107 research outputs found
The wave-function description of the electromagnetic field
For an arbitrary electromagnetic field, we define a prepotential , 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
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 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
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.Comment: 5 pages , 1 figur
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.Comment: 15 pages 1 figur
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
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