Local Lorentz Frame Research Articles

A Causal Net approach to Relativistic Quantum Mechanics and Gravitation

In this paper we discuss a causal network model to describe quantum mechanics and gravittation, where space–time is built solely from point events and connecting probabilities. A causal net provides a representation which combines the quantum complementary features of both partticles and waves as each vertex on the causal net represents a possible point event or particle observation. Simultaneity on the causal net is defined by hyperplanes of equivalent proper time. The causal net model when constructed in Minkowksi space–time is shown to lead to a formulation for relativistic quantum mechanics including the Dirac equation. In a curved Riemann space–time the causal paths of the causal net are geodesics and in the local Lorentz frame the net probabilities and the Dirac formalism are preserved. The variation of space–time density of events in the causal paths modifies the metric and provides a space–time curvature leading to the Hilbert action associated with general relativity. Consideration of the Schwarzchild metric shows that in classical limit the perturbation in the density of possible events is proportional to the Newtonian gravitational potential.

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.

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.

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.

Proposal for the proper gravitational energy–momentum tensor

We propose a gravitational energy–momentum (GEMT) tensor of the general relativity obtained using Noether’s theorem. It transforms as a tensor under general coordinate transformations. One of the two indices of the GEMT labels a local Lorentz frame that satisfies the energy–momentum conservation law. The energies for a gravitational wave, a Schwarzschild black hole and a Friedmann–Lemaitre–Robertson–Walker (FLRW) universe are calculated as examples. The gravitational energy of the Schwarzschild black hole exists only outside the horizon, its value being the negative of the black hole mass.

Local Lorentz transformations and Thomas effect in general relativity

The tetrad method is used for an introduction of local Lorentz frames and a detailed analysis of local Lorentz transformations. A formulation of equations of motion in local Lorentz frames is based on the Pomeransky-Khriplovich gravitoelectromagnetic fields. These fields are calculated in the most important special cases and their local Lorentz transformations are determined. The local Lorentz transformations and the Pomeransky-Khriplovich gravitoelectromagnetic fields are applied for a rigorous derivation of a general equation for the Thomas effect in Riemannian spacetimes and for a consideration of Einstein's equivalence principle and the Mathisson force.

Construction of energy–momentum tensor of gravitation

We construct the gravitational energy–momentum tensor in general relativity through the Noether theorem. In particular, we explicitly demonstrate that the constructed quantity can vary as a tensor under the general coordinate transformation. Furthermore, we verify that the energy–momentum conservation is satisfied because one of the two indices of the energy–momentum tensor should be in the local Lorentz frame. It is also shown that the gravitational energy and the matter one cancel out in certain space-times.

Derivative of the light frequency shift as a measure of spacetime curvature for gravitational wave detection

The measurement of frequency shifts for light beams exchanged between two test masses nearly in free fall is at the heart of gravitational wave detection. It is envisaged that the derivative of the frequency shift is in fact limited by differential forces acting on those test masses. We calculate the derivative of the frequency shift with a fully covariant, gauge-independent and coordinate-free method. This method is general and does not require a congruence of nearby beams' null geodesics as done in previous work. We show that the derivative of the parallel transport is the only means by which gravitational effects shows up in the frequency shift. This contribution is given as an integral of the Riemann tensor --the only physical observable of curvature-- along the beam's geodesic. The remaining contributions are: the difference of velocities, the difference of non-gravitational forces, and finally fictitious forces, either locally at the test masses or non-locally integrated along the beam's geodesic. As an application relevant to gravitational wave detection, we work out the frequency shift in the local Lorentz frame of nearby geodesics.

Low energy description of quantum gravity and complementarity

We consider a framework in which low energy dynamics of quantum gravity is described preserving locality, and yet taking into account the effects that are not captured by the naive global spacetime picture, e.g. those associated with black hole complementarity. Our framework employs a “special relativistic” description of gravity; specifically, gravity is treated as a force measured by the observer tied to the coordinate system associated with a freely falling local Lorentz frame. We identify, in simple cases, regions of spacetime in which low energy local descriptions are applicable as viewed from the freely falling frame; in particular, we identify a surface called the gravitational observer horizon on which the local proper acceleration measured in the observer's coordinates becomes the cutoff (string) scale. This allows for separating between the “low-energy” local physics and “trans-Planckian” intrinsically quantum gravitational (stringy) physics, and allows for developing physical pictures of the origins of various effects. We explore the structure of the Hilbert space in which the proposed scheme is realized in a simple manner, and classify its elements according to certain horizons they possess. We also discuss implications of our framework on the firewall problem. We conjecture that the complementarity picture may persist due to properties of trans-Planckian physics.

SU(2) gauge symmetry in gravity phase space

The Hamiltonian formulation of the Holst action in vacuum and in the presence of matter fields is analyzed in a generic local Lorentz frame. It is elucidated how the SU(2) gauge symmetry is inferred by reducing the set of constraints to a first-class one. The consequences of the proposed approach for Loop Quantum Gravity and Spin Foam models are discussed.

Gravity in the presence of fermions as an SU(2) gauge theory

The Hamiltonian formulation of the Holst action in the presence of a massless fermion field with a nonminimal Lagrangian is performed without any restriction on the local Lorentz frame. It is outlined that the phase-space structure does not resemble that of a background-independent Lorentz gauge theory, as some additional constraints are present. Proper phase-space coordinates are introduced, such that SU(2) connections can be defined, and the vanishing of conjugate momenta to boost variables is predicted. Finally, it is demonstrated that for a particular value of the nonminimal parameter, the kinematics coincides with that of a background-independent SU(2) gauge theory, and the Immirzi parameter becomes the coupling constant of such an interaction between fermions and the gravitational field.

Matter in loop quantum gravity without time gauge: A nonminimally coupled scalar field

We analyze the phase space of gravity non-minimally coupled to a scalar field in a generic local Lorentz frame. We reduce the set of constraints to a first-class one by fixing a specific hypersurfaces in the phase space. The main issue of our analysis is to extend the features of the vacuum case to the presence of scalar matter by recovering the emergence of an SU(2) gauge structure and the non-dynamical role of boost variables. Within this scheme, the super-momentum and the super-Hamiltonian are those ones associated with a scalar field minimally coupled to the metric in the Einstein frame. Hence, the kinematical Hilbert space is defined as in canonical Loop Quantum Gravity with a scalar field, but the differences in the area spectrum are outlined to be the same as in the time-gauge approach.

Towards Loop Quantum Gravity without the Time Gauge

The Hamiltonian formulation of the Holst action is reviewed and it provides a solution of second-class constraints corresponding to a generic local Lorentz frame. Within this scheme the form of rotation constraints can be reduced to a Gauss-like one by a proper generalization of Ashtekar-Barbero-Immirzi connections. This result emphasizes that the loop quantum gravity quantization procedure can be applied when the time-gauge condition does not stand.

Unified Field Theory From Enlarged Transformation Group. The Covariant Derivative for Conservative Coordinate Transformations and Local Frame Transformations

Pandres has developed a theory in which the geometrical structure of a real four-dimensional space-time is expressed by a real orthonormal tetrad, and the group of diffeomorphisms is replaced by a larger group called the conservation group. This paper extends the geometrical foundation for Pandres’ theory by developing an appropriate covariant derivative which is covariant under all local Lorentz (frame) transformations, including complex Lorentz transformations, as well as conservative transformations. After defining this extended covariant derivative, an appropriate Lagrangian and its resulting field equations are derived. As in Pandres’ theory, these field equations result in a stress-energy tensor that has terms which may automatically represent the electroweak field. Finally, the theory is extended to include 2-spinors and 4-spinors.

Interaction of plane gravitational waves with a Fabry-Perot cavity in the local Lorentz frame

We analyze the interaction of the plane `$+$'-polarized gravitational waves with a Fabry-Perot cavity in the local Lorentz frame of the cavity's input mirror outside of the range of long-wave approximation with the force of radiation pressure taken into account. The obtained detector's response signal is represented as a sum of two parts: (i) the phase shift due to displacement of a movable mirror under the influence of a gravitational wave and the force of light pressure, and (ii) the phase shift due to the direct interaction of a gravitational wave with light wave inside the cavity. We obtain the formula for the movable mirror's law of motion paying close attention to the phenomena of optical rigidity, radiative friction, and direct coupling of a gravitational wave to light wave. Some issues concerning the detection of high-frequency gravitational waves and the role of optical rigidity in it are discussed. We also examine in detail special cases of optical resonance and small detuning from it and compare our results with the known ones.

Transformations of Ramond–Ramond fields and space–time spinors

We explicitly construct the SO(d,d) transformations of Ramond-Ramond field strengths and potentials, along with those of the space-time supersymmetry parameters, the gravitinos and the dilatinos in type-II theories. The results include the case when the SO(d,d) transformation involves the time direction. The derivation is based on the compatibility of SO(d,d) transformations with space-time supersymmetry, which automatically guarantees compatibility with the equations of motion. It involves constructing the spinor representation of a twist that an SO(d,d) action induces between the local Lorentz frames associated with the left- and right-moving sectors of the worldsheet theory. The relation to the transformation of R-R potentials as SO(d,d) spinors is also clarified.

T-duality, space-time spinors and R–R fields in curved backgrounds

We obtain the T-duality transformations of space-time spinors (the supersymmetry transformation parameters, gravitinos and dilatinos) of type-II theories in curved backgrounds with an isometry. The transformation of the spinor index is shown to be a consequence of the twist that T-duality introduces between the left- and right-moving local Lorentz frames. The result is then used to derive the T-duality action on Ramond–Ramond field strengths and potentials in a simple way. We also discuss the massive IIA theory and, using duality, give a short derivation of “mass”-dependent terms in the Wess–Zumino actions on the D-brane world-volumes.

Note on manifest Lorentz and general coordinate invariance in duality symmetric models

We consider a generalization of a duality symmetric model proposed by Schwarz and Sen [J.H. Schwarz and A. Sen, Nucl. Phys. B 411 (1994) 35]. It is based on enlarging the model with a dynamical vector field being a time-like component of a local Lorentz frame. This allows one to preserve the manifest Lorentz invariance of the model in flat space-time. The presence of this field is regarded as a relic of gravitational interaction which respects the general coordinate invariance in curved space-time but breaks the local Lorentz symmetry in tangent space down to its spacial subgroup.

Synchrotron Radiation: an Inverse Compton Effect

Synchrotron radiation in a static homogeneous magnetic field is considered from the viewpoint of inverse Compton scattering of equivalent photons in a generalization of the Fermi-Weizsacker-Williams method. The charged particle trajectory in its orbital plane is treated as a set of infinitesimal segments and, in a corresponding local Lorentz frame, the influence of each segment on the particle, is approximated by an equivalent electromagnetic wave which undergoes Compton interaction with the particle. The complex amplitudes of the scattered radiation from all elements are added coherently, on returning to the laboratory frame, to yield the total radiated intensity

Relativistic transport theory for cosmic rays

The general relativistic form of Liouville's equation or the Boltzmann equation is used to derive relativistic equations describing the transport of cosmic rays in a magnetized plasma supporting a spectrum of hydromagnetic waves. A local Lorentz frame (the comoving frame) moving with the waves or turbulence scattering the cosmic rays is used to specify the individual particle momentum. Since the comoving frame is in general a noninertial frame in which the observer's (spatial) volume element is expanding (contracting) and shearing, geometric energy change terms appear in the cosmic-ray continuity equation which consist of the relativistic generalization of the adiabatic deceleration term obtained in previous analyses, and a further term involving the acceleration vector of the scatterers. Moment equations which are differential with respect to the magnitude of the particle momentum p' are obtained. When integrated over all momenta p', the moment equations lead to a hydrodynamical description of cosmic-ray transport. The diffusion approximation is used to close the moment equations, and to obtain a convection-diffusion form of the continuity equation. A brief discussion of the drift approximation is given, which in the lowest order approximation leads to a pitch-angle-dependent propagation equation for the cosmic rays. Possible astrophysical applications of themore » equations are discussed.« less