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Yaakov Friedman

Publications and source records attributed to Yaakov Friedman.

At least 19 recordsLinked to original sources
arXiv2026

Polarization structure of gravitational waves in extended relativity

We analyze the polarization structure of gravitational waves in the framework of Extended Relativity (ER), using the deviation tensor as the fundamental observable quantity. Starting from the point-source solution, we derive the radiation field of a compact binary in the wave zone and express the deviation tensor in a form in which the spacetime dependence is carried entirely by the retarded phase, while the tensorial coefficients depend only on the inclination angle of the source. This representation allows for a unified treatment of detector responses. For interferometric detectors, the signal is governed by the tidal matrix, which depends on second derivatives of the deviation tensor. For pulsar timing arrays (PTAs), the response follows from null geodesic propagation and reduces to boundary terms, so that the observable is determined by the projection $k^\mu k^\nu h_{\mu\nu}$ evaluated at the emission and reception points. A key result is that the polarization components are not independent: the relative amplitudes of tensor, vector, and scalar contributions are fixed by the source geometry. This leads to a constrained family of polarization states and corresponding PTA correlation patterns. The formulation provides a direct connection between the theoretical structure of ER and observable signatures.

gr-qc↗
arXiv2021

Representation of symmetry transformations on the sets of tripotents of spin and Cartan factors

There are six different mathematical formulations of the symmetry group in quantum mechanics, among them the set of pure states $\mathbf{P}$ -- i.e., the set of one-dimensional projections on a complex Hilbert space $H$ -- and the orthomodular lattice $\mathbf{L}$ of closed subspaces of $H$. These six groups are isomorphic when the dimension of $H$ is $\geq 3$. Despite of the difficulties caused by $M_2(\mathbb{C})$, rank two algebras are used for quantum mechanics description of the spin state of spin-$\frac12$ particles, there is a counterexample for Uhlhorn's version of Wigner's theorem for such state space. In this note we prove that in order that the description of the spin will be relativistic, it is not enough to preserve the projection lattice equipped with its natural partial order and orthogonality, but we also need to preserve the partial order set of all tripotents and orthogonality among them (a set which strictly enlarges the lattice of projections). Concretely, let $M$ and $N$ be two atomic JBW$^*$-triples not containing rank-one Cartan factors, and let $\mathcal{U} (M)$ and $\mathcal{U} (N)$ denote the set of all tripotents in $M$ and $N$, respectively. We show that each bijection $Φ: \mathcal{U} (M)\to \mathcal{U} (N)$, preserving the partial ordering in both directions, orthogonality in one direction and satisfying some mild continuity hypothesis can be extended to a real linear triple automorphism. This, in particular, extends a result of Moln{á}r to the wider setting of atomic JBW$^*$-triples not containing rank-one Cartan factors, and provides new models to present quantum behavior.

quant-ph↗
arXiv2019

New metrics of a spherically symmetric gravitational field passing classical tests of General Relativity

A general form of a metric preserving all symmetries of a spherically symmetric gravitational field and angular momentum in spherical coordinates is obtained. Such metric may have $g_{01}(r)\neq 0$. The Newtonian limit uniquely defines $g_{00}(r)$. Geodesic motion under such metric exactly reproduces the precession of a planetary orbit, periastron advance of a binary, deflection of light and {Shapiro time delay} if the determinant of the time-radial parts of the metric is $-1$. In this model, the total time for a radial round trip of light is as in the Schwarzschild model, but it allows for light rays to have different speeds propagating toward or from the massive object. The value of $g_{01}(r) $ could be obtained by measuring these speeds. All of these metrics do satisfy Einstein's field equations

physics.gen-ph↗
arXiv2019

Relativity from the Geometrization of Newtonian Dynamics

Based on the Generalized Principle of Inertia, which states that: \emph{An inanimate object moves freely, that is, with zero acceleration, in its own spacetime, whose geometry is determined by all of the forces affecting it,} we geometrize Newtonian dynamics for any conservative force. For an object moving in a spherically symmetric force field, using a variational principle, conservation of angular momentum and a classical limit, we construct a metric with respect to which the object's worldline is a geodesic. For the gravitational field of a static, spherically symmetric mass, this metric is the Schwarzschild metric. The resulting dynamics reduces in the weak field, low velocity limit to classical Newtonian dynamics and exactly reproduces the classical tests of General Relativity. The metric of gravitoelectromagnetism is extended to handle a gravitational field generated by several sources.

physics.gen-ph↗
arXiv2017

Relativistic Newtonian Dynamics

Planck's formula and General Relativity indicate that potential energy influences spacetime. Using Einstein's Equivalence Principle and an extension of his Chock Hypothesis, an explicit description of this influence is derived. We present a new relativity model by incorporating the influence of the potential energy on spacetime in Newton's dynamics for motion under a central force. This model extends the model used by Friedman and Steiner to obtain the exact precession of Mercury without curving spacetime. We also present a solution of this model for a hydrogen-like atom, which explains the reason for a probabilistic description.

physics.gen-ph↗
arXiv2017

Relativistic Newtonian Dynamics for Objects and Particles

Relativistic Newtonian Dynamics (RND) was introduced in a series of recent papers by the author, in partial cooperation with J. M. Steiner. RND was capable of describing non-classical behavior of motion under a central attracting force. RND incorporates the influence of potential energy on spacetime in Newtonian dynamics, treating gravity as a force in flat spacetime. It was shown that this dynamics predicts accurately gravitational time dilation, the anomalous precession of Mercury and the periastron advance of any binary. In this paper the model is further refined and extended to describe also the motion of both objects with non-zero mass and massless particles, under a conservative attracting force. It is shown that for any conservative force a properly defined energy is conserved on the trajectories and if this force is central, the angular momentum is also preserved. An RND equation of motion is derived for motion under a conservative force. As an application, it is shown that RND predicts accurately also the Shapiro time delay - the fourth test of GR.

physics.gen-ph↗
arXiv2016

Uniform Acceleration in General Relativity

We extend de la Fuente and Romero's defining equation for uniform acceleration in a general curved spacetime from linear acceleration to the full Lorentz covariant uniform acceleration. In a flat spacetime background, we have explicit solutions. We use generalized Fermi-Walker transport to parallel transport the Frenet basis along the trajectory. In flat spacetime, we obtain velocity and acceleration transformations from a uniformly accelerated system to an inertial system. We obtain the time dilation between accelerated clocks. We apply our acceleration transformations to the motion of a charged particle in a constant electromagnetic field and recover the Lorentz-Abraham-Dirac equation.

gr-qc↗
arXiv2013

The wave-function description of the electromagnetic field

For an arbitrary electromagnetic field, we define a prepotential $S$, which is a complex-valued function of spacetime. The prepotential is a modification of the two scalar potential functions introduced by E. T. Whittaker. The prepotential is Lorentz covariant under a spin half representation. For a moving charge and any observer, we obtain a complex dimensionless scalar. The prepotential is a function of this dimensionless scalar. The prepotential $S$ of an arbitrary electromagnetic field is described as an integral over the charges generating the field. The Faraday vector at each point may be derived from $S$ by a convolution of the differential operator with the alpha matrices of Dirac. Some explicit examples will be calculated. We also present the Maxwell equations for the prepotential.

physics.gen-ph↗
arXiv2013

Covariant Uniform Acceleration

We show that standard Relativistic Dynamics Equation F=dp/dτis only partially covariant. To achieve full Lorentz covariance, we replace the four-force F by a rank 2 antisymmetric tensor acting on the four-velocity. By taking this tensor to be constant, we obtain a covariant definition of uniformly accelerated motion. We compute explicit solutions for uniformly accelerated motion which are divided into four types: null, linear, rotational, and general. For null acceleration, the worldline is cubic in the time. Linear acceleration covariantly extends 1D hyperbolic motion, while rotational acceleration covariantly extends pure rotational motion. We use Generalized Fermi-Walker transport to construct a uniformly accelerated family of inertial frames which are instantaneously comoving to a uniformly accelerated observer. We explain the connection between our approach and that of Mashhoon. We show that our solutions of uniformly accelerated motion have constant acceleration in the comoving frame. Assuming the Weak Hypothesis of Locality, we obtain local spacetime transformations from a uniformly accelerated frame K' to an inertial frame K. The spacetime transformations between two uniformly accelerated frames with the same acceleration are Lorentz. We compute the metric at an arbitrary point of a uniformly accelerated frame. We obtain velocity and acceleration transformations from a uniformly accelerated system K' to an inertial frame K. We derive the general formula for the time dilation between accelerated clocks. We obtain a formula for the angular velocity of a uniformly accelerated object. Every rest point of K' is uniformly accelerated, and its acceleration is a function of the observer's acceleration and its position. We obtain an interpretation of the Lorentz-Abraham-Dirac equation as an acceleration transformation from K' to K.

physics.gen-ph↗
arXiv2013

Spacetime Transformations from a Uniformly Accelerated Frame

We use Generalized Fermi-Walker transport to construct a one-parameter family of inertial frames which are instantaneously comoving to a uniformly accelerated observer. We explain the connection between our approach and that of Mashhoon. We show that our solutions of uniformly accelerated motion have constant acceleration in the comoving frame. Assuming the Weak Hypothesis of Locality, we obtain local spacetime transformations from a uniformly accelerated frame $K'$ to an inertial frame $K$. The spacetime transformations between two uniformly accelerated frames with the same acceleration are Lorentz. We compute the metric at an arbitrary point of a uniformly accelerated frame.

physics.gen-ph↗
arXiv2012

Making the Relativistic Dynamics Equation Covariant: Explicit Solutions for Motion under a Constant Force

We derive a 4D covariant Relativistic Dynamics Equation. This equation canonically extends the 3D relativistic dynamics equation $\mathbf{F}=\frac{d\mathbf{p}}{dt}$, where $\mathbf{F}$ is the 3D force and $\mathbf{p}=m_0γ\mathbf{v}$ is the 3D relativistic momentum. The standard 4D equation $F=\frac{dp}{dτ}$ is only partially covariant. To achieve full Lorentz covariance, we replace the four-force $F$ by a rank 2 antisymmetric tensor acting on the four-velocity. By taking this tensor to be constant, we obtain a covariant definition of uniformly accelerated motion. This solves a problem of Einstein and Planck. We compute explicit solutions for uniformly accelerated motion. The solutions are divided into four Lorentz-invariant types: null, linear, rotational, and general. For null acceleration, the worldline is cubic in the time. Linear acceleration covariantly extends 1D hyperbolic motion, while rotational acceleration covariantly extends pure rotational motion.

physics.gen-ph↗
arXiv2012

Testing Einstein's time dilation under acceleration using Mössbauer spectroscopy

The Einstein time dilation formula was tested in several experiments. Many trials have been made to measure the transverse second order Doppler shift by Mössbauer spectroscopy using a rotating absorber, to test the validity of this formula. Such experiments are also able to test if the time dilation depends only on the velocity of the absorber, as assumed by Einstein's clock hypothesis, or the present centripetal acceleration contributes to the time dilation. We show here that the fact that the experiment requires $γ$-ray emission and detection slits of finite size, the absorption line is broadened; by geometric longitudinal first order Doppler shifts immensely. Moreover, the absorption line is non-Lorenzian. We obtain an explicit expression for the absorption line for any angular velocity of the absorber. The analysis of the experimental results, in all previous experiments which did not observe the full absorption line itself, were wrong and the conclusions doubtful. The only proper experiment was done by Kündig (Phys. Rev. 129 (1963) 2371), who observed the broadening, but associated it to random vibrations of the absorber. We establish necessary conditions for the successful measurement of a transverse second order Doppler shift by Mössbauer spectroscopy. We indicate how the results of such an experiment can be used to verify the existence of a Doppler shift due to acceleration and to test the validity of Einstein's clock hypothesis.

physics.class-ph↗
arXiv2012

Dynamics of hydrogen-like atom bounded by maximal acceleration

The existence of a maximal acceleration for massive objects was conjectured by Caianiello 30 years ago based on the Heisenberg uncertainty relations. Many consequences of this hypothesis have been studied, but until now, there has been no evidence that boundedness of the acceleration may lead to quantum behavior. In previous research, we predicted the existence of a universal maximal acceleration and developed a new dynamics for which all admissible solutions have an acceleration bounded by the maximal one. Based on W. Kündig's experiment, as reanalyzed by Kholmetskii et al, we estimated its value to be of the order $10^{19}m/s^2$. We present here a solution of our dynamical equation for a classical hydrogen-like atom and show that this dynamics leads to some aspects of quantum behavior. We show that the position of an electron in a hydrogen-like atom can be described only probabilistically. We also show that in this model, the notion of "center of mass" must be modified. This modification supports the non-existence of a magnetic moment in the atom and explains the relevance of the conformal group in the quantum region.

physics.class-ph↗
arXiv2010

The maximal acceleration, Extended Relativistic Dynamics and Doppler type shift for an accelerated source

Based on the generalized principle of relativity and the ensuing symmetry, we have shown that there are only two possible types of transformations between uniformly accelerated systems. The first allowable type of transformation holds if and only if the Clock Hypothesis is true. If the Clock Hypothesis is not true, the transformation is of Lorentz-type and implies the existence of a universal maximal acceleration $a_m$. We present an extension of relativistic dynamics for which all admissible solutions will have have a speed bounded by the speed of light $c$ and the acceleration bounded by $a_m$. An additional Doppler type shift for an accelerated source is predicted. The formulas for such shift are the same as for the usual Doppler shift with $v/c$ replaced by $a/a_m$. The W. Kündig experiment of measurement of the transverse Doppler shift in an accelerated system was also exposed to a longtitudal shift due to the acceleration. This experiment, as reanalyzed by Kholmetskii et al, shows that the Clock Hypothesis is not valid. Based on the results of this experiment, we predict that the value of the maximal acceleration $a_m$ is of the order $10^{19}m/s^2$. Moreover, our analysis provides a way to measure experimentally the maximal acceleration with existing technology.

physics.class-ph↗
arXiv2010

A new relativistic kinematics of accelerated systems

We consider transformations between uniformly accelerated systems, assuming that the Clock Hypothesis is false. We use the proper velocity-time description of events rather than the usual space-time description in order to obtain linear transformations. Based on the generalized principle of relativity and the ensuing symmetry, we obtain transformations of Lorentz-type. We predict the existence of a maximal acceleration and time dilation due to acceleration. We also predict a Doppler shift due to acceleration of the source in addition to the shift due to the source's velocity. Based on our results, we explain the W. Kündig experiment, as reanalyzed by Kholmetski \textit{et al}, and obtain an estimate of the maximal acceleration.

gr-qc↗
arXiv2009

The relativistic phase space and Newman-Penrose basis

We define a complex relativistic phase space which is the space $\mathbb{C}^4$ equipped with the Minkowski metric and with a geometric tri-product on it. The geometric tri-product is similar to the triple product of the bounded symmetric domain of type IV in Cartan's classification, called the spin domain. We show that there are to types of tripotents-the basic elements of the tri-product in the relativistic phase space. We construct a spectral decomposition for elements of this space. A description of compatibility of element of the relativistic phase space is given. We show that the relativistic phase space has two natural bases consisting of compatible tripotents. The fist one is the natural basis for four-vectors and the second one is the Newman-Penrose basis. The second one determine Dirac bi-spinors on the phase space. Thus, the relativistic phase space has similar features to the quantum mechanical state space.

physics.gen-ph↗
arXiv2008

Representations of the Poincare group on relativistic phase space

We introduce a complex relativistic phase space as the space $\mathbb{C}^4$ equipped with the Minkowski metric and with a geometric tri-product on it. The geometric tri-product is similar to the triple product of the bounded symmetric domain of type IV in Cartan's classification, called the spin domain. We define a spin 1 representations of the Lie algebra of the Poincaré group by natural operators of this tri-product on the complex relativistic phase space. This representation is connected with the electromagnetic tensor. A spin 1/2 representation on the complex relativistic phase space is constructed be use of the complex Faraday electromagnetic tensor. We show that the Newman-Penrose basis for the phase space determines the Dirac bi-spinors under this representation. Quite remarkable that the tri-product representation admits only spin 1 and spin 1/2 representations which correspond to most particles of nature.

math-ph↗