The Fine Structure Constant, Quantum Theory, and
Additional Structure of the Photon
Joseph M. Brown1
The fine structure constant, alpha (α), has a value of
1/137.03599976. It first appeared as the velocity in speed of light
units of the orbiting electron in its lowest energy state in a hydrogen
atom. The analysis of the orbital velocity gives the equation 2
𝑣𝑜𝑟𝑏𝑖𝑡
𝑐
𝑒2
1
ℏ𝑐
137.03599976
=∝= = 0.007297352533=
(1)
where e is the charge of the electron ħ is Planck’s constant, and c is
the speed of light.
The fine structure constant is the ratio of electromagnetic
forces to nuclear forces. Furthermore, alpha appears throughout
quantum electrodynamic (QED) theory. QED physicists use the
constant throughout their analyses of the interactions of charged
particles and photons. However, they have not the least idea of its
origin. Many physicists reading a book, when they come to page 137,
will pause and wonder what the origin of α is.
During the years 1967 to 1970, the McDonnell Douglas
Company funded the Advanced Propulsion Research Group to
develop a new physical theory which, hopefully, would lead to
extremely advanced propulsion. The group consisted of Joseph M.
Brown (PhD Purdue - Mechanical Engineering), Darell B. Harmon, Jr.
(PhD UCLA - Physics), Leon A. Steinert (PhD Colorado - Physics), and
Robert M. Wood (PhD Cornell - Physics).
The research centered on developing a theory of physics
based on an absolute space - separate absolute time universe filled
with an ether of extremely small, smooth, elastic spheres. We
President of Basic Research Press and Retired Professor of
Mechanical Engineering at Mississippi State University. Paper
prepared June, 2015.
2 This equation is based on a fixed proton.
1
dubbed this the kinetic particle theory of physics. Two parameters
characterizing such a gas are the particle mean speed vm and the
particle RMS speed vr. Toward the end of the research effort, we
discovered the relation
(
𝑣𝑟 −𝑣𝑚 2
𝑣𝑚
) =
1
= 0.007293481
137.108733
(2)
The value 0.007293481 results since vr/vm = √3𝜋/8. This expression,
modified by the orbital analysis of the atom using the atom center of
mass system, gave the factor 0.007289410. This quantity agreed
with the value of the fine structure constant within one percent, see
the paper by Brown, Harmon, and Wood [1].
Based upon the agreement of this arrangement of the kinetic
particle gas parameters and the fine structure constant, our group
felt greatly encouraged that the kinetic particle theory of physics
should be developed.
We assumed that nuclear particles consisted of
condensations of the ether gas and that a condensation would act
like a (fluid mechanic) doublet. Further, matter had to consist of
mass orbiting at the speed of light. This was required to give matter
energy as E=mc2. The computation of the interaction of one nucleon
with another consisted of the analysis of two doublets. From this it
was deduced that the strength of the strong nuclear force was
proportional to the square of the mean velocity and, of course,
proportional to the ether mass density. Thus, nuclear forces are
proportional to ρvm2. This analysis was reported by Brown and
Harmon in reference [2].
We soon concluded that these condensations moving at the
speed of light in a circle making matter had been neutrinos
translating in a straight line (at the speed of light, of course). For a
condensation to be stable, it had to suck in gas particles, align them,
and then expel them in two extremely fine streams. This required a
pumping mechanism and streams that were so fine that this outflow
would not interfere with the inflow. This fine stream requirement
necessitated an extremely large mean free path to particle diameter
ℓ/d ratio. The ℓ/d for the ether gas is 1018, see page 51 of [3].
It was noted that when particles were taken from a MaxwellBoltzmann gas, aligned to be parallel and directed with the same
sense, then squeezed together so that they formed a solid stream
without changing their energy, then the translational velocity will
jump from vm to vr, an 8.5% increase in velocity. The neutrino does
what is specified above. This means that the neutrino will translate
at the velocity vr-vm. Therefore, the speed of light is c =vr-vm. This
discovery was reported in references [4] and [5].
Knowing that the speed of light is vr-vm, we know that
electromagnetic forces are the background density ρ times (vr-vm)2.
With this information and knowing that the strong nuclear force is
proportional to ρvm2 we now know that
𝜌(𝑣𝑟 −𝑣𝑚 )2
𝜌𝑣𝑚 2
𝑣𝑟 −𝑣𝑚 2
=[
𝑣𝑚
]
(3)
is the ratio of the electromagnetic force to the strong nuclear force.
The neutrino has two fine streams of ether particles exiting
in opposite directions from the spherical neutrino. The stream
directed forward is a solid stream translating at the velocity vr. The
stream directed aft is at the velocity vm. When a neutrino is in a
circular orbit, being a nuclear particle, such as the proton, then it
produces a spherical wave with a velocity amplitude vr followed by a
velocity amplitude vm. Thus, one of the primary characteristics of the
electrostatic field is wavespaces with dimensions of 10 -16m (the
orbital radius of the proton, see page 60 of [3]). The waves advance
spherically symmetric from the proton at the velocity vr-vm, or c.
The interactions of photons and electrostatic charge are
dominated by these wavespaces. A photon consists of a string of the
ether gas particles strung out uniformly over a harmonic wave. For
high energy photons each wavespace has many particles and for very
low energy photons many wavespaces along the harmonic curve may
have no particles. The wavespaces always travel radially from the
charged particle at the speed of light. Thus, the speed of light is
always the same, which is vr-vm. The wavespaces encapsulate the
particles making up the photon.
The Bohr (i.e., Newtonian) analysis of electron orbits is
based upon a smooth electrostatic field, not this bumpy field
consisting of these 10-16meter sized wavespaces which actually exist.
Experiments of the radiation from atoms, which are used to infer
orbital velocities, could not be made to be consistent with the
classical theory. Clearly any one given experimentally determined
velocity could be made consistent by adjusting the values of any, or
all, of the constants e, ħ, and c. It was not possible to obtain a
satisfactory analysis using the Bohr theory for all orbits.
A solution to this problem was obtained by using an
equation discovered by Erwin Schrödinger in the early 1920’s. The
equation could be used to determine the probable location of an
electron when subjected to a potential (such as that produced by a
proton when interacting with an electron). The one-dimensional
equation is
−
ℏ2 𝜕2 𝜓
2𝑚 𝜕𝑥 2
+V(𝑥, 𝑡)𝜓 = 𝑖ℏ
𝜕𝜓
𝜕𝑡
(4)
where m is the particle mass, x and t are the space and time
coordinates, V(x,t) is the potential, and ψ is the probability function.
The probability function times its conjugate gives the probability
density. Thus, the probability that a particle will be in a given
interval x = a to x = b is
𝑏
p =∫𝑎 𝜓𝜓 ∗ 𝑑𝑥
(5)
The Schrödinger equation is the cornerstone of quantum mechanical
theory.
Equations of this type, i.e., Schrödinger equations, have been
used for almost a century to obtain research results as well as to
produce industrial and commercial products. There is no question
that the equations model reality.
Earlier it was noted that spectral data from which electron
velocities could be determined could not be correlated using the
Bohr theory. Using quantum theory, the correlations were obtained.
The value of α has been determined to one part in 1010. Quantum
theory reigns supreme in the world of the small.
The break of quantum mechanics form Newtonian
mechanics is due to the strong signal presented by the Schrödinger
equation. The Schrödinger equation gives accurate predictions of
the interaction of photons and charged particles. To this date
(2015), no one has been able to derive the partial differential
equation from physical models. The equation apparently was
guessed at by Erwin Schrödinger. Just what is the physics from
which this equation stems?
One of the simplest applications of the Schrödinger equation
is for a proton moving back and forth in a box when there is no
potential, i.e., V(x,t) = 0. In this case m is the proton mass. One
physical situation is for the width of the box to be a half wavelength
of the proton wave. The wavelength of the proton is
λ=
ℎ
(6)
𝑚𝑣
The velocity v is the average of the velocity from one wall to the next.
At the wall, the velocity is reversed and the proton travels to the next
wall. The solution of the Schrödinger equation for this case is
illustrated in the Figure 1.
Figure 1. Proton in a Box
The parameter ψ times its conjugate ψ* gives a probability
frequency of some characteristic of the proton. From our analysis of
the proton-in-a-box we venture the hypothesis that ψ ψ* is the
probability distribution frequency of the proton energy (i.e., its
kinetic energy of its travel).
In order to try and understand the physics occurring which
produce the above result, let us see if we can gain some insight from
the derivation of the differential equation for the free lateral
vibration of an elastic beam. The deflection of a beam is related to
the bending moment M in the beam by
M = EI
𝑑𝜃
𝑑𝑥
(7)
where E is the beam material modulus of elasticity, I is the area
moment of inertia about the bending centroidal axis, dθ is the
differential angular change of the beam longitudinal axis, and dx is
the differential longitudinal length. Now
θ=
𝑑𝑦
(8)
𝑑𝑥
so that
M= EI
𝑑2𝑦
(9)
𝑑𝑥 2
The shear force Q in the beam is related to the moment by
Q=
𝑑𝑀
𝑑𝑥
= El
𝑑3𝑦
(10)
𝑑𝑥 3
The load on a continually loaded beam with a load W newtons per
unit length is related to the shear by
W=
𝑑𝑄
𝑑𝑥
= El
𝑑4𝑦
(11)
𝑑𝑥 4
The vibration load is the differential mass ρAdx so that the
inertial load per unit length is ρA
EI
𝜕4 𝑦
𝜕𝑥 4
= 𝜌𝐴
𝜕2 𝑦
𝜕𝑡 2
𝜕2 𝑦
𝜕𝑡 2
. From this we have
(12)
Equation (12) is similar to the Schrödinger equation. We
can think of the right term in (12) as the driver and the response is
the lateral deflection of the beam. Let us look at the electrostatic
field of the proton and see if we can identify a driver and a responder.
Notwithstanding this discussion of the Schrödinger equation, we still
do not know how to derive it. We certainly do not think the equation
comes form the magic of (non-newtonian) quantum mechanics any
more than we thought that the magic of (non-newtonian) space-time
mechanics of Einstein was needed to explain mass growth, matter
shortening, and time dilation with velocity, see pages 98 to 107 of
[3].
We want to consider the behavior of the proton without any
potential, i.e., free proton traveling back and forth from one wall of a
box to the other (in the special case where the wall width d = λ/2 =
h/(2mv) ).
First, let us look at the neutrino which became the proton.
The neutrino absorbed ether particles and emitted them in two fine
streams along its propagation vector -- the aft stream at velocity vm
and the forward stream at velocity vr , where vm and vr are the mean
and RMS velocities of the ether gas which has a Maxwell-Boltzmann
distribution of speeds, see [1] or [2]. The neutrino takes random
energy from the ether gas and produces organized energy.
When the neutrino becomes a proton, it begins orbiting and
establishes its electrostatic field which consists of three-dimensional
wave spaces whose dimensions are on the order of the orbital radius
of the proton (10-16m). The orbital velocity is vr–vm (i.e., the speed of
light c, of course). The wave spaces all travel at the speed of light
radially from the proton. Each wave space has a circulation velocity
of vm where the plane of vm passes through the center of the proton,
but the wave space travels at the speed vr–vm.
These wave spaces characterize the electrostatic field. The
ratio of the translating velocity (vr–vm) to the circulatory flow vm i.e.,
(vr–vm)/ vm) = (√3𝜋/8 - 1) is 0.085401882. This is believed to be the
origin of the coupling constant for electrostatic fields. The coupling
force between two electrostatic fields is proportional to the square of
this velocity (as are all forces in the kinetic particle universe). We
also would expect the coupling to be proportional to the square of
this number, although we do not understand the mechanism. If so,
then the fine structure constant α is given by
α =(
𝑣𝑟 −𝑣𝑚 2
(13)
)
𝑣𝑚
Let us return now to the Schrödinger equation and perform
two crude integrations of the terms in the equation.
We start with
−
ℏ2 𝜕2 𝜓
2𝑚 𝜕𝑥 2
= 𝑖ℏ
𝜕𝜓
𝜕𝑡
(14)
Integrating each term once and ignoring the factor i since it only
affects phasing.
−
Integrating again
ℏ2 𝜕𝜓
2𝑚 𝜕𝑥
= ℏ𝜓
(15)
−
ℏ2
2𝑚
𝜓 = ℏ ∫ 𝜓 𝑑𝑡
(16)
The term on the right of (16) would have to be due to the
continual stream of energy emitted from the proton. (Recall that the
proton has to put out energy at the same rate the neutrino (making
the proton) was taking in energy.) Now the term on the left of (16) is
how the proton responds (presumably).
Let us now discuss the details of how the proton responds.
First of all we need to review how a charged particle is caused to
move. Let us review the structure of the photon and how it interacts
with the electrostatic field. This information is obtained from [3] and
from the appendix. The photon is produced or absorbed by the
change of the electron orbit in an atom or by the change of velocity of
an atom. The process involved in the electron orbital energy
reduction is easier to explain. Ether particles are collected uniformly
from all around the orbit circle. The particles moving at the speed of
light are encapsulated uniformly in the wave spaces which wave
spaces move from the center of the charged particle at the speed of
light. The number of ether particles is the photon energy divided by
the energy of the individual ether particles (i.e., the particle mass m
times c2). Some photons will have many particles in each wave space
(high energy-short wave length photons) to some photons with only
one particle in a large string of wave spaces. The harmonic shape of
the photon is due to the emission by winding the photon mass out of
a circular path.
Let us return now to the proton-in-a-box. While the proton
is translating, its neutrino takes a two-dimensional spiral path and
the mass that caused it to translate has a translational energy of mv2
and has a large plane spiral path with an angular momentum of ħ.
When the proton meets the wall, this spiral string of ether particles is
emitted and the proton stops. A photon coming from the opposite
direction has a uniform distribution of the encapsulated ether
particles absorbed in an elliptic path (as seen from a reference
system attached to the new translating proton) or a plane spiral path
seen from the box reference system. A new lower energy photon is
scattered off (as proven by the Compton scattering experiments).
The interaction is governed by the conservation of mass,
conservation of linear momentum, and the conservation of energy, of
course.
Let us now examine the mechanism involved in the photon
travel between the walls of the box. First we need to examine how a
photon interacts with a charged particle to accelerate (and
decelerate) it. We then need to see how the charged particle stops at
the wall and starts from the wall.
The gross characteristics of the acceleration are developed
on pages 112-114 of [3]. A photon of energy E impacts a proton at a
distance rc from the mass center of the proton. To satisfy energy and
linear momentum conservation, and consistent with the Compton
scattering experiments, part of the photon mass is captured (Mc) and
part is scattered as a lower energy photon (Ms). The captured mass
accelerates the photon as does the scattered mass. The scattering
direction is equally likely to be in any direction over 4π steradians
with its average being perpendicular to the impacting photon
direction. Thus, the average momentum imparted is the scattered
mass ms times c. The momentum imparted by the captured mass is
the captured mass mc times c. Thus, the average momentum
imparted is the impacting mass times c.
The momentum imparted produces an angular momentum
equal to ħ. Thus, the proton undulates harmonically as it translates.
The wavelength λ of this undulation is now computed.
ħ = Prc = movrc, h = 2πħ = 2π movrc = movλ
(17)
In this, P is the photon momentum which is also the proton
momentum mov resulting from the impact.
From this, the
wavelength is
λ = h/mov
(18)
This is the relation postulated by deBroglie for matter in motion.
The wavelength is called the deBroglie wavelength. The captured
mass of the photon is stored in a closed curved elliptic shape when
viewed from a frame moving with the proton.
At the center of the path (between the two walls) the center
of the elliptic ring of (photon) mass is at the top (or bottom) of its
path and is translating horizontally at its maximum horizontal speed.
Figure 2 shows the horizontal component of the velocity of the
charge.
Figure 2. Horizontal Component of the Velocity of the Charge
At the right of the path, the charge center is moving essentially
vertically. The charged center then reverses and starts toward the
left wall. These velocities are generated by the motion of the center
of the captured mass of the photon and this captured mass carries
the electrostatic field with it. As this field translates, it also rotates in
a circular path so its horizontal velocity varies harmonically between
the walls.
If we define ψ as the probability frequency of the magnitude
of horizontal velocity of the electron then ψ ψ* could be proportional
to the energy probability. In this case, this classical analysis of the
proton-in-a-box gives similar results to the Schrödinger equation.
Schrödinger, as well as all QED researchers, almost certainly
did not know of the bumpy characteristics of the electrostatic field.
Nonetheless, Schrödinger did discover the equations. Further, any
physicist who studies the physics chapters of reference [3] might
conclude that the Schrödinger equation models the classically
derived bumpy electrostatic field. However, to our knowledge, no
one has proven that the Schrödinger equation can be derived from
the characteristics of the 10-16 meter sized wave spaces of the
electrostatic field. We present further discussion of this problem on
pages 91-95 of [3]. At the end of the day, however, we still do not
know why the speed of an electron in its lowest orbit is
approximately [(vr–vm)/vm]2, in velocity of light units.
Appendix: Structure of the Photon and How it
Changes the Orbit of an Electron
Introduction
The gross characteristics of the photon were discovered in
2011 and reported by the author in reference [6]. The theory of the
photon is based upon the postulates that identical, small, spherical,
elastic particles moving at an average speed over ten times the speed
of light make up a gaseous ether which pervades the universe. All
neutrinos, matter, photons—everything—is made of these tiny
elastic particles, which we call brutinos. The photon is a string of
brutinos uniformly distributed along a complete sine wave. The
brutinos move slowly compared to the average speed of the
background particles. Their speed, of course, is the speed of light, c,
and their total mass times the square of their speed is the energy
they transport. The particles making the sine wave do not undulate
as the photon travels; the photon travels like a wire bent in the shape
of a sine wave.
Since the publication of [6] we have made additional
discoveries about the photon structure.
The brutinos are
encapsulated in a string of spheroidal wavespaces which have linear
dimensions of 10-16 m. These wavespaces are links making up a
sinuoidal chain the length of the photon. Also, we have additional
insight into the mechanism by which the photon increases the orbital
path of an electron in an atom.
First, we describe the characteristics of the electrostatic
field.
The Electrostatic Field
Each matter particle, such as the proton, is composed of a
neutrino (moving at the speed of light) which takes a circular path.
In the case of the proton, the path has a radius approximately 10 -16
m. The neutrino continually expels brutinos from its front end in a
fine stream at speed vr, the RMS speed of the background gas, and
another fine stream out the aft end at the mean speed, v m, of the
background gas.
Then two outflows from the neutrino at several diameters of
distance from the orbital circle produce an oscillating, near spherical
wave which advances at the speed vr-vm (i.e., the speed of light). Since
𝑣𝑟 /𝑣𝑚 = √3𝜋/8 for a Maxwell-Boltzmann gas, which the background
gas is, we have 𝑣𝑟 − 𝑣𝑚 = √3𝜋/8 𝑣𝑚 − 𝑣𝑚 = 𝑐. Thus 𝑣𝑚 =
2/(√3𝜋/8 − 1) = 3 × 108 ⁄0.0854 = 3.51 × 109 𝑚⁄𝑠. The expanding
wave consists of three-dimensional wavespaces with dimensions in
all three directions in the order of 10-16 m. Each wave has a radial
velocity amplitude of vr followed by a velocity amplitude vm in the
same direction.
The three-dimensional wavespaces have polarity. The
positive electrostatic field is produced by the proton which consists
of a right-handed neutrino. The negative electrostatic field is
produced by an orbiting left-handed neutrino making the electron.
Two charged particles produced by opposite spin attract each other
while those produced by the same spin repel each other. For more
background, see pages 72 - 75 of [7].
The waves progressing from a charged particles have
motions like that produced by a breathing sphere immersed in a gas.
When two charged particles are placed in the vicinity of each other
the waves interact to produce attraction when the waves are 180°
out of phase and repulsion when in phase. Phasing of the waves is
controlled by the twist components of the fields produced by the
neutrino spin
Photon Formation and Structure
A photon is formed when, for example, the electron in a 1H
atom in its next lowest energy state drops to its lowest energy state.
It expels brutinos (the ether particles) continually from the atom at
the velocity of light, of course. The brutinos were uniformly
distributed around a circle in the atom and, thus, are uniformly
distributed along the photon. Once released, each brutino is
confined to one of the wavespaces which wavespace is formed by the
meshing of the proton and electron electrostatic fields. These fields
can extend to the edge of the visible universe (Ru≗1028 m).
The energy E of a photon is nmc2, where m is the mass of the
brutino (≗10-66 kg), and n is the number of brutinos in the photon.
These brutinos are spread uniformly along the length of the photon.
The energy is given by two equations
𝑐
𝐸 = ℎ and 𝐸 = 𝑛𝑚𝑐 2
(1)
ℎ𝑐
(2)
𝜆
𝜆
= 𝑛𝑚𝑐 2 or 𝜆 = ℎ⁄(𝑛𝑚𝑐)
In these equations h is planck’s constant which is 6.63 × 10−34 𝑘𝑔 −
𝑚2 /𝑠.
The wavelength, in meters, of the photon having one brutino
per wavespace is given by
𝜆1 = 10−16 𝑛
(3)
Using 𝜆 from the second equation in (2) and equating to 𝜆 from (3)
gives
𝜆1 = ℎ⁄(𝑛𝑚𝑐) = 10−16 𝑛
(4)
𝑛 = √ℎ⁄(10−16 𝑚𝑐)
(5)
or
Using the mass of the brutino from Appendix B of reference [2] gives
𝑛=√
6×10−34
10−16 ×3×10−66 ×3×108
= 8 × 1019 particles
(6)
Now the wavelength 𝜆1 , of the photon with one brutino for each
wavespace is
𝜆1 = 8 × 1019 × 10−16 = 8 × 103 𝑚
(7)
This wavelength is the upper range of radio waves.
Figure 1 shows a plot of the photon having one brutino per
wavespace.
a.
Sine Wave of 9x103m Long Photon
b.
Detail of Block A in Figure a.
Figure 1. Photon with One Brutino Per Wavespace
it is
The wavelength 𝜆𝑚𝑎𝑥 of the photon with only one brutino in
ℎ
𝜆𝑚𝑎𝑥 = (1)𝑚𝑐 =
6×10−34
3×10−66 ×3×108
= 1024 m
(8)
The length is approximately the radius of the observable universe.
(Actually, the brutino might be smaller than 3 × 10−66 kg which
would make 𝜆𝑚𝑎𝑥 larger and more nearly equal the observable
radius of 1028 m.) A photon with one brutino would not be
recognizable as a photon.
Figure 2 shows a photon consisting of just one brutino.
Figure 2. Photon Consisting of One Brutino
The one brutino is shown on the right side along with its velocity c.
Obviously such a photon is unrecognizable. Since photons lose one
brutino per wavelength of travel (see page 80–86 of [6], the photon
shown could be a 10-7m wavelength photon which was emitted from
a star 1011 light years from the earth and just now appeared here.
The structure of the photon with a wavelength of 10-16 m is
determined now. From equation (2)
𝜆 = 10−16 = ℎ/(𝑛𝑚𝑐)
(9)
and
𝑛 = ℎ⁄(10−16 𝑚𝑐) = 6 × 10−34 ⁄(10−16 × 3 × 10−66 × 3 × 108 ) (10)
= 0.7 × 1040
The number of brutinos placed touching each other in a single row
10-16 m long is 10−16 ⁄10−34 ≈ 1018 . The number nr of these rows
required for the 10-16m square cross section photon is
𝜂 2 𝑟 ≈ 1040 ⁄1018 = 1022 and 𝜂𝑟 = 1011
(11)
A square cross-section photon would require 1011 by 1011 rows.
Thus, the width of a square cross-section photon with a wavelength
of 10-16m is
1011 × 10−34 = 10−23 𝑚
(12)
The dimensions are 10−23 𝑚 × 10−23 𝑚 × 10−16 𝑚 and the cross
section is approximately 10−46 𝑚2 . This value is near the maximum
cross section of the core of a square neutrino. Since this core size is
the maximum size of any neutrino and such condensations
producing these cores produce the photon it is concluded that the
minimum wave length of a photon must be around 10-16m. Figure 3
shows a photon with a wavelength of 10-16 m.
Figure 3. Photon 10-16m Long (One Wavespace)
The wavelength at the middle of the optical spectrum is
5.5 × 10−7 m. There are 5.5 × 10−7 ⁄10−16 = 5.5 × 109 wavespaces
in this photon. The number of brutinos in a photon of wavelength
5.5 × 10−7 is
𝑛=
ℎ
𝜆mc
=
6×10−34
5.5×10−7 ×3×10−66 ×3×108
= 1030
(13)
Thus, there are
1030 ⁄(5.5 × 109 ) ≈ 2 × 1020 brutinos/wavespace. (14)
There are approximately 1020 brutinos per wavespace for optical
photons.
Mechanism by which the Photon Changes Electron Orbits
Consider a hydrogen atom having one nucleon (i.e. 1H)
where the electron is in its lowest orbit. A photon can impact the
atom and cause the electron to increase its orbit to the next higher
energy state. In this process, the electron potential energy is
increased and the electron velocity decreases to decrease the
electron kinetic energy.
The electron wave length is always given by
𝜆 = ℎ ⁄ (𝑚𝑣)
(15)
Where m is the electron mass and v is its velocity. For the lowest
energy orbit the orbit circumference is this wave length which we
denote by 𝜆1. Letting v1 be the orbital velocity in the state we have.
𝜆1 = ℎ⁄(𝑚𝑣1 )
(16)
Letting r1 be the orbital radius we have
𝑟1 = 𝜆1 ⁄2𝜋 = ℎ⁄(2𝜋𝑚𝑣1 ) = ℏ⁄(𝑚𝑣1 )
(17)
For the next higher energy orbit the orbital circumference is two
electron wavelengths. Thus
𝜆2 = 2ℏ⁄(𝑚𝑣2 )
(18)
and
𝑟2 = 𝜆2 ⁄2𝜋 = 2ℎ⁄(2𝜋𝑚𝑣2 ) = 2ℏ⁄(𝑚𝑣2 )
(19)
Balancing the centrifugal force with the electrostatic
attraction force we have
𝑒 2 ⁄𝑟1 2 = 𝑚𝑣1 2 ⁄𝑟1 and 𝑒 2 ⁄𝑟2 2 = 𝑚𝑣2 2 ⁄𝑟2
(20)
𝑒 2 ⁄𝑟1 = 𝑚𝑣1 2 and 𝑒 2 ⁄𝑟2 = 𝑚𝑣2 2
(21)
or
Substituting r1 and r2 from (17) and (19) goes
(𝑒 2 ⁄ℏ) 𝑚𝑣1 = 𝑚𝑣1 2 and 𝑒 2 𝑚𝑣2 ⁄(2ℏ) = 𝑚𝑣2 2
(22)
𝑣1 = 𝑒 2 ⁄ℏ and 𝑣2 = 𝑒 2 ⁄(2ℏ)
(23)
or
Using the fine structure constant 𝛼 where
𝛼 = 𝑒 2 ⁄ℏ𝑐
We have
(24)
𝑣1 = 𝛼𝑐 and 𝑣2 = 𝛼𝑐 ⁄2
(25)
The potential energy P1 for the lowest energy orbit is
∞ 𝑒2
𝑃1 = ∫𝑟
1 𝑟
𝑑𝑟 = −
𝑒2
𝑟1
= −𝑚𝑣1 2 = −𝑚(𝛼𝑐)2
(26)
and for the next higher orbit the potential energy P2 is
∞ 𝑒2
𝑃2 = ∫𝑟
2 𝑟
𝑑𝑟 = −
𝑒2
𝑟2
= −𝑚𝑣2 2 = −
𝑚(𝛼𝑐)2
4
(27)
The kinetic energy K for each orbital is
1
1
2
2
𝐾1 = 𝑚(𝛼𝑐)2 and 𝐾2 = [𝑚(𝛼𝑐/2)2 ]
(28)
Let us denote 𝑚(𝛼𝑐)2 as 𝐵
then
1
1
1
4
2
8
(29)
𝑃1 = −𝐵, 𝑃2 = − 𝐵, 𝐾1 = 𝐵, 𝐾2 = 𝐵
we see that
3
3
4
8
Δ𝑃 = 𝑃2 − 𝑃1 = 𝐵, ΔK = 𝐾2 − 𝐾1 = − 𝐵
(30)
We, therefore conclude that the potential energy increases from the
3
lowest to the next higher orbit by 𝐵 and the kinetic energy
4
decreased by half this amount. Further, the orbital velocity halved.
And the orbital radius quadrupled.
The energy required to change the electron orbit from the
lowest energy to the next higher state is
3
3
3
3
4
8
8
8
∆𝐸 = 𝐵 − 𝐵 = 𝐵 = 𝑚𝑒 (αc)2
(31)
where 𝑚𝑒 is the electron mass. The photon energy which must be
captured for the orbit change is given by (31). Thus we have
3
𝐸𝛾 = ℎ 𝑐 ⁄𝜆 = 𝑚𝛾 𝑐 2 = 𝑚𝑒 (αc)2
8
where 𝑚𝛾 is the photon mass. Solves for 𝜆 from (32) gives
(32)
𝜆 = 8ℎ⁄(𝑚𝛼 2 𝑐)
= 8 × 6.63 × 10−34 × (137.1)2 ⁄(9.11 × 10−31 × 3 × 108 )
(33)
= 3.65 × 10−7 𝑚
Placing these in a circular pattern results in a radius r of
𝑟 = 𝜆⁄(2𝜋) = 3.65 × 10−7 ⁄(2𝜋) = 5.81 × 10−8 𝑚
(34)
The characteristics of such a photon are
𝑁 = 3.65 × 10−7 ⁄10−16 = 3.65 × 109 wavespaces
(35)
𝑛 = ℎ⁄𝑚𝑐𝜆 = 6.67 × 10−34 ⁄(2.89 × 10−66 × 3 × 108 × 3.65 × 10−7 )
= 2.11 × 1030 Brutinos
(36)
𝑛⁄𝑁 = 2.11 × 1030 ⁄3.65 × 109
= 5.78 × 1020 brutinos/wavespace
(37)
A photon with a wavelength approximately 10−7 m (i.e., a
photon) more energetic with more brutinos than those in the
3.65x10-7 photon, can impact 1H in its lowest energy state resulting
in quadrupling the electron orbital radius and decreasing the orbital
velocity by a factor of two.
When the 10−7 m wavelength photon impacts the hydrogen
atom, it must be wrapped around the atom. This process requires
energy. The energy is supplied by the potential produced by the
electrostatic fields of the atom. This potential is similar to the
gravitational potential of a star acting on a passing photon. However
the electrostatic potential is some 1039 times as strong as the
gravitational potential. Remember that the photon consists of these
10-16 m wavespaces all along its sine wave structure and that the
hydrogen atom also consists of these 10-16 m wavespaces. The sine
wave of the photon is changed to a circle with a radius
approximately a thousand times the magnitude of the electron
orbital radius.
The forces pulling the photon into the electron pull the
electron outward. The electron must slow down so that twice its
wavelength will be that of a complete circle around the proton.
a. Photon Approaching a Hydrogen Atom
b. Electron Capturing the Photon
c.
Orbit Change is Complete – Photon Mass is Captured in the
Electron Orbit Circle
Figure 4. A Hydrogen Atom Capturing a Photon
Figure 5 shows the final orbit of the electron and shows the
photon mass in its final location.
Figure 5. Final Location of Electron and Photon
Mass
Concluding Remarks
The mechanism of the photon as presented here is
spectacular, to say the least. The fundamental 10-16m wavespaces
formed by a charged particle always moving at the speed vr-vm (i.e.,
the speed of light) provide the key to the photon characteristics.
Photons always move at the same speed. The mass transported is
always encapsulated in the wavespaces so that the mass always
consists of brutinos moving at speed c which is approximately a
tenth the average speed of the background brutino gas particles.
Capturing a photon by an atom is likened to a macroscopic
mechanical process of taking a portion of the brutinos from each
wavespace putting part into other wavespaces to make a lower
energy photon which is emitted and putting the remaining brutinos
into a circular ring of wavespaces surrounding the nucleus. The
photon mechanism emphasizes the role of the background gas
parameters vr (the background RMS speed) and vm the background
particle mean speed. Even with these insights into the electrostatic
field there is still much to learn about quantum electrodynamics. For
example, we still do not know why the electron in its lowest energy
state in 1H translates at the speed [(𝑣𝑟 − 𝑣𝑚 )⁄𝑣𝑚 ]2 , in speed of light
units.
The role of the wavespaces encapsulating brutinos and
requiring that they move at less than one tenth the mean speed of
the background particles (i.e., at the speed of light) provides
additional insight into the role of a single brutino regarding the finite
life of photons and into the mechanism of gravitation. Both the
electrostatic and gravitational fields consist of 10−16 𝑚 sized
wavespaces. As the photon travels it loses a single brutino from its
initial large number of brutinos for each wavelength of travel. The
gravitational field is produced by a single brutino causing the
amplitude of one spherically shaped electrostatic field to oscillate
about another electrostatic field with the amplitude of the brutino
diameter (see pages 90–92 of [7]).
References
1. Brown, J.M., Harmon Jr., D.B., and Wood, R.M., “A Note on the Fine
Structure Constant,” McDonnell Douglas Astronautics
Company Paper MDAC WD 1372 Huntington Beach, CA, June
1970. Available from Basic Research Press.
2. Brown, J.M., Harmon, Jr. D.B., “A Kinetic Particle Theory of
Physics,” J. Mississippi Academy of Sciences, VXVIII, Pages 126, 1972. Available from Basic Research Press.
3. Brown, J.M., The Mechanical Theory of Everything, ISBN: 978-09712944-9-3, Basic Research Press, Starkville, MS, 2015.
4. Brown, J.M., “A Counter Example to the Second Law of
Thermodynamics”, Abstract p.98, Journal of the Mississippi
Academy of Sciences, Vol. XXVI Supplement, 1981. Available
from Basic Research Press.
5. Brown, J.M., “Force Production from Interacting Gas Flows for
BMD Applications”, Final Report on U. S. Army Contract
DAS6-80-C-0034 Administered by U. S. Army Ballistic
Missile Defense Agency, Box 1500, Huntsville, Al. 35807,
October 1, 1981. Available from Basic Research Press.
6. Brown, J.M., “Photons and the Elementary Particles,” ISBN: 978-09712944-5-5, Basic Research Press, Starkville, MS 39759,
USA – 2011.
7. Brown, J.M., “Foundations of Physics,” ISBN: 978-0-9883180-0-7,
Basic Research Press, kStarkville, MS 39759, USA – 2012.