fields along the propagation direction and zero spin. The last property requires revision of the gauge invariant definition of the spin density operator which is supposed to produce spin one states for the massless vector gluon field. We construct a gauge invariant definition of the classical gluon spin density operator which is unique and Lorentz frame independent.

Vlasov simulations of thermal plasma waves with relativistic phase velocity in a Lorentz boosted frame.

For certain classes of relativistic plasma problems, performing numerical calculations in a Lorentz boosted frame can be even more advantageous for gridded momentum-space-time (e.g., Vlasov) problems than has been demonstrated for position space-time problems and result in a potential reduction in the number of calculations needed by a factor ∼γ_{b}^{6}. In this study, the Lorentz boosted frame technique was applied to the problem of warm wave-breaking limits of plasma waves with relativistic phase velocity. The numerical results are consistent with analytic conclusions. By appropriate normalization and for sufficiently warm plasma, the dynamics for the Vlasov equation in different Lorentz frames were found to be independent of γ_{p}.

Lorentz constraints on massive three-point amplitudes

Using the helicity-spinor language we explore the non-perturbative constraints that Lorentz symmetry imposes on three-point amplitudes where the asymptotic states can be massive. As it is well known, in the case of only massless states the three-point amplitude is fixed up to a coupling constant by these constraints plus some physical requirements. We find that a similar statement can be made when some of the particles have mass. We derive the generic functional form of the three-point amplitude by virtue of Lorentz symmetry, which displays several functional structures accompanied by arbitrary constants. These constants can be related to the coupling constants of the theory, but in an unambiguous fashion only in the case of one massive particle. Constraints on these constants are obtained by imposing that in the UV limit the massive amplitude matches the massless one. In particular, there is a certain Lorentz frame, which corresponds to projecting all the massive momenta along the same null momentum, where the three-point massive amplitude is fully fixed, and has a universal form.