arXiv subjects

Yaakov Friedman

Publications and source records attributed to Yaakov Friedman.

22 records · Page 2Linked to original sources

arXiv2006

A new view on relativity: Part 1. Kinematic relations between inertial and relativistically accelerated systems based on symmetry

Several new ideas related to Special and General Relativity are proposed. The black-box method is used for the synchronization of the clocks and the space axes between two inertial systems or two accelerated systems and for the derivation of the transformations between them. There are two consistent ways of defining the inputs and outputs to describe the transformations and relative motion between the systems. The standard approach uses a mixture of the two ways. By formulating the principle of special and general relativity as a symmetry principle we are able to specify these transformations to depend only on a constant. The transformations become Galilean if the constant is zero. Validity of the Clock Hypothesis for uniformly accelerated systems implies zero constant. If the constant is not zero, we can introduce a metric under which the transformations become self adjoint. In case of inertial systems, the metric is the Minkowski metric and we obtain a unique invariant maximal velocity. The ball of the relativistically admissible velocities is a bounded symmetric domain under projective maps. For uniformly accelerated systems the existence of an invariant \textit{maximal acceleration} is predicted. This is the only method of describing transformations between uniformly accelerated systems without assuming the Clock Hypothesis.

physics.class-ph↗

arXiv2006

A new view on relativity: Part 2. Relativistic dynamics

The Lorentz transformations are represented on the ball of relativistically admissible velocities by Einstein velocity addition and rotations. This representation is by projective maps. The relativistic dynamic equation can be derived by introducing a new principle which is analogous to the Einstein's Equivalence Principle, but can be applied for any force. By this principle, the relativistic dynamic equation is defined by an element of the Lie algebra of the above representation. If we introduce a new dynamic variable, called symmetric velocity, the above representation becomes a representation by conformal, instead of projective maps. In this variable, the relativistic dynamic equation for systems with an invariant plane, becomes a non-linear analytic equation in one complex variable. We obtain explicit solutions for the motion of a charge in uniform, mutually perpendicular electric and magnetic fields. By the above principle, we show that the relativistic dynamic equation for the four-velocity leads to an analog of the electromagnetic tensor. This indicates that force in special relativity is described by a differential two-form.

physics.class-ph↗

arXiv2005

Explicit solutions for relativistic acceleration and rotation

The Lorentz transformations are represented by Einstein velocity addition on the ball of relativistically admissible velocities. This representation is by projective maps. The Lie algebra of this representation defines the relativistic dynamic equation. If we introduce a new dynamic variable, called symmetric velocity, the above representation becomes a representation by conformal, instead of projective maps. In this variable, the relativistic dynamic equation for systems with an invariant plane, becomes a non-linear analytic equation in one complex variable. We obtain explicit solutions for the motion of a charge in uniform, mutually perpendicular electric and magnetic fields. By assuming the Clock Hypothesis and using these solutions, we are able to describe the space-time transformations between two uniformly accelerated and rotating systems.

gr-qc↗

arXiv2005

Geometric tri-product of the spin domain and Clifford algebras

We show that the triple product defined by the spin domain (Bounded Symmetric Domain of type 4 in Cartan's classification) is closely related to the geometric product in Clifford algebras. We present the properties of this tri-product and compare it with the geometric product. The spin domain can be used to construct a model in which spin 1 and spin1/2 particles coexist. Using the geometric tri-product, we develop the geometry of this domain. We present a geometric spectral theorem for this domain and obtain both spin 1 and spin 1/2 representations of the Lorentz group on this domain.

math-ph↗