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FINE STRUCTURE
CONSTANT
ELECTRIC CHARGE
James A. Putnam
Theory
Introduction Page Website Homepage
Table of Contents
ã 2003
Usefulness and Correctness of Theory
How possible is it to be theoretically wrong and still predict accurate
empirical data? How useful can incorrect theory be? Is usefulness a reliable
indicator of the degree of correctness of a theory? I will test
well-established theory by changing its derivation. The results will help to
answer these questions. I choose to use the theory of electric charge. It has
been very useful in theoretical physics. Since its inception, electric charge
has been an important part of every comprehensive theory. If electric charge
has been misinterpreted, it would change a great deal of theory. Therefore, the
stakes are high for theoretical physics that electric charge be real. I will
proceed to change the interpretation and character of electric charge. I will
show what effect this change causes to the definitions of electric permittivity
and the fine structure constant.
In order for this example to be convincing, I make a completely
radical change. However, even though it will be in complete contradiction to
its current interpretation, I want to use it to demonstrate a principle I believe
should always be adhered to in physics theory. It is: Every phenomenon must be
expressible in units of distance, time, or various combinations thereof, or it
is not yet correctly understood. The reason for this requirement is that all of
our information comes to us through the observation of changes of velocity.
These changes of velocity contain units of distance and time only. Everything
else introduced into theoretical physics must be derivable from the information
contained in data about changes of velocity. Any idea of theoretical physics
that cannot meet this requirement is evidence of an empirically unsupported
educated guess about the properties that may exist in the universe.
If unity of origin exists in the real physical world then theoretical
physics should need only one ‘given’ for all of its needs. Not a ‘given’ as a
late afterthought or as evidence of symmetries among fundamentally diverse
sub-theories, but a single ‘given’ right from the start. Everything else should
be derivable from it. Although I am not attempting to do that at this time, I
mention it because I will use this example to demonstrate, in an introductory
way, how this kind of approach would work. So, I choose electric charge to
represent something expressible in terms of distance and/or time. Without
explanation or justification I will change electric charge to be represented
theoretically as simply a measure of time. This change should be sufficient to
give the appearance of having no orthodox chance of achieving successful
theoretical results. It will serve to demonstrate how a radically different,
seemingly incomprehensible interpretation can be successful.
Electric charge will no longer be the mysterious source of
electrical and magnetic forces. It is only a measure of time and carries the
units of seconds. Therefore, instead of the magnitude and units of electron
charge being represented as:
coulombs
It will be represented by:
seconds
Since electric charge is a very important fundamental concept, and
since the speed of light is also a very important fundamental concept, I will
see what association might exist between them. The units for the speed of light
C are meters/sec, and the units of electric charge e
are seconds. Therefore, in this example it is proper to multiply
them. I multiply C by e and obtain:
meters
This distance is very much like the size of the radius of the
hydrogen atom. Therefore, I will take advantage of this and use a simple model
of the hydrogen atom as the vehicle to test my new interpretation of electric
charge. In order to do this I will allow Dx to
represent this specific length:
I take the liberty of expressing this relation as equality:
Putting this interpretation of electric charge to the test, I will
use it to derive electric permittivity in the mks system of units. In the
following example I introduce this new result into the formula for the fine
structure constant. It will help to demonstrate the physical basis of the
fine structure constant.
Electric Permittivity
The common formula for electric force contains two quantities that
do not have clear physical explanations. The cause of charge q is unknown. Also, the permittivity is only
understood as a part of k, the
constant of proportionality for the formula. I will derive an expression for
permittivity using electric charge as a measure of time. This result will be
used to interpret the physical origin of the fine structure constant.
The formula for electric force is:
I substitute the new interpretation for electric charge. The force
acting on the electron of the hydrogen atom becomes:
For the first energy level of the hydrogen atom:
Force is also expressed as:
For this example, the increment of distance in the denominator is
the length Dx I am using to represent the radius of
the atom. Unless I state otherwise, whenever I express a rate of change with respect
to distance I will use this same Dx in the
denominator.
Setting the two expressions for force equal to each other gives:
Simplifying:
Solving for permittivity:
I substitute a new symbol representing the new interpretation for electric
charge:
Now I have:
My Dx and
Dt have specific pre-assigned values that
allow me to use:
Substituting and simplifying:
Multiplying by unity:
Yielding:
Rearranging terms:
The proportionality constant of the electric force equation is:
Substituting the above expression for permittivity into this
equation:
Using the relation:
Then k can be expressed simply as:
The proportionality constant of the Coulomb electric force
equation is equal to the product of the force being exerted on the first energy
level electron and the speed of light squared. Next I will apply the results
from this work to the definition of the fine structure constant.
Fine Structure Constant
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 are of great interest about it are the particular constants making
up its definition. It contains constants that come from electromagnetic theory,
relativity theory and quantum theory. There should be a real clue to true unity
contained in the definition of the fine structure constant.
I will use my new interpretations for e and k to help show a physical origin for the
fine structure constant. The formula defining the fine structure constant is:
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.
This action mixes new interpretation with old interpretation. I will show how
this mix can work together to explain the fine structure constant.
With the exception of Planck's constant, I substitute the terms in
the equation with expressions derived using electric charge as a measure of
time. The expression derived for k is:
Or:
Canceling Dx:
My expression for e is:
Therefore:
The definition of the velocity of light is:
The normal use of h is:
Where w represents frequency. Since I am considering the hydrogen atom,
I am working with incremental values. Distance is Dx.
Time is Dt. The energy for which the frequency is
to be calculated is DE:
Substituting:
Now, substituting all of the above expressions into the equation for
the fine structure constant gives:
Simplification yields:
This suggests the fine structure constant is a measure of an angle
in radians. Since the fine structure constant appears to relate in some direct
way to the properties of the hydrogen atom, then I might expect this result to
pertain directly to the hydrogen atom.
The frequency of this motion can be calculated from the above
result. Solving for frequency:
I know the numerical value of Dt. So,
substituting the numerical values for each term:
This frequency solution is close, within about ten percent, to the
orbital frequency of the electron. The interpretation of the fine structure constant
may be deduced: It is the angle in radians moved by the electron during the time
required for light to travel from the nucleus to the electron. 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 measure of time Dt:
The numerical results are not wildly extreme and without any
connection to empirical data. Perhaps what is even more significant is that my original
change had to do with a radical change in units. The result has units that
match. The point to be emphasized is that most units of physics are
theoretical and are subject to the possibility of revision. They are theoretical
by virtue of being introduced for the purpose of substituting for missing
knowledge. They allow us to proceed with the development of higher level theory
even though the natures of fundamental properties remain unexplained. They have been very
useful, but they may also be very wrong.