# **Electron Model of the Photon**

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#### ** ****Marlin N.
Schuetz**

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#### ** ****1 / 20 /
88**

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#### ** ****Revised 10 / 1 /
92**

As with many students who seek intuitive understanding of the tenets of
physics, I was disturbed that as we approached the more fundamental entities,
our descriptions became more complicated. Clearly we are required to depart
from physical and intuitive descriptions to more purely mathematical ones.
The photon, with its quizzical properties of duality, speed variance,
masslessness, energy transfer and quantum nature was most unsettling.
It is my belief that our difficulty in such matters is not that they are
intrinsically physically inexplicable, but rather that we have placed
ourselves in a position of having the wrong perspective. This paper is
a humble attempt to look at the photon from a different view while hopefully
clinging to physical fundamentals. Sadly, much is left that is not intuitively
clear, however, what has been examined appears to be a close fit with
observational phenomenon.

The photon model to be described is one in which fundamental relationships
are employed in ordinary ways. Although it utilizes a particle that
has been previously explained otherwise, its resurrection in terms that
are to be described seem appropriate.

#### DIRAC'S SEA OF NEGATIVE ELECTRONS

Figure 1

Dirac's picture of the energy level distribution of the particles
with positive and negative mass. On the left (a) all negative energy
levels are completely lined up, and only six ordinary electrons can
exist on the normal positive levels. On the right (b) one of the electrons
from a negative level is lifted to a positive level, leaving behind
a "hole" which behaves as an ordinary positive electron with positive
mass. If this extra electron from a positive level falls back into the
hole (annihilation process of an e- and e+ the energy difference will
be emitted as X-radiation.

The concept of all energy states being filled is not possible to visualize.
The idea of infinite negative mass occupying all infinitesimally small
volumes of space is simply beyond fathom. It is equally disturbing that
if there were an incomplete set of free negative energy particles about,
they would all clump together since they accelerate in direct opposition
to their Coulomb forces. A variation on this theme, however, has beauty,
balance and relieves us of most of these problems.

#### A VARIATION ON DIRAC'S THEME

First, suppose that the idea of negative energy is an artifact. Consider
that although we will use negative energy in our mathematics we are
really dealing with negative mass and that negative mass can acquire
positive energy, i.e., adding positive energy to a negative mass increases
its velocity. We must also assume that positive mass electrons can never
become negative mass electrons by "falling into a hole in the sea of
negative energy states." The converse of this must also be assumed.
We will also assume that positrons are free negative mass negatively
charged electrons which fate is to quickly pair up with ordinary positive
mass electrons. In this model, as in Dirac's, symmetry prevails. However,
instead of all negative energy states being filled below the -moc2 energy
level, each negative mass electron is paired with a positive mass electron.
As will be shown, the pair, unless stimulated by an external force,
will exist on the zero energy level as a stable system. The picture
of the static electron universe then is quite different from Dirac's
view.

Interaction between the particles with a positive and those with a
negative mass.

Figure 2

#### PAIRING

The pairing process, fundamental to this model has been considered
before by Dirac and is described in Gamow's, "Thirty years that shook
physics." Pairing was dismissed due to our inability to confirm it's
existence. Pairing involves a relatively simple, but most interesting
process. Let us first examine the separate particles. A normal, positive
mass electron accelerates in the direction of an applied force. A negative
mass electron, however, will accelerate in direct opposite to an applied
force. If two electrons with numerically equal masses, but of opposite
signs are paired together the results according to Coulomb's law will
be that they will accelerate in the same direction keeping a constant
distance between them and speeding up to the limit of the speed of light.

All pairs, unless stimulated, exist only on the zero energy line.
Pair annihilation yields two oppositely directed photons through stimulation
of other pairs by the time varying magnetic fields of the accelerating
positive mass electron (pme) and the negative mass electron (nme). The
newly formed pair may also become a photon if there remains a net energy
surplus after pairing.

Figure 3

The pair carries with it no mass, energy or momentum since:

Note: At velocity = c in our reference frame (2) the pair has no dimension
in its direction of travel (z) and cannot be distinguished from a single
particle with zero mass. It is also assumed that the photon energy in
reference frame (1) (photons) is equal to the energy in reference frame
(2) (ours). That is, the system from which the photon was originated
is in the same reference frame (2) as the receptor and no Doppler shift
is incurred and,

and that the energy transform from r.f. 1 to r.f.2 is

which allows free movement between the reference frames. Therefore,
in the text of the paper the subscripts have been dropped. One is tempted
to ask what the equilibrium separation distance (ref. frame 1) is between
the two bodies of the pair. As yet, there is no clear answer to this
question, but it seems only to be related to the initial conditions
of momentum exchange since the pair is stable at any separation distance.
In our reference frame, since the pair is traveling at the speed of
light, there can be no separation distance between them in the direction
of travel (z). This is consistent with current electromagnetic theory
where an electromagnetic plane wave has no z component. The idea of
a pair of particles summing to zero mass, momentum and energy, traveling
at the speed of light and existing in equilibrium, now may start to
make a little sense. One objection to this concept might be that since
both particles are charge carriers their motion represents a current
flow and should be detectable. Yet if we assume that the universe is
filled with these particle, moving randomly, there would be no macroscopic
(net) current flow or detectable magnetic field.

#### ENERGY TRANSPORT MECHANISM

With this basis, we can now consider how a paired system might carry
with it some energy and thus assume the role of a photon. Given that
a pair exists, if a time varying field is impressed upon the system,
the two particles, still traveling at the speed of light, will be caused
to revolve about a center of masslessness. To show this one must develop
the force balance equations for the system in the photon reference frame
(1). Using Coulomb's law and assuming point charges,

Note : Epsilon has units of mass and therefore carries the sign of
the mass of the particle.

Then considering relativistically the centripetal force

Substituting and combining terms yields the force balance equations
for the photons reference frame (1)

Taking either case and solving for r

Assuming that all of the energy added to create the photon is positive.
Then

or

substituting hc / y for m_{o}V 2/T in equation (10) yields

and the ratio l / r is the constant 3444.2 +. It is also interesting
to note that the fine structure constant is equal to l / 8 *pi*/
r.

From equation (11)

or

Solving quadractically for V 2/T and ignoring the imaginary root we
obtain

For the present, at least, we shall ignore the imaginary root. The
constant l / r provides insight into the dynamics of the photon and
its stability. It is the ratio of the period of the photon and the communication
time across the diameter of the photon at the speed of light.

communication time t = 2 r/ c Period T = 1 / v

It is now useful to translate the two body system at Vz = c

**Figure 5**

From equation 15 it may be seen that in reference frame (1), the tangential
velocity increases with photon frequency. Now, observing the photon
as a particle in our reference frame (2), SINCE THE PHOTON HAS NO Z
DIMENSION, THE ELECTRONS ORBITAL VELOCITY MAY BE SEEN TO EXIST ONLY
In the x direction.

Reference Frame 1

**Figure 6a**

Reference Frame 2

**Figure 6b**

The average electron velocity in the x direction must be

which is constant

Over the spectrum how can Vx vary from zero to near the speed of light
in one reference frame and be a constant in another? There is some help
in noting that in reference frame (2) equation 17 is used, while the
transform needed to get back to reference frame (1) is obtained by dividing
equation 17 with equation 14 and solving VT .

Aside from the relationship n = c/ l this result is our first opportunity
to transform from one reference frame to another with a DVz = c. __
Everything still works well in our reference frame when Vx is a constant
since

and, as may be seen in table 1, is numerically valid throughout the
spectrum. There is also a new relationship for the speed of light in
that c = Vxl / 4r.

An interesting feature of equations 12 and 15 and table 1 is that
when the frequency of the photon is increased to the high end of the
gamma ray spectrum, the tangential velocity converges with c, and the
photon radius shrinks to less than that of the classical radius of the
electron.

#### QUANTUM MECHANICAL ASPECTS

When the current view of the photon is such that it is quantized at
the time of stimulation, the new model may exhibit a quantum nature
in itself. There are at least three ways in which this particle might
be quantized. First, consider the integer requirements that the Debroile
wavelength places upon the circumference of the particle. Starting with
the relationships:

We wish to solve for N, the number of possible states.

Substituting c/ Nv for ^d and solving for v

Then

**Table 1**

It should be noted that

Which has the same form as the quantum mechanical relationship

where

A short computer program reveals the number of quantum states possible
over an interesting (nonrelativistic VT ) portion of the spectrum. In
Table 2, for example, at about 1013 Hz there are 3,162 possible states
with a frequency resolution of 1.5 x 103 . Since it is known from observation
that these are far to few states, there must be other modes which will
reduce the quantum steps. In all of the previous paragraphs, the photon
has been limited only to two dimensions. If one considers that there
is almost surely motion in the third dimension, then a low frequency
rotation about the z axis would, similar to Table 1, expand the possible
quantum states to an extremely large number. Additionally, there would
be three electron spin states which would be a multiplier of the number
of possible quantum states. Clearly, the number of quantum states would
be so large as to appear to be a continuum and the photon can take on
any quantum value impressed upon it during emission.

**Table 2**

Quantum Numbers of A Photon with Motion in Two Dimensions

#### CONCLUSIONS

The assumption presented early in this paper are clearly in conflict
with currently accepted ideas. The positron, for example, long considered
to have the equivalence of positive mass with positive charge, nevertheless
can be redefined as a negative mass having negative charge and still
be phenomenologically consistent. Almost surely, however, the assumptions
will require modification to be more general. The reader that stops
at the assumptions, because of basic disagreement, will have missed
the most salient features of the paper.

The precise agreement of the mathematics with the gross features of
the known spectrum cannot be dismissed as merely coincidental. If relativity
were not part of the explanation, it might be possible to suggest that
the simple exponential relationships provided only superficial agreements
similar to early modeling of the atomic structure. However, agreement
with the spectrum over 25 decades and with features such as the convergence
of tangential velocity and the speed of light and the forced photon
stability due to the collocation of fields consistent with force balance
are just too compelling to be easily dismissed.

I believe that duality, diffraction, refraction, and all of the other
attributes of light can be explained in terms of classical interactions
with photons being absorbed and reemitted or simply redirected. However,
to present a model without being able to predict previously unobserved
or unexplained phenomenon has been argued by some to have no or only
heuristic value. Although a growing number of scholars believe this
to be a false tenet it is gratifying that this theory does provide sufficient
information to fit the former criteria.

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