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*From*: David Rutherford <drutherford@SOFTCOM.NET>*Date*: Mon, 5 Feb 2001 21:50:52 -0800

I have a physics article that I've posted on my webpage at the URL,

http://www.softcom.net/users/der555

under the link "New Transformation Equations and the Electric Field

Four-vector, Fifth Edition (PDF File)".

I've included the abstract, introduction, and conclusions below.

ABSTRACT:

In special relativity, spacetime can be described as Minkowskian.

We intend to show that spacetime, as well as the laws of

electromagnetism, can be described using a four-dimensional

Euclidean metric as a foundation. In order to formulate these laws

successfully, however, it is necessary to extend the laws of

electromagnetism by replacing the Maxwell tensor with an electric

field four-vector. In addition, to assure the covariance of the

new laws, we introduce equations that, completely, replace the

Lorentz transformation equations and Lorentz group. The above

replacements, we believe, lead naturally to a unification of the

electromagnetic field with the gravitational and nuclear fields.

We introduce, also, a new mathematical formalism which facilitates

the presentation of our laws.

INTRODUCTION:

Lorentz first derived his famous set of transformation equations

from the electromagnetic field equations of Maxwell. They assure

that Maxwell's equations will have the same form in any inertial

frame of reference. Unfortunately, if Maxwell's equations are

shown to be incomplete, then it is likely that the Lorentz

equations are incorrect. We intend to show that this is the case.

Maxwell's equations are, essentially, a set of

three-dimensional partial differential equations. That is,

each equation contains the partial derivatives with respect to

only three of the coordinates. In four-dimensional

spacetime, a three-dimensional description of anything is

inherently incomplete. We will extend Maxwell's equations so that

they form a set of four-dimensional equations. In so doing, it is

possible to encompass all of Maxwell's equations in a

single vector equation by introducing an electric field

four-vector. In addition to the electromagnetic field, we believe

the new equation incorporates the gravitational and nuclear

fields. This equation, however, is not Lorentz invariant

and requires a new set of transformation equations in order that

it has the same form in all inertial frames.

The Lorentz transformation equations forbid any contraction or

expansion of coordinates transverse to the direction of motion. We

present a new Euclidean set of transformation equations which

require a rotation of the coordinates transverse to the

direction of motion. There is also an analogous rotation in the

plane described by the direction of motion and the time

coordinate.

Due to the dependence of each of the Lorentz force equations on

only three of the components of the four-velocity, they also form

an incomplete set of equations. Therefore, we extend these

equations to four-dimensions, as well. The equation of motion then

follows naturally from our new force equation.

In expressing the force equations in terms of the fields, we

arrive at an energy-momentum tensor with components which include

the time component of our electric field four-vector. These

components offer, among other things, a new description of the

mechanism behind the flow of field energy.

A new mathematical formalism is introduced which substantially

simplifies the expression of our laws and helps give a deeper

understanding of the geometry behind them. This new formalism

borrows its structure, in part, from Hamilton's quaternions and

the Clifford algebras, but differs fundamentally from both.

CONCLUSIONS:

The special Lorentz transformation describes an imaginary rotation

of coordinate systems. We have described a real rotation of

coordinate systems including an automatic rotation

transverse to the direction of motion, which the Lorentz

transformations do not describe. These rotations are not

necessarily observable as rotations, however, but as precession,

time dilation, length contraction, etc.

In conventional theory, the magnitude of a charged particle is

invariant. In this paper, the magnitude of a charge is reduced as

its velocity is increased, however, the charge density in

the region of the charge is invariant. Thus, the quantity of

charge in a given volume does not change as long as no charge

enters or leaves the region. It is the invariance of charge

density, not the conservation of charge, which accounts for the

neutrality of atoms. This indicates that charge is most likely a

property of the field, rather than the particle itself.

It can be seen from the T_44 component of (103) that the

energy of the field can be negative. Rather than interpreting this

as a liability, we suggest the possibility that the field of a

particle is its antiparticle. We suspect that the creation

of a particle travelling forward in time is accompanied by the

creation of its antiparticle travelling backward in

time. We refer to particles (or antiparticles) travelling

forward in time as particles, since they have the characteristics

of particles, and particles (or antiparticles) travelling backward

in time as antiparticles having the characteristics of fields.

Since an antiparticle travelling backward in time may be said to

have negative energy and since the energy of the field from

T_44 is negative for E_t^2 < E_x^2 + E_y^2 + E_z^2, we

suggest that the antiparticle travelling backward in time appears

to us as the field of the particle. We are not referring,

for example, to the particle/antiparticle pair created in the

disintegration of an energetic photon. In that case, there is an

electron and an anti-electron (positron) created. However, both of

these ``particles'' are travelling forward in time.

Associated with each of these particles, is a field which we claim

is its antiparticle travelling backward in time. These

particle/field (or particle/antiparticle) pairs are the pairs to

which we refer. In this case, there are actually two

particle/antiparticle pairs created. The electron and its field

(antiparticle) comprise one particle/antiparticle pair, and the

positron and its field (antiparticle) comprise the other

particle/antiparticle pair. Since the antiparticles appear to us

as (and are) the fields of the particles, one might even entertain

the notion, that space and matter travelling backward in time are

one and the same thing.

Due to this apparent particle/antiparticle link, we also conclude

that there are no electric monopoles (since every charged

particle is accompanied by its field), just as there are

apparently no magnetic monopoles. These conclusions might offer a

logical explanation for the puzzling absence of antimatter in the

universe. If our suspicions are correct, this "missing" antimatter

exists all around us as the fields of matter and, possibly, as

space itself.

The equation for an expanding four-dimensional ``spherical'' light

wave front is (8), in this paper. The wave front

propogates in four-dimensions (3 space and 1 time), rather

than the usual three-dimensions (3 space), as in conventional

theory. This assures that the spatial speed of light in all

inertial reference frames is the invariant c.

The form and terminology of many of the equations in this paper

are, deceptively, similar to those of conventional physics,

however, they differ in several ways. It is important that one not

assume the equivalence of the definitions presented here with the

analogous definitions in conventional theory. In most cases, they

are not exactly the same. For example, the definition of the

scalar electric potential phi includes the spacetime interval

s in the denominator, not the spatial interval r. This

prevents an infinite potential at r = 0, a problem that plagues

conventional electromagnetic theory.

It would also be incorrect to assume that the electric field is

defined in the same manner as in conventional electromagnetic

theory. For example, it is easy to interpret the components of the

energy-momentum tensor T incorrectly as containing only the

components of the conventional electric field when, in fact, they

contain the components of the electric, magnetic, and possibly the

gravitational and nuclear fields, as well.

What we have provided, here, is to be considered only as a

foundation upon which a deeper and more unified understanding of

laws of nature might be built.

--------------------------------

I would apprectiate any comments or questions. I'm also looking for

someone to sponsor my submission of this paper to the LANL archives (I

have the Latex version that can be sent to LANL). Any help would be

greatly appreciated.

Thanks,

Dave Rutherford

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