A NEW GENERAL THEORY
OF PHYSICS
Part
III
James A. Putnam
© 1995-2007
PART I PART II PART III PART IV
ELECTRIC EFFECTS AND
THE HYDROGEN ATOM 
The hydrogen atom has a nucleus of a single proton with a single
electron orbiting the proton. Both of these are charged particles. They
interact with each other, for any measurable amount, only through
electromagnetic means. This interaction is the simplest natural environment in
which to analyze the cause of electromagnetic effects.
I am not saying the action of a hydrogen atom is simple. I am
saying I will examine electromagnetism from a simple atomic perspective. The
origins of electromagnetism must be expected to be a part of the properties of
each photon. I will use a simple model of the hydrogen atom for the purpose of
theoretically isolating the properties of a single photon.
What I rely upon, for my fundamental unit of time, is the time of
passage of a photon to pass a given point. In this theory, that time is a
fundamental constant. I don't have a constant fundamental unit of distance. I
use the length of a photon that is a varying unit of length. When I look for
another natural unit of length there is the radius of the atom to consider.
When this radius changes, due to an electron moving between energy levels, a
single photon is involved. This length of radius and its variations are not
accidental. There must be a clear physical cause for their size.
The length of a photon is directly related to the speed of light.
The measurement of the speed of light is ultimately dependent upon the length of
a photon. Therefore, the locally measured speed of light is a fundamental
constant. The fundamental unit of time is everywhere a constant. Even the
photon length has to be accepted as the local fundamental constant unit of
length.
For this section the speed of light and the length of a photon are
treated as constants. This has the effect of averaging their values and
permitting the equations to give some numerical results in agreement with
empirical measurements made from our macroscopic perspective.
The electric force due to the proton nucleus acts upon the
orbiting electron, and the electron exerts an equal but opposite electrical
force upon the proton. This force is predicted by the formula:
The values of electric charge for the electron and proton are
represented in the numerator on the right side. Both of these values are the
same measure of the fundamental unit of electric charge.
The fundamental unit of electric charge is an empirically
determined constant of electromagnetic theory. The value of electric charge is
commonly given the units of coulombs. As I have stated earlier, anything
defined in units higher than distance and time is evidence we may not have
correctly determined its origin. We really have only distance and time to work
with when measuring any physical event. Therefore, all empirical evidence is
some measure of distance or time or both of these.
The measure of force described by the above equation is commonly
given the units of newtons. Here again, there is a need to look to the
demonstrable properties of photons for a physical interpretation of what is force. There is in the denominator on the right side a quantity called electrical
permittivity represented by the character e. This is an empirically determined
quantity having no clear explanation as to its physical origin.
There is only one term in the equation that is a measure of
something physically observed. This is the letter r
for the radius of the atom. Everything else in the equation needs yet to be
explained by physics. However, the magnitudes of everything in the equation
have been empirically determined, and I will use them to begin my analysis.
Substituting the appropriate known values, actually their absolute
values, into the above force equation:
I am purposefully avoiding polarities for electric charge. The
cause of polarities needs yet to be identified. It is accepted that the
electron and proton attract each other by a force of magnitude:
I wish to describe a photon coming from the proton and acting upon
the electron. To attempt this, I will use the formula:
The numerator is all, or some division of, the potential energy between
the proton and the electron. The size of the increment of energy depends upon
what increment of distance is used in the denominator. I will shortly decide
this.
The potential energy of the electron is known to be twice the
electron's kinetic energy. The kinetic energy of the electron is:
Doubling this gives:
This is the magnitude of the potential energy of the electron.
This value divided by the radius of the orbit would give the magnitude of the
force shown above.
What must be decided at this point is what will be the first trial
length of the photon? Then also, what corresponding division of the potential
energy is carried by an individual photon? There is only one fundamental
physical representation of length; therefore, until the results suggest
otherwise, it is reasonable to assume the length of a photon and the length of
the radius of the first energy level of an atom to be the same.
I will make this assumption for my starting point. I substitute
the appropriate values into the second form of the force equation given above:
Whether or not the denominator is the true length of a photon will
be made clear in later calculations where the length of the photon is critical
to giving correct known results.
The assumption being made is that there is a single photon that has
been emitted by the proton. At a particular instant of time, its length reaches
from the proton to the electron. This assumption is only for the purposes of
introducing a concept. It does not preclude the possibility that many photons may be
arriving and departing at anytime. This more general treatment is not being
addressed at this time.
The primary purpose of this exercise is to assume a reasonable
beginning value for the length of a photon. If the length of a photon can be
determined, then its value, divided by the speed of light, will yield the time of passage of a photon passing a given point. This value would be a true fundamental constant and must have
primary importance in physics.
I want to show a relationship between the photon and the energy
that is transferred from one particle to the other. The complete nature of
stored energy in a photon cannot be defined until mass is defined in terms of
distance and time. For this reason, I will simplify the problem and treat the
whole incremental value of energy involved as just stored energy.
I will solve for this energy increment by assuming it to be stored
in a single photon traveling between the electron and the proton of a hydrogen
atom. It is commonly known that the electron is accelerating toward the proton even
though its radius of orbit does not change. The acceleration of the electron is
given by:
The left side denotes the radial acceleration of the electron. The
right side denotes the square of the tangential velocity of the electron divided
by the radius of orbit. I solve for the change in velocity:
The radius is also the length of the photon, and the increment of
time is the time of passage for the photon. Therefore:
Substituting:
For this example, the common reference of measurement is the
universal increment of time dtc. I
can, therefore, use equations analogous to those developed for the acceleration
due to gravity. For measurements of acceleration:
Substituting this into the equation above:
Rearranging:
Multiplying by the mass of the electron yields an equality of
energies:
The energy term on the left is an expression of photon energy. The
expression on the right is the potential energy of the electron. This equation says:
A photon moving between the electron and proton and holding the electron in
orbit carries the potential electrical energy necessary to accomplish this. Why
do we not observe photons to be emitted by the orbiting electron? The assumed
answer is that when the electron is in a stable orbit, the photons involved in
holding it there are passed back and forth between the electron and proton
only. They do not leave the atom. This situation allows for a new approach to
interpreting electric charge.
The electron and proton of the hydrogen atom are said to
be equally and oppositely charged. They carry the fundamental constant called
electric charge with them. The magnitude of this value appears empirically to
be the same for both. The current explanation of electric charge is given by
electric field theory. It is normally said that a charged particle radiates an
electric field away from it at the speed of light. Theoretically, for a
particle that has always existed, this field is never ending. It is in
existence over the size of the universe.
Since there is no empirical evidence for the substance of an
electric field, its existence is only an assumption. This new theory does not
use the electric field model. There is only the variation of the speed of
light. Electromagnetic effects must then be derived from the variable speed of
light. For all the variables and constants used in electromagnetic field
theory, there needs to be a physical explanation arising naturally from the
variation of the speed of light.
The first challenge is to explain the fundamental constant nature
of the effect we call electric charge. I will not be distinguishing between
opposite polarities at this time. The origin of opposite polarities needs to
await the definition of mass. The source of the fundamental constant electric
charge, however, can be identified at this time. The formula for electric force
is:
The letter q
represents the electric charge. The example problem I am using to analyze
electromagnetic effects is the hydrogen atom. The letters qq,
therefore, represent the electric charge of an electron and a proton. These
values are empirically determined to be of the same magnitude but to have opposite
signs.
It is necessary to pursue an introductory explanation of the
nature of the fundamental property of electric charge as it can be ascertained within
the parameters of this new theory. Electromagnetic field theory does not
provide a definition for electric charge. It is empirically determined and,
therefore, it is a given. It is explained through its effects.
Since there is no empirical evidence for the substance of anything
defined as a field, I need to see if this new theory can give a clear physical
meaning to the origin of the phenomenon identified as electric charge. The
empirical value of q is:
This value is a fundamental constant, and I should expect it to
reappear as such in this new theory. The only fundamental constant I have
identified for this new theory is the time period for a photon to pass a given
point.
The example problem I am using is the hydrogen atom, and I have assumed the radius of the first orbit, or energy level, might be the length of a photon. This is only an assumption, but I will see if it can help to provide some useful predictions. I will use this assumption to determine a value for the increment of time required for a photon to pass a given point. This time period can be calculated to a good approximation by using the known value for the speed of light.
This theory defines the velocity of light by the expression:
The value for the increment of time in the denominator on the right side is this fundamental time period. It is also the normal increment of time I will use throughout this theory. Time is the companion to all events. This universal measure of time will be used to unify the theory.
It was Einstein's use of time dilation that allowed the theory of
relativity to be applied to almost all physical events without deriving their
direct physical connection. For this new theory time will again help to connect
almost all physical events. However, because this increment of time has a clear
physical meaning it will also help to provide the physical connections for
almost all events.
The value of this increment of time can be calculated to a good
approximation using:
Substituting the measured value for the speed of light, and the
Bohr radius for the length of a photon gives:
The magnitude of the fundamental increment of time is very close
to the magnitude of q. In fact,
if the radius of the orbit for a hydrogen atom is assumed to be approximately:
As is indicated by empirical evidence, then:
The coincidence of the magnitudes of the two fundamental constants grows curiously stronger. This gives cause to wonder if they are the same phenomenon. This may seem very strange to try to equate one value having the units of coulombs to another value having the units of seconds. However, a coulomb is a high level artificial unit. A guiding principle of this new theory is: A physical quantity is not properly defined until it can be explained in units of time and/or distance.
The existence of electric charge is a theoretical assumption
without a physical explanation. No one knows what is electric charge. The fundamental increment of time
used in this theory has a clear physical explanation. If this period of time is the real
origin of the concept of electric charge then it will help and not hurt to use
it in the derivation of electromagnetic effects. If the units of seconds are
wrong, then the units will not match and the results will be nonsense.
I will use the fundamental increment of time in place of electric
charge. It was for this reason that I did not use polarities with electric charge.
Time cannot have polarities. Polarity will later be identified as a property of
mass. Mass is not just a neutral resistance to force. Mass causes positive and
negative variations of the speed of light. This positive and negative variation
is the cause of polarity.
The common formula for electric force contains two quantities that
have not had clear physical explanations. The charge q represents an unknown nature. Also, the
permittivity is only understood as a part of k,
the constant of proportionality for the formula. However, since permittivity
does vary, then k is not a true constant of
proportionality. It might then be possible to establish k as having a physical relationship to electric
force.
I wish to determine an expression for permittivity using the
variables of this theory. It will be an interim expression to serve in place of
the final expression that will be defined as a part of the development of my
analogy to electromagnetic field theory. The reason for this interim step is
that I
can use it to demonstrate the physical origin of the fine structure constant.
I will use the formula for force to help form the expression for
permittivity. I also use the fundamental increment of time in the place of
electric charge. If this step is valid, then a crucial block to achieving a
unified theory will have been removed.
The example will deal with electromagnetic effects of the hydrogen
atom. The use of the hydrogen atom example allows me to conduct the derivations
of electromagnetic effects as they might apply to a single photon. The formula
for electric force is:
As explained above, I substitute the fundamental increment of time
for the electric charge. For atomic dimensions it cannot be approximated as a
differential quantity. Therefore:
Force is also generally defined as:
For this new theory, and for this example, this formula takes the
form:
Setting the two expressions for force equal to each other gives:
For the first energy level of the hydrogen atom:
The subscript c is used to
denote this increment of length is specifically the length of a photon.
Substituting:
Simplifying:
For convenience, I replace the left side with the appropriate
energy symbol:
The subscript c on the left-hand side denotes this quantity
of energy to be the increment of kinetic energy carried by the photon. Solving for
permittivity:
Multiplying by unity:
Yielding:
Where H1
represents the first energy level of the hydrogen atom. The proportionality constant
of the electric force equation is:
Substituting the expression for permittivity into this equation:
The proportionality constant of the Coulomb electric force
equation is equal to the product of the increment of force carried by the photon
and the speed of light squared. The value of force is that which applies to an
electron in the hydrogen atom's first energy level.
The magnitude of the fine structure constant is the ratio
of the speed of an electron in the first energy level of a hydrogen atom to the
speed of light. What is of great interest about it are the values that make up
its definition. It contains constants that come from electromagnetic theory,
relativity theory and quantum theory. I have previously redefined some of these
constants using expressions from this new theory.
I will demonstrate how these new interpretations offer a clear,
simple physical origin to the fine structure constant. The standard formula
defining the fine structure constant is:
And in this theory is:
Where e is electron charge. I have previously
redefined each expression on the right side with the exception of h or Planck's constant. For the purposes
of this section, I will use Planck's constant as it would normally be used.
With the exception of Planck's constant, I substitute expressions from this new
theory for the constants contained in the equation. The expression I derived
for k is:
The expression for e is:
Therefore:
My definition of the velocity of light is:
The normal use of h is:
This says; The energy of a photon divided by its corresponding frequency
is equal to Planck's constant. Substituting all of the above expressions into
the equation for the fine structure constant gives:
Simplification yields:
This suggests that the fine structure constant may be a measure of a
specific angle in radians of something moving in a circular or sinusoidal
motion for the period of time required for a photon to be emitted. Since the
fine structure constant appears to relate in some direct way to the properties
of the hydrogen atom, then I might expect the use of my theory to produce a
result pertaining directly to the hydrogen atom.
The frequency of this motion can be calculated from the above
result. Solving for frequency:
Substituting the appropriate values:
This answer is close to the frequency of the electron that is
orbiting in the first energy level of the hydrogen atom.
Most significantly, I made a radical change to the units of electric charge;
however, the units that appear in this result fit properly. It leads to the
interpretation that the fine structure constant is the angle in radians moved
by the electron during the time required for a photon to be released. The
angle, in radians, is the distance the electron has moved divided by the radius
of the orbit:
Dividing the numerator and denominator by the fundamental
increment of time:
The units of this result also fit properly. The result shows that the
distances traveled by the electron and the photon in the fundamental increment
of time are relevant to the origin of the fine structure constant. It is in
agreement with the initial assumption that the radius of the first energy level of
the hydrogen atom is equal to the length of a photon. I chose to manipulate the
known definition of the fine structure constant, because it adds credibility to
this interpretation.
It is known through empirical evidence that there is a direct connection between the existence of a varying electric field and the existence of a varying magnetic field. The varying electric field is credited with bringing into existence the varying magnetic field. The magnitude and behavior of the varying magnetic field are functions of the varying electric field. The varying magnetic field is said then, in turn, to cause the varying electric field. In other words the electric field and magnetic field are said to be continuously producing each other as both move through a given distance. The relationship between the electric and magnetic fields will be described later.
For now, it is the known relationship between electrical
permittivity and magnetic permeability which is of specific interest. Electrical permittivity is
related to the proportionality constant of the electrical force equation.
Magnetic permeability is related to the proportionality constant of the
magnetic force equation. It is known, in the case of electromagnetic radiation,
that the two are related to each other by the formula:
Or, for this theory:
Solving for permeability:
I have derived:
Substituting this gives:
This equation says permeability is a function of the force felt by
an electron in the first energy level of the hydrogen atom.
I postponed my derivation of electromagnetism for the purpose of
first introducing the concept of electric charge as the fundamental increment
of time. This was necessary in order to properly use this increment of time in
the differential equations that make up this analysis. I will next derive
equations showing the connection between my definitions of photon momentum and
photon energy to electromagnetic theory.
ORIGIN OF
ELECTROMAGNETIC RADIATION
Electromagnetic radiation is a phenomenon physics associates with
particles of light called photons. However, the particles of charged matter are
the sources for all electromagnetic photons. The properties of the charged
particles, in general, give rise to the properties of the emitted photons.
Therefore, the mathematics describing the properties of photons should be
translatable into expressions using the properties of the charged particles
that emitted them.
The fundamental properties which are of principal use in describing
particles are: mass, velocity, and rate of change of velocity. The rate of
change of velocity can be measured with respect to either time or distance. Two
very useful higher-level properties are energy and momentum. These two
properties are complex forms of the fundamental properties of
mass and velocity. It is commonly accepted that energy and momentum are
qualities applicable to both material particles and photons.
I will use these properties to derive equations analogous to electromagnetic
field theory. For convenience in comparing mathematical expressions from
electromagnetic field theory with analogous expressions from this theory, I
will take the liberty of using differential instead of incremental expressions
in the following analysis.
Since photons are themselves incremental and not so small as to be
defined by differential values, this approach is not entirely correct. However,
the true incremental values are of sufficiently small size so that, for macroscopic
purposes, using this approach loses nothing of significance. The benefit gained
will be clarity when showing correlation to electromagnetic field theory.
I will now derive equations for this new theory to describe the effects
attributed to electromagnetic fields. Force can be expressed as a function of a
change in energy:
The force can also be expressed as a function of a change in
momentum:
Combining these two expressions:
This formula has a form similar to this one from electromagnetic
field theory:
And since:
I compare it also with:
The similarity in form between this formula and the one above
expressed in terms of energy and momentum is striking. I will show there is an
indirect connection. Before I can show this, I will develop new formulas that
will account for electromagnetic effects. It is known:
Which can be rewritten for this new theory as:
Solving for the electric field gives:
And since:
I can write:
This formula suggests our concept of electric field is equivalent
to the second derivative of the emitting particle's momentum with respect to
time. Taking the derivative of the electric field with respect to time yields:
I have presented this formula because it, along with three others
to be derived next, begins the process of expressing the phenomenon described by
electromagnetic field equations in terms of the properties of the emitting
particle.
I will now derive the other three equations. Returning to the
equation:
I can substitute:
Making the substitution:
Taking the derivative of the electric field with respect to time:
This is the second equation I will be using for the purpose expressed
above. The remaining two equations are:
And:
These two equations result from taking the derivative of the
electric field with respect to distance. In the first case I take the
derivative of the electric field where it is expressed as a function of
particle momentum. In the second case I take the derivative of the electric
field where it is expressed as a function of energy.
The increment of distance used in taking the derivative cannot be
the same increment of distance the particle moved during the same increment of
time. This new increment of distance has to do with observing the motion of
photons after they have been emitted from the particle. The increment of
distance is not yet a specific value. It represents a moving observer making
measurements of the motion of photons as they move away from their source.
Also, the incremental change of distance cannot be equal to the
length of a photon, in that case the observer would necessarily be moving at
the speed of light. The observer would be traveling at the same speed as the
photons. The observer could not then detect a change in the motion or even
orientation of the photons with respect to time.
The observer also cannot be standing still, or there could be no
change observed with respect to distance. Therefore, the observer is assumed to
have a magnitude of velocity between zero and the speed of light, and is moving
in the same direction as the photons. Further development of electromagnetic
effects will offer an interesting identity for the observer’s magnitude of
velocity.
The work of Maxwell has been interpreted to prove the existence
and the uniting of a varying electric field and a varying magnetic field. He
produced equations that are credited with fundamentally defining electromagnetic
radiation effects. I will now derive analogous equations from this new theory.
2. Definition of Electric Field
The equations I will derive are not just symbolic substitutes
adding nothing to Maxwell's discoveries. The very first step in this derivation
goes to the heart of separating the results of this theory from electromagnetic
field theory. The electric field is defined as:
I will use this equation as it applies to a force caused by a
single charged particle. Since I am seeking to form equations using concepts
developed for this theory, then I can substitute:
In this theory, the fundamental quantity of electric charge is
actually the fundamental time period for passage of a photon. I make this
substitution:
With this substitution I separate the work that follows from any
theoretical connection with electromagnetic field theory. The resulting
equations will be analogous in form, but will have interpretations very
different from field theory.
3. Electric
Field Varying With Distance
I now proceed to derive electromagnetic equations analogous to the
Maxwell equations. Since force can in general be expressed as:
Then I can substitute this definition into the electric field
equation given above:
Taking the derivative with respect to an increment of distance
which a photon would move during a fundamental increment of time: