AOH :: HIDDEN.TXT
The Hidden Variable Solution, (formerly On the Quantum as a Physical Entity), Postulate for a Theory of the Universe.
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Subject: HIDDEN VARIABLE SOLUTION
Newsgroups: sci.physics
Organization: Cinenet Communications,Internet Access,Los Angeles;310-301-4500
Summary:
Keywords:
Newsgroups: sci.physics
Organization: Cinenet Communications,Internet Access,Los Angeles;310-301-4500
Summary: A solution is necessarily *physical*.
Keywords: EPR, Bell
THE HIDDEN VARIABLE SOLUTION
Formerly
ON THE QUANTUM AS A PHYSICAL ENTITY
Dedicated to the memory of my daughter Vivian and her life extension Bridgette
PREAMBLE
Perhaps the most universally pressing problem in modern physics is to
ascertain the true underlying nature of what is most generaly termed
the 'quantum reality'.
This is aptly displayed in the EPR Paradox vs Bell's Theorem dialogue.
The wave function quantum theory has been emminently successful in
results but there is no understanding of just *how* it works and
the reality behind it.
Such things as non-locality, uncertainty, wave/particle duality, wave
entanglement, and phase conjugation all cry out for a physical
representation or explanantion.
Such is offered here in the thesis at hand.
There is no claim that all the puzzling aspects of quantum theory are
worked out -- nor is it admitted that the answers do *not* lie in the model.
The assertion is that it explains a great deal, and with further endeavor
by many may possibly explain all.
V.V.
July, 1995
-<*>-
Note, all copyright laws apply. Placing On The Quantum as a Physical
Entity in electronic form does not change that. Copying is granted
strictly for personal use only. Permission for retransmission in any
form is not granted.
*<->*<->*<->*<->*<->*<->*<->*<->*<->*<->*<->*<->*<->*<->*<->*<->*<->*<->*
THE HIDDEN VARIABLE SOLUTION
Formerly
ON THE QUANTUM AS A PHYSICAL ENTITY
Postulate Base for a Theory of the Universe
Einstein based his special relativity theory on two postulates, the
present theory is based on one.
We must, in composing a theory of the fundamental construction of the
universe, commence with a clear ideal.
This means we start at the very basic, most simple, yet comprehensive
level.
Being aware that the universe is in a great measure the way we see it
the postulate must exclude anthropological interpretation. Therefore,
THE POSTULATE
The objective universe consists only of matter, space between matter,
and the motion of matter through that space, the rest is anthropic.
In elucidation thereof:
Man perceives matter, to quantify it he perceives "mass".
Matter exists objectively, mass is a concept only.
Matter resists motion or alteration of motion. Man perceives that as
"inertia" which in turn quantifies mass.
Matter moves with varying quantities of motion. Man compares all quantities
of motion to one used as a standard which is constant. This standard motion
is divided into arbitrary units. The transit of the standard through one
unit is designated as time. (The rotation of the earth is a standard motion.
One rotation is designated as a day {time} with arbitrary subdivisions.)
All other motions are then compared to a unit of time. Thus, at base,
time is the comparison of motions.
The quantification of motion in terms of time is conceptualized as
"velocity". Ultimately this is a comparison of motions against the standard.
The quantification of the motion of matter in terms of mass and velocity
is conceptualized as "momentum", i.e., there is a simultaneous determination
of the quantity of matter *and* the quantity of motion it possesses.
Matter moves and changes that motion by interaction. Man perceives
the rate of change as "force", i.e., the change of momentum with respect to
time. Collaterally he perceives "acceleration".
Matter interacts with matter forming an altered configuration in reaction.
Man regards that as "energy"
There is space between matter. Man perceives that and quantifies it by
arbitrary standards of matter. Thus is created the concepts of "dimension"
and "distance".
-<*>-
So we see that dimension, space, time, mass, inertia, momentum,
acceleration, force, and energy are all subjective interpretations by
man of matter and its motion through space.
* * * *
There are only two requirements of the theory here to be evolved, that it
interpret the universe true to this basic postulate, and that it be
consistent both internally and with experiment.
There is no requirement that the criteria of present physics be met.
* * * *
The reader is advised to dispense with *all* preconceived concepts.
Accept nothing learned before as absolute. Do accept that which is
presented here on its face value -- provided the self consistency,
consistency with empiricism and consistency with the postulate are
maintained.
- - - - - - - - - - - - - - - - - - - - - - - - -
There is an ever increasing awareness in the physics community that
despite its accomplishments the present view of quantum mechanics is
lacking. There is a growing desire for a more holistic physical model.
Following is a proposed model that explains much of the workings of
QM. Much is not explained. The presentation here should be considered
only as a blueprint or scaffolding that supplies a substructure upon
which can be built further knowledge and upon which new heights can
be reached.
At first it may appear too simple, however a substantive assemblage will
soon be apparent.
One of the problems in assimilating this model is that it is in
actuality a new paradigm. Therefore, one must open ones mind to new
vistas and a fresh viewpoint. One must exercise patience to go further,
having faith that all will "fit" in the end.
Great care has been taken to make certain the theory is consistent
within itself *and* consistent with empiricism. Any theory meeting that
criteria should be acknowledged as equal in stature to any existing theory
if not a replacement for it.
Prediction is a fallout. The primary purpose of any theory is to
explain interconnecting phenomena.
This model of the quantum as a physical entity determines:
(a) the density of neutrons, protons and electrons
(b) minimum force
(c) minimum torque
(d) minimum linear momentum
(e) minimum angular momentum
(f) minimum energy
(g) minimum angular energy
(h) minimum angular velocity
(i) the constancy and value of the equatorial velocity of particle spin
(j) the constancy of angular momentum
(k) the radii of the electron, proton and neutron
(l) that special relativity does not apply to subatomic physics
(m) the nature of the binding forces
(n) the mass of the neutrino
(o) the mass of the photon
(p) that the rest mass and the moving mass of the photon are the
same -- albeit the rest mass is absorbed
(q) that the apparent increase in the inertial mass of an accelerated
particle is in reality a physical mass accrual due to the absorption
of mass from the impelling radiation.
(r) that the density of fermions and photons is directly proportional
to the fourth power of the frequency and the causal mechanics of
this phenomenon
(s) that the quantum is the ultimate particle of the universe,
comprising both matter and radiation
(t) a resolution of the wave/particle duality
(u) the origin of the fundamental forces including gravity
(v) the quantization of gravity
(w) the mechanics of gravity
(x) the mechanism of the strong force
(y) the structure of the neutron
(z) that the nature of quantum aggregates is such that statistical
mechanics and wave mechanics is the optimum technique to deal
with it.
(A) the deterministic cause of the characteristics of light polarization
(B) a possible explanation for wave entanglement and non-locality
(C) a plausible explanation for the greater than c non-thermal expansion
in the "inflationary model" of the Big Bang theory
... and more
If this seems like a cornucopia, one should not be surprised. Is it not
likely that finding the key to the basic structure of the universe
would unlock many puzzles and answer many questions? That, after all, is
the purpose of a key.
=======================
Given: For a ponderable body in free space kinetic energy accrues only
during acceleration. Therefore, we can write
E_k = m a d = mv^2
But v is an *averaged* velocity based on the mid-point of
acceleration time. So we write
1
E_k = mv^2/2 or mv^2 * ---
2
This is a Newtonian expression and valid for relatively low velocities.
By considerations contained in the Dual Velocity Theory of Relativity
(another work of this author) the factor 1/2 is replaced by
1
---------
R + R^2
[where R = Lorentz transformation]
Thus we write the expression for kinetic energy as
[Eq 1]
mv^2
E_k = ---------
R + R^2
It will be found this is exactly equal to Einstein's
1
E_k = mc^2 ( - - 1)
R
THE CORPUS QUANTUM
In the existing model a "quantum" is thought of essentially as an
increment. We speak mainly of quantum increments in energy levels.
Thus "a quantum" is also thought of as a quantum of energy.
Planck's constant h is a unit of action and may be written m a d t.
(which is energy * time or momentum * distance)
Regardless of the magnitudes of m, a, d and t, h/t = the basic unit of
energy and is 6.625661 x 10^-27 erg. This unit is called the "Planck"
and denoted as h_0.
m a d t
Thus ---------- = mad = h_0
t
The energy of radiation is given as h nu. Now nu, being frequency
can be interpreted as n times per second or n/sec. Thus E = h n/sec.
We write h, the unit of action as m a d t, and nu as n/sec :
madt n
thus h nu = --------- = n mad
t
Thus if we equate n to frequency, i.e., n/sec = nu then we may write
the energy of radiation as nh_0.
For clarification,
madt n
h nu = ---- * --- = mad n = h_0 n
t
"One second" arises here as an arbitrary unit of choice determined by
the frequency being given as n per second. Although_"t"_may_be_any_
interval_of_time,_in reference to radiation it is one second. This
in turn determines the magnitudes of m, a and d.
Thus, in ferreting out the characteristics of the quantum *in radiation*,
one second is considered a fundamental unit. The magnitudes of the other
parameters are determined by it. It will be found that the quantum so
determined is fundamental to particles as well.
-<*>-
Often the objection is voiced that the "quantum" can't be a particle
because it is merely an increment in energy (although h is a unit
of action).
The quantum as a unit of energy is most apparent in radiation where
E is given as h nu, meaning n units of energy.
The question is, how can we equate that to a particle?
We close our eyes and reach out into that great black void searching
for *something* to give us a clue.
Wait a minute, let's try this. Energy is matter in motion. Then we
can conclude that "something" has to move -- and in increments of
6.625661 x 10^-27 erg.
That "something" has to be a particle.
*How* would it move in those increments?
A certain distance? No. First of all, what would determine that distance?
Second of all energy times distance is *not* a unit of action.
Energy times *time* is.
We begin to think in terms of rotation. Even though known particles have
spin, that does not give us much of a clue. But it does suggest something
similar, expansion and contraction.
We examine radiation (light, etc.) for more clues.
Since radiation energy is equated to frequency, i.e., vibrations or
oscillations per second and is "energy increments" times n (where n is
equivalent to nu) then we try to isolate it by extrapolating down to a
frequency of one per second.
A picture begins to emerge of a particle that expands and contracts once
per second, that expansion, or contraction to be associated with
6.625661 x 10^-27 erg -- which we now call "a Planck" and denote by h_0.
Since that expansion/contraction takes place over the distance of one
light second (the wavelength of a frequency of one) in one second, we
conclude that the velocity of expansion/contraction must be c.
We define energy as mass in motion. Therefore, we now seek the mass
of the expansion/contraction, i.e., the mass of the particle as it
expands/contracts (pulsates).
We take mass as E/c^2, or h_0/c^2, this gives us a mass of
7.37203854 x 10^-48 gr. we label this m_q.
*That* it seems is our basic particle. It now behooves us to add other
attributes to it that fit and answer other parameters and phenomena to
hopefully give us a new perspective on quantum mechanics.
The individual freestanding quantum consists of a greatly rarefied,
*perfectly* resilient, non-divisible *substance* extending to a finite
spheroid boundary. It is internally frictionless and pulsates (expands
and contracts) continually. When expanded it may be considered to be
in the kinetic energy mode, when contracted -- and to the extent
contracted -- the potential energy mode. Notwithstanding their
indivisibility, quanta in the low quantity modes of agglomeration are
mutually permeable or co-spatial. The permeability is conditional,
dependent upon the density, i.e., as the quantity of quanta increases the
density increases and permeability is increasingly resisted. upon
reaching a certain point it is no longer tolerated.
The quantum, being substance, has mass. A single quantum has a mass, m_q,
of 7.37203854 x 10^-48 gram.
The energy of expansion and contraction is 6.625661 x 10^-27 erg (h_0).
This energy is potential when the quantum is fully contracted, and
kinetic when fully expanded.
When fully expanded the diameter is one light second (LS). The velocity
of expansion and contraction is c.
The quantum also has spin. That will be dealt with in some detail later.
Force applied to a free body will impart motion, and thereby kinetic
energy, to it. We may therefore consider force as the transference of
energy.
The transference of energy from the internal (contracted) mode to the
external (expanded) mode can be considered force and is
2.21008 x 10^-37 gr cm/sec^2. This is the minimal force and will be
explained in more detail later.
When escaping particles (large agglomerates), the individual quantum
attains an expansion rate of c virtually instantaneously taking one
second to fully expand.
If we use the definition of force as the change of momentum with
respect to time, /\P//\t, we see that in the primal case at hand /\P
proceeds from 0 to m_qc during the course of the one second escape.
Therefore, although the *rate* of expansion is attained
"instantaneously", the condition is expressed as /\P//\t. Where
/\t = 1 second, the /\ P is the change of momentum accruing in the
expanded portion of the quantum during that second. Thus the fully
escaped quantum has a momentum, m_qc attained in one second which we
may write as
/\P /\m_qc 2.21008 x 10^-37 gr cm/sec
---- = --------- = -------------------------------- = force
/\t sec sec
We note with interest this description is devoid of acceleration,
although if
/\ (m_qc) LS
----------- is read as m_q ------- such could be construed.
sec sec^2
Thus, for the individual quantum the kinetic energy may be written
/\ (m_qc)
E_k = F * d = ---------- LS = 6.625561 x 10^-27 erg
sec
or it may be written in the form
E_k = F * d = m_q a d
c
= 7.37203854 x 10^-48 ----- LS = 6.625661 x 10^-27 erg
sec
But the latter is not an accurate representation of the conditions as
it involves a pseudo acceleration of c/sec whereas the acceleration is
much greater and occurs during a very small fraction of a second
(to be demonstrated later). The energy of the quantum may be more
accurately portrayed by
E_k = m_qc^2 = 6.625661 x 10^-27 erg, (h_0)
called the Planck and considered the smallest unit of energy extent.
All this reinforces the position that in quantum considerations the
concept of force being mass times acceleration is not valid.
Note: when there is acceleration, the expression for E_k contains a
1
modifying factor --------- . When acceleration is not a factor the
R + R^2
modifying function should be absent. *It is.* For emitted radiation
quanta E_k = m_qc^2. There is no function.
Also of note is that special relativity does *not* apply to the
radiant state of matter.
Relativity is the mechanics of fast moving (cosmological) bodies
interacting through *observation* ,i.e., with radiation as the
intermediary causation. It does not apply to the radiation itself
which, additionally, does not qualify as a "ponderable" mass.
It follows that it is inappropriate to apply *any* relativistic equations
to the photon.
-<*>-
We now wish to reconcile the kinetic energy of particles or ponderable
mass with the kinetic energy of electromagnetic radiation.
It is more apropos to consider the latter as photons rather than waves.
The photon may be thought of as an electromagnetic particle. As such we
seek its mass, and subsequently its kinetic energy and momentum, in terms
of mass and velocity rather than h nu.
The mass is given in terms of (n m_q) where n corresponds to nu or n/t.
This is based on evidence (displayed later) that the photon is comprised
of a multiplicity of quanta and that each quantum creates one vibration
per second due to its pulsation. Thus the number of quanta in a photon
corresponds to nu. The velocity of course is c.
The momentum of the photon is given as h nu/c which is equivalent to
(nm_q)c. Likewise for energy h nu = (nm_q)c^2 which is of the form mc^2.
Where m = m_q, a = c/sec, d = LS and t = 1 second,
this may be developed by
LS
-----
n c sec
h nu = madt * --- = n mad = (n m_q) ----- LS = (n m_q) ====== LS
t sec sec
LS LS^2
= (n m_q) ------- LS = (n m_q) ------- = (n m_q) c^2
sec^2 sec^2
The momentum can be developed by the same process.
Note, this supports the dimensions of the quantum given above.
Experimentally E = cP. By the above, E = c (nm_q)c = (nm_q)c^2
Note: These equations are for mass in the form of radiation, i.e.,
free quanta traveling at c, grouped in a Gaussian group wave pattern,
and following the laws of superposition but essentially in a sequential
mode.
It stands that there are two *basic* forms of matter, both comprised of
quanta. One is radiation as described above, the other is ponderable
bodies comprised of quanta that are *concentrically* grouped. Thus they
form particles the mechanics of which are governed by
Newtonian/relativistic mechanics.
The radiation quanta are of such quantities that their density easily
allows co-spatial existence.
Particles, on the other hand, are comprised of such quantities that
co-spatial existence has reached its tolerance level and further
quanta are resisted, eventualy to be rejected.
There are two things to note in this regard, one, the rejection of
additional quanta takes place in a zone rather than suddenly. Thus
we see the situation where "hard" photons begin to exhibit particle
characteristics. The harder the photon, the more particle like it
becomes. In fact we see activity (pair production, beta decay, etc.)
in which photons change into particles and particles change into
photons.
The electron may be considered to be the inhabitant of the "twilight"
zone. Loosely speaking it is semi particle, semi radiation -- but
favoring the particle (ponderable mass) mode.
-<*>-
We now seek to reconcile the kinetic energy of material particles with
the kinetic energy of electromagnetic radiation.
It is more apropos to consider the latter as photons rather than waves.
The photon may be thought of as an electromagnetic particle. As such we
utilize its mass in comparisons.
The core of the endeavor to reconcile the kinetic energy of an
electromagnetic particle with the *corresponding* kinetic energy of a
ponderable particle is the correlation of the c of the former with the
sub c velocity of the latter.
Seeking a bridge, we write,
1
h nu = n(m_qc^2) = mc^2 ( --- - 1 )
R
The crux lies in the second and third terms which we write
1
(nm_q)c^2 = mc^2 ( --- - 1 )
R
Where nm_q = m_ph , mass of the photon:
1
m_phc^2 = mc^2 ( --- - 1 )
R
1
Thus if m_ph = m, ( --- - 1 ) must be equal to 1 to maintain the
R
equality.
If R = .5 this requirement is met. A velocity of .8660254 c or
(.75)^1/2 c has the requisite R of .5
Therefore, by utilization of nm_q we conclude that (for example) a photon
of frequency 1.23561 x 10^20 has a mass equal to that of the electron
and that both will have the same kinetic energy when the velocity of
the electron is (.75)^1/2 c.
To restate the case for clarity:
If a photon (velocity c) were to suddenly transform into a particle
of identical mass it would, in obeying the conservation of kinetic energy,
have a velocity of .8660254 c
Photon Absorption
When a photon is *completely* absorbed, typically by an orbiting electron,
its kinetic energy (n m_q c^2) is transferred. Concurrently, its mass
n m_q is added to that of the electron. The photon ceases to exist as a
photon and in that context we can say the rest mass of the photon is
zero. However, what *was* the photon is incorporated into the electron,
both its mass and kinetic energy.
The kinetic energy resides in the form of an elevated energy state.
However, inasmuch as no *external* motion results we see an illusion
that the kinetic energy of the photon is converted to mass for there is
additional mass with no increase in velocity of the absorbing *body*.
One often hears dictum to the effect that "kinetic energy disappears
and mass is created in its place." (or vice versa). Obvious error.
In addition to raising energy states, the transferred kinetic energy,
*when sufficient*, may also result in motion to the absorbing body.
A photon may be only partially absorbed, the remainder being the recoil
or scattered photon.
The absorbed portion is the *inelastic* portion of the photon and carries
the kinetic energy transferred.
EMPIRICAL CONFIRMATION
^^^^^^^^^^^^^^^^^^^^^^
An analysis of the Compton effect will substantiate the above by
tracing an actual photon collision with an electron.
THE COMPTON EFFECT
(illustration below)
A 1 MeV photon in a direct collision (scattering angle 180 deg) with a free
electron (considered at rest) will impart a recoil velocity to it such
that E_k = .797 MeV --[[ Scientific Encyclopedia, Van Nostrand, 5th ed.
p. 638 ]]--
Converting the 1 MeV to ergs and utilizing nu = E/h , we ascertain the
frequency of the incident photon to be 2.418024 x 10^20.
[Eq. 2]
mc^2
Utilizing h nu' = ------------------------
mc^2
1 - cos theta + ------
h nu
(m = electron mass)
( Continued below )
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
A mass m_q may be assigned to each cycle of frequency which in turn is
considered representative of one individual quantum.
m_q = quantum mass = 7.3720385 x 10^-48 gr
m_ph = photon mass
m_e = electron mass R = Lorentz transformation
`````````````````````````````````````````````````````````````````````````````
In this work there are a few fundamental physical constants used
in a variety of relationships. Often one that is quite accurate in one
relationship does not maintain that accuracy to an appreciably significant
decimal place elsewhere. Yet it is apparent that the usage is correct and
applies.
The opportunity lies, in this computerized age, of assembling all the
usages and then balancing them, one against the other, to obtain a series
that works perfectly to the sixth or seventh decimal place. We may then
enjoy the accuracy. The values used in the development of this work are
slightly out of date but have been adjusted and do work quite well
together. They are:
h = 6.625661 x 10^-27 m a d t (erg second) (momenton light second)
c = 2.9979254 x 10^10 cm/sec
m_e = 9.1089534 x 10^-28 gr
m_q = 7.37203854 x 10^-48 gr
* * * * * * * * * * * * * * * * * * * * * * * * * *
MASS AND ENERGY TRANSFER IN A COMPTON COLLISION
[Fig. 1]
E = hnu = 1.602101 x 10^-6 erg
nu = 2.418024 x 10^20
m_ph = 1 MeV = 1.782576 x 10^-27 gr
_ - - _ ph
- |. . . . . . . - e
nu = 2.418024 x 10^20 | . . . . . . . . . - _ _ _
- |. . . . . . . . . . - - -
: - |. . . . . . . . . . . .- - -
: - |. . . . . . . . . . . . - - -
: - |. . . . . . . . . . . . .- - -
: 3.62763 | . . . . . . . . . . . . .-- -
: x 10^-28 | 1.419814 x 10^-27 gr . . -- 9.108953 x 10^-28 gr -
: - gr | . . . . . . . . . . . . - - -
: - | . . . . . . . . . . . . - - -
: - | . . . . . . . . . . . - - -
: - | . . . . . . . . . . . - - -
: - | . . . . . . . . . . - - _ -
: - | . . . . . . . . . - - -
- _ _ _ - \ E_k = 0
nu - nu' = 1.925945 x 10^20 \
: \ /\m
: \
: \ e'
: \ - - - _
nu' = 4.920785 x10^19 - . . . . . . | -
_ - . . . . . . . .| -
- - - . . . . . . . . | -
- - - . . . . . . . . . | -
- - \ / - . . . . . . . . . . | -
- - <----- * -------> - . . . . . . . . . . | -
- 3.62763 x 10^-28 - / \ - . . . . . . . . . . |9.108953 -
- gr - - . . . . . . . . . . |x 10^-28 -
- - - . . . . . . . . . . | gr -
- _ - - . . . . . . . . . . | -
- . . . . . . . . . | -
- . . . . . . . . . | -
(prime indicates recoil condition) - . . . . . . . . | -
- . . . . . . . | -
E_ph x .7964954 = E_k_e' - _ . . . .| _ -
m_ph x " = /\m - -
nu_ph x " = /\nu
E_ph x .2035046 = E_ph'
m_ph x " = m_ph'
nu_ph x " = nu' v = .9204658 c
E_k = .7965 MeV
(1/R - 1)m_e = /\m = 1.276066 x 10^-6 erg
m_e v^2
(1/R - 1)m_e c^2 = E_k_e'= --------
R + R^2
m_e' = m_e + /\m = 2.330709 x 10^-27 gr
m_e
---- = m_e' nu e' = 3.161554 x 10^20
R
CAPTION FOR Fig. 1
BEFORE AND AFTER COLLISION OF A 1 MeV PHOTON WITH AN "AT REST" ELECTRON.
The two spheres at the top are at the moment of contact; those at the
bottom are immediately afterward. The incident photon (top left) has
almost twice the mass of the electron. The shaded portion is the portion
of the incident photon that transfers to the electron on contact. Having
mass, this portion carries momentum and energy with it. The *quantitative*
results are exactly the same as those given by relativistic mechanics.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
( Continued from above )
We find the frequency of the scattered photon to be 4.920785 x 10^19, a
frequency loss nu - nu' of 1.925946 x 10^20. Since each element of the
frequency represents a quantum, this figure represents the quantity of
quanta n lost to the photon and absorbed by the electron. Thus
(nm_q) = /\ m_ph = /\ m_e = 1.419814 x10^-27 gr
and is the mass transferred. The energy of this mass is
(nm_q^c2) = 1.276066 x 10^-6 erg (hnu) which manifests as kinetic energy
transferred to the recoil electron. This converts to .7965 MeV which
agrees quite well with the .797 MeV of experiment.
The only energy imparted to the electron is that contained in /\ m_ph.
Thereby /\ m_ph c^2 is converted to
(1/R - 1) m_e c^2 [Eq. 3]
Thus /\ m_ph c^2 = (1/R - 1) m_e c^2 [Eq. 4]
Therefore /\ m_ph = (1/R -1) m_e [Eq. 5]
Finally /\ m_ph = (m_e/R - m_e) = /\ m_e [Eq. 6]
which clearly demonstrates that *the_relativistic_expression_in_the_center
is_nothing_other_than_the_mass /\m_ph absorbed_from_the_photon* and which
carries the total kinetic energy now resident in the recoil electron (on
the assumption that the free electron is considered essentially at rest.
For clarification, we can write Eq. 6 as
[Eq. 6A]
m_e
--- = (m_e + /\ m_ph) = (m_e + /\m_e)
R
Hence the term "increase in inertial mass" has a clear mechanistic
explanation not forthcoming in relativity theory. Note, this is so only
for e.m. accelerated particles.
We also note from Eq. 6A that the ratio of the electron mass before and
after absorption is equal to the Lorentz transformation:
m_e
---------------- = R .
m_e + /\ m_e
and Eq. 5 shows that (1/R -1) m_e is the quantity of mass transferred
in the collision.
We summarize the conditions:
If the quanta absorbed by the electron is nu - nu' = nu'' = n ,
then E_k = h nu'' = (nm_q) c^2 = /\ m_ph c^2 = (1/R - 1) m_e c^2 .
from which we can readily calculate R and v.
The shaded portion of the incident photon is the /\ m_ph that transfers
in the collision, imparting a velocity of 92% c.
The rebounding photon, having suffered the loss of /\ m has a frequency
that is lowered by /\ m/m_q.
The percentage loss of mass by the photon is /\ m_ph/m_ph x 100.
*This_is_a _79.65 %_inelastic_collision._Consequently,_that_is_the
percentage_of_the_photon mass_transferred*
m_ph x .7964952 = 1.419814 x 10^-27 gr = /\m
MOMENTUM
Here the situation is a bit more complicated than for energy.
Therefore, it may be best to proceed on a step by step basis at the
end of which the proportionality of momentum distribution will be clearly
evident. Then, following, will be a table displaying the proportionality
of distribution for mass, energy, momentum and frequency.
( Continued below )
###########################################################################
A SCHEMATIC MOMENTUM DIAGRAM OF THE COMPTON EFFECT
[Fig. 2]
(not to scale)
ph' reaction*
5.344032 x 10^-17 + 1.087534 x 10^-17 = 6.431566 x 10^-17
>>>>>---------------------------> -->>>>>--------------------------> Eq.[9]
INCIDENT PHOTON | RECOIL ELECTRON |
| | (see)
h nu | h nu' |
P_ph = ---- = (nm_q)c = nP_1 | ----- = (n'm_q)c = n'P_1 |
c | c |
| = nu'P_1 |
= nu P_1 | |
|4.256496 ^-17 + 2(1.087534 ^-17) | see
|-------------->----------------->| Eq.[8]
| INELASTIC : ELASTIC |
| IMPULSE : IMPULSE |
| : |
|p'_e' = /\ mc : P''_e' |
<--------------------------<<<<<| : |
RECOIL PHOTON | h(nu - nu'): h nu' |
| = ---------- : = 2 ----- = |
h nu' | c : c |
P_ph' = - ----- = - (n'm_q)c | : |
c | = (n'' m_q)c : = 2(n'm_q)c |
| : |
= - n'P_1 = - 1.087534 ^-17 | = n'' P_1 : |
| : |
* To every action there is an equal and opposite reaction.
THE ABOVE IS A NON-STANDARD METHOD OF MOMENTUM NOTATION
- - - - - - - - - - - - - - - - - - - - - - - - - -
STANDARD CONSERVATION OF MOMENTUM STATEMENT
P_ph + P_e = P_ph' + P_e'
============================================================================
[prime sign indicates recoil condition]
[double prime indicates impulse parameter]
P''_e' = Elastic impulse of recoil electron
P'_e' = Inelastic impulse of recoil electron
P_e' = Recoil electron momentum
P_e = Momentum of initially at rest electron
P_ph' = Momentum of recoil photon
P_ph = Incident photon momentum
P_1 = Absolute minimum momentum, m_q c
n = nu , frequency or, equivalently, number of quanta
n'' = pertains to /\m (/\m/m_q). Determines impulse
#############################################################################
( Continued from above )
We have for the momentum of the recoil electron
(m_e + /\ m_ph) v = P_e' [Eq. 7]
m_e v
The more usual expression for same is -------- .
R
m_e v
Therefore, (m_e + /\ m_ph) v = --------
R
which is a simple non-relativistic explanation of the expression for the
relativistic increase in momentum due to the increase in mass. (see Eq. 6A)
The transfer of momentum, despite its apparent simplicity, is not so
straightforward as Eq. 7 would indicate. This equation is for *perfectly
inelastic* collisions. As there is a recoiling photon, it is obvious that
we do not have such a collision.
Neither do we have a perfectly elastic collision; not only because of Eq. 7
but because the *total* velocity before and after impact is not equal. This
equality is characteristic of the perfectly elastic collision.
Note:
BEFORE IMPACT: velocity of photon = c
velocity of electron = 0
AFTER IMPACT: velocity of recoil photon = c
velocity of recoil electron = v
c + 0 (not = to) c + v
--[[ These measurements are of the laboratory frame where c + v is
permissible because each velocity is relative to the frame. ]]--
What we do have is a *combination* elastic-inelastic collision. Following
is a discussion of the proportional distribution:
IN A PERFECTLY ELASTIC COLLISION THERE IS 0 MASS TRANSFER.
IN A PERFECTLY INELASTIC COLLISION THERE IS A 100% MASS TRANSFER.
Therefore,
IN AN X % INELASTIC COLLISION THERE IS AN X % MASS TRANSFER.
Thus we may discuss photon-electron collisions in terms of being a certain
percent *inelastic*, i.e., this percentage is the percent of the mass
transferred. The balance of course is the percentage of mass recoiling,
viz., the mass of the recoil photon.
*This proportionality also holds for energy and momentum.*
FOR ENERGY:
h nu - h nu' h(nu - nu') nu - nu'
Inelastic portion = ------------ or ------------- or ----------
h nu h nu nu
nu - nu' nu'
Elastic portion: = 1 - --------- or ----
nu nu
We now proceed with the analysis.
Step (1) We regard *only* the portion of the collision that is inelastic.
Thus P'_e' = /\ m c. (See Fig. 2)
--[[ P'is inelastic impulse. P'' is elastic impulse ]]--
(2) To this partial momentum (or inelastic impulse) must be added
the impulse of the *elastic* portion:
P''_e' = 2 P_ph' = 2 m_ph' c
(3) Thus
[Eq. 8]
P_e' = P'_e' + P''_e'
[ inelastic ] [ elastic ]
or
P_e' = (/\m + m_e)v' + 2 m_ph' c
--[[ where v' is the inelastic impulse velocity = /\m c/ (m_e + /\ m) ]]--
--[[ and v'' is the elastic impulse velocity = 2 (P_ph'/ (m_e + /\ m) ]]--
--[[ Note: v' + v'' = v_e' ]]--
which displays the proportionality. (Note, both portions are positive.)
We may restate this equation by entering the elemental parameters:
(nu -nu') m_q c
P_e' = [ (nu - nu') m_q + m_e ] -------------------- + 2(nu' m_q) c
(nu -nu') m_q + m_e
which reduces to
P_e' = m_q c (nu + nu')
= P_1 (nu + nu').
*This is correct if we ignore vectorial form.* (which will be addressed later)
As a variation this equation may be written
incident photon momentum reaction impulse of ph'
P_e' = (nu m_q) c + (nu' m_q) c
= m_ph c + m_ph' c
= P_ph + P_ph' [Eq. 9]
(See Fig. 2)
Here is another example of the caveat we must heed when dealing with
mathematical treatments (and this is the most simple mathematics). There
is much that is concealed from view by nature. Sometimes mathematical
treatments enhance that concealment. (See "Standard Conservation of Momentum
Statement", -- Fig. 2)
Following is a table displaying the characteristics of each portion of the
combination collision:
ELASTIC PORTION INELASTIC PORTION
============================ ======================================
nu' nu - nu'
---- ---------
nu nu
^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
nu' nu - nu'
----- x m_ph = m_ph' -------- x m_ph = /\ m_ph = /\m_e'
nu nu
*
x P_ph = P_ph' (negative) x P_ph = P_e' (positive)
x E_ph = E_ph' x E_ph = E_e'
x nu_ph = nu_ph' x nu_ph = nu - nu'
---------------------------------------------------------------------------
*
Is the inelastic portion of the incident photon momentum -- and is the
momentum *impulse* to which is added the additional elastic impulse of
2 P_ph', yielding the total P_e' .
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
For those inclined toward visualization, this example of the Compton effect
presents a beautiful picture.
What we notice in the main is that when the electron is impacted by the
photon the kinetic energy of /\ m *passes_through_unchanged* and is the
kinetic energy of the recoil electron, i.e., of the *entire* mass the same
as does momentum in a perfectly inelastic collision). Note:- /\ mc^2 is the
relativistic expression for kinetic energy.
In a compound collision the momentum of /\ m passes through to the electron
-- but to it is added the momentum of the part of the incident photon that
reacts in an *elastic* manner, i.e., the photon is part elastic and part
inelastic in its collision. This proportionality is (in this example).7965
inelastic to .2035 elastic. The inelastic portion determines the mass and
energy transfer. In the beginning we had a big banner to that effect:
It was stated, A 1 Mev photon imparted .7965 MeV to the recoil electron.
The above proportions are for the example given. Collisions at other angles
and energies will have other proportions.
Radiating Quanta
1 erg
A photon of n quanta will escape in a time = 1/N sec (where N = ----------
erg/photon
1
equiv: ----- )
h nu
The ratio of mass of one quantum to its internal energy is
7.37203854 x 10^-48 gr to 6.625661 x 10^-27 erg which is the ratio of
1 to c^2.
m_q 1
We write this --- :: ----- the cross product being E = mc^2 .
E c^2
For each quantum emitted from a body, that body will lose m_q which
manifests as h_0. Thus for each gram released |c^2| ergs of kinetic
energy manifests.
Agglomeration
There are two basic forms of quanta agglomeration:
(1) In an escape mode, traveling at the speed of light.
(2) In a concentric (particle) mode, each and every quantum
sequentially expanding and contracting.
In the first mode the quanta escape from matter in great quantities
forming multiple trains traveling in a common direction at slightly
varying velocities. As a result of their perfect resiliency and
their ability to permeate each other, they undergo the mechanics of
waves including superposition.
This results in an interference pattern traveling in the opposite
direction at the same velocity.
(Such waves are predicted by Maxwell's equations which show *infalling*
waves arriving at the transmitter from an infinite distance.)
In consequence, there is produced a *standing group wave* having no
motion with respect to a source and any observer. Only the frequency
is affected by the relative motion of the two.
The standing group wave consists of complex sub waves traveling back
to front (source to observer). These are photons. Their velocity through
the standing group wave is constant, and as the standing group wave
has no velocity with respect to source and observer, then the
velocity of the photons is constant with respect to source and
observer -- regardless of any motion. Thus_there_exists_the_phenomenon_
of_the_constancy_of_the_velocity_of_light_.
The process of superposition effects the merging of quanta into
photons. As the number of quanta in each photon increases, i.e., as
the frequency rises, the photons become smaller in "effective" size
and higher in energy as well as more massive. In this process they gather
more and more of the standing group wave unto themselves. At extremely
high frequencies, so much of the standing group wave is gathered to the
photon that it becomes increasingly particlelike. This process continues
through the range of x-rays to gamma rays where the photon consists of
1 x 10^20 quanta or more.
The frequency (nu) is equivalent to the number (n) of quanta in a photon.
Therefore, the mass of the photon is nm_q, and its effective diameter
is LS/n. (where LS = light second)
The veracity of this is immediately apparent if we introduce the time
parameter into the expression:
LS
---
sec c LS
======== = ---- = lambda = ---- = diameter
n nu n
-----
sec
(Note the qualifying term, "effective". This is used for particles also.
Whenever the wavelength or particle diameter is spoken of, the
appellation includes, unspoken, the term "effective", the reason being
that the diameter of *all* quanta agglomerations is one light second
because that is the full extent of the pulsation of the individual
quanta. However, due to density falling off as the *fourth* power of
the radius the *effective* size of the particle is at the dense core.
This is analogous to *considering* the mass of a body as being located
at its center of mass. There are exceptions in both cases.)
The dimensions and manifestations of lower frequency photons are more
vague than those of higher frequency. The particlelike characteristics
of high energy photons such as those of x-rays or gamma rays become
clearer when the energy is expressed as E = h nu = (n m_q) c^2 .
Considering the mass aspect of the photon it should offer no surprise
that the vector of a photon is altered by a strong gravity field
although the response may differ from that of ponderable mass.
CORPOREAL AND RADIANT MASS
We have noted before that a photon and particle of equal mass have
differing velocity requirements in generating an equal E_k, i.e., although
the mass of a particle and the mass of a photon are equal, they require
different velocities to generate the same kinetic energy.
*This_means_that_the_mechanics_for_ponderable_particles_is_different_
from_the_mechanics_for_radiation.* The mechanics for ponderable mass
is relativistic, -- and therefore the mechanics for radiation
is *not* relativistic. Thus, we can say that special relativity
is not applicable to the photon.
The difference between relativistic/Newtonian (corporeal) kinetic energy
and that of radiation is that in the *latter* acceleration is ignored -- or
put another way is considered instantaneous . In addition there is no mass
increase, neither actual or observational. We have what we might think
of as a pure expression of kinetic energy. Therefore, d is given as
v t *not* 1/2a t^2, and F is given as
/\ P
---- *not* m a. Thus we write (where /\P = P_0 = P = mv)
t
/\P mv
E_k = F * d = --- vt = ---- vt = P v = mv^2
t t
and since v = c, we have E_k = Pc = mc^2.
REST MASS OF THE PHOTON
A photon may be *considered* to be at rest when it is absorbed by matter,
in which case a photon of (nm_q)c^2 energy adds (nm_q) mass to the body
absorbing it. Therefore, (nm_q) may be considered the rest mass of the
photon as well as its mass in motion. Here, again, we observe that the
Lorentz transformation does not apply. We also observe that the mass times
c^2 yields the energy -- both "rest" and kinetic.
We note, however, that the absorbed photons lose their identity and in
that respect the rest mass of the photon is a moot concept. Here we see
the reverse process of the release or conversion of "rest energy"
(nm_q)c^2 to kinetic energy which takes the form of radiation,
neutrinos or high velocity particles.
MATTER
Quanta agglomeration in the concentric mode manifests as matter, i.e.,
electron, protons, and neutrons. these three (plus the photon) are the
only stable particles in the universe. In fact they are the only
particles. The members of the "subatomic zoo" are not particles.
More on that later.
A particle consists of n concentric spherical quanta sequentially
expanding and contracting. Each makes a complete cycle per second.
Thus n (corresponds to) nu.
Given the parameters of the quantum, we can calculate the density and
*effective* diameter of particles.
The *prime* density , D_1 is the density of one quantum fully expanded,
i.e., the diameter d = one light second (LS) and therefore the radius
r_q = 1/2 light second.
If we visualize a particle as a series of concentric spheres (quanta)
we observe that those more centralized are more contracted and therefore
more dense. As one proceeds from the core outward, the density diminishes
as the forth power of the radius. This is a rather rapid rate. Therefore,
in experimental procedures it is the core that is considered the particle.
What would be considered as the surface is tenuous and indefinite and,
therefore, so would be the radius, volume, and density.
To determine the density of a particle we consider the following:
A particle of n quanta has an *effective* radius considered to be
r_q 1/2 LS
--- or ------ = r .
n n
The density of a solitary fully expanded quantum is
m_q
D = ------------ or D_1
4/3 pi r^3
and equal to 5.225484 x 10^-79 gr/cc. This is the "primary"
or minimum density in the universe.
The core density of a particle of n quanta is
Eq. [10]
(where r = effective radius)
nm_q
D_p = ------------
4/3 pi r^3
1/2 LS
Since r = ------, we write Eq. 10 as
n
Eq. [10a]
nm_q n^4 m_q
D_p = ==================== or -------------------
4/3 pi (1/2 LS)^3 4/3 pi (1/2 LS)^3
-----------------
n^3
Thus we see the particle density varies as the fourth power of n.
m_q
As ------------------- is the primary density, D_1, we may also state
4/3 pi (1/2 LS)^ 3
that the particle density at the core is n^4 times the primary
density, D_1, or D_p = n^4 D_1.
Since each quantum represents an oscillation, we conclude that the density
varies as the fourth power of the frequency. We also note that, as all
particle quanta are in various stages of expansion and contraction and
essentially evenly distributed, commencing from the core the density
falls off inversely as the fourth power of the radius.
A MORE DETAILED EXAMINATION OF PARTICLE RADII
As stated, for a sphere of ever diminishing density proceeding outward
from the core, a true surface is none existent. Therefore, the radius
cannot be measured from center to surface.
We might establish a theoretical, or "essential" radius by the following
reasoning.
The mass of a sphere can be treated as though the *entire* mass were
located at the center. *We so regard fermions.* Thus, we regard (say)
the electron as having its entire mass at the center.
There the analogy seemingly ends. Whereas a non-compressible uniform
sphere has a uniform density, the electron does not. In calculating the
density of the non-compressable sphere we utilize the radius as extending
from the center to the surface. This is denied us in the case of the
electron as there is no definite surface.
Therefore, we seek a viable *essential* radius by noting that the electron
is comprised of n concentric quanta. We regard the nth, or most central
quantum as also being the center of the electron. Thus the mass center and
the spatial center coincide.
What we have then is a defined sphere of definite mass and radius.
The mass is nm_q and the radius is
1/2 LS
---------
n
We refer to this radius as the "essential" radius. However, in the text
it is referred to simply as the "radius". We must be constantly aware
though that the *full* radius is 1/2 LS.
We now consider another approach:
mass
Consider the relationship volume = ---------
density
from which the radius is obtainable:
____________
/ vol
3 / -------
r = \/ 4/3 pi
As an example, given the mass of the neutron as 1.674954 x 10^-24 gr,
the frequency m/m_q (equivalent to n) is 2.272037 x 10^23.
The mean density, then, is n^4 D_1 = 1.392477 x 10^15 gr/cc.
This density is confirmed by the known density of neutron stars.
mass
Thus we have vol = --------- = 1.202860 x 10^-39 cc
density
____________
/ vol
and 3 / ------- = 6.597440 x 10^-14 cm.
r = \/ 4/3 pi
The 1/2 LS
-------- used earlier yields the same result. -- which is not
n
surprising for if we substitute the apropos elements into the two above
equations they reduce to
1/2 LS
--------
n
The elements:
density = n^4 D_1
mass = n m_q
m_q
D_1 = ----------
4/3 pi r^3
We remain aware that in actuality fermions have a varying density.
By rewriting Eq. 10 we have an equation that determines the density
of a particle at any distance from the absolute center:
Eq [10b]
r_q m_q
D = --------------
4/3 pi r^4
Note, r is the only variable. We accept it as correct since it yields D
commensurate with the density of the neutron (in turn confirmed by the
density of neutron stars).
Where m_p (mass of the particle) is the only variable we have
Eq [10b-1]
6 m_p^4
D = ---------------
pi LS^3 m_q^3
Equation [10b] differs from equation [10] in that it displays density in
terms of only *one* variable, that variable being the radius. In
Equation [10] both n and r are variable (but interdependent).
We see by equation [10a] the density is directly proportional to the
fourth power of n -- and by equation [10b] the density is inversely
proportional to the fourth power of r, and by equation [10b-1] the
density is directly proportional to the fourth power of the particle mass.
Note, in equation [10b] if r = 1/2 LS, i.e., the outer limit of quantum
expansion, D = D_1.
ENERGY DENSITY -- MASS DENSITY
Mass density is the more familiar density. However, there is also an
energy density D_E which consists solely of internal energy, i.e., the
degree to which quanta are agglomerated is the degree to which the density
increases -- both mass density and energy density.
One quantum fully extended has full kinetic energy (h_0) and zero potential
energy. Such is expended in the expansion of m_q within a particle.
The same quantum fully contracted has zero kinetic energy and h_0
potential energy (analogous to a coil spring). There are, of course,
conditions between.
Consider the first condition -- fully expanded. We may write the kinetic
energy as
E_k = m_q c^2 = h_0 .
We may also write it in terms of
Energy Density x Volume = Energy
(Which is analogous to Mass Density x Volume = Mass.)
Having considered and formulated mass density, we now examine energy density
D_1_E.
Eq. [10c]
h_0
D_1_E = -------------- = 4.696433 x 10^-58 erg/cc
4/3 pi r_q^3
Thus for the fully expanded quantum we have
D_1_E x Vol = E_k = h_0
4.696433 x 10^-58 erg/cc x 1.410786 x 10^31 cc = 6.625662 x 10^_27 erg
We now consider the second condition, fully contracted. The fully contracted
solitary quantum has zero kinetic energy, all its energy is potential, i.e.,
internal. The extent contracted is determined by the *radius" of the
particle. (Note:- The individual quantum may be part of a group that is in
translatory motion. In which case it would also possess a kinetic energy
involving that motion and its mass m_q. We see here the concept of total
energy.)
For the *individual fully contracted* quantum we write (using as an example
the radius of the electron):
D_E x Vol = E_p = h_0
h_0
------------ x 4/3 pi r_e^3 = E_p = h_0
4/3 pi r_e^3
Therefore, we see expanded (kinetic) energy is converted to an equivalent
contracted (potential) energy or
E_k_q = E_p_q
Thus the energy is sequentially and cyclically converted back and forth.
However, the energy in both phases is internal and remains so. It is
irrespective of translatory motion.
Where n = number of quanta in an electron
nE_p_q = m_e c^2 = potential energy
nE_k_q = m_e c^2 = kinetic energy
Collectively (in both phases) this oscillating energy is known as rest
energy or internal energy, E_0 or E_i.
The motive power for quanta expelled from matter is the density factor
which forbids occupancy to excess quanta. Since these quanta can no
longer remain, when expanded to the kinetic energy phase they simply
keep going -- at the expansion rate of c. Therefore, the translatory kinetic
energy is equal to the internal energy and the m of the contracted
quanta is converted to m c^2 .
Note:- This equivalent kinetic energy is in the form of radiation and/or
sub-particles and not to be confused with the energy of translatory motion
of the body. These relationships hold for the electron, proton and neutron.
In the case of the photon its internal energy, i.e., mass is not
conversionable for it is the result of a prior conversion. The internal
energy is, however, *transferable* to a particle.
THE RELATION OF BOTH DENSITIES TO BOTH ENERGIES
Mass density, energy density, internal energy and kinetic energy are all
related through the innate characteristics of the quantum,
We now ask: What is the relation between mass density and energy density?
As one would expect, we find the relationship to be c^2. It is the factor
relating mass to energy (mc^2 = E) and it likewise is the factor relating
mass density to energy density.
Thus we write
D_1_m x c^2 = D_1_E
5.225484 x 10^-79 gr/cc x c^2 = 4.696433 x 10^-58 erg/cc
By rewriting equation [10b] , the energy density of a particle at any
distance r from the center is
Eq. [10d]
r_q h_0
D_E = -------------
4/3 pi r^4
As a reminder in dealing with the co-spatial tolerance of quanta
agglomeration, there are two resonant frequencies that produce stable
particles, that of the electron and proton.
Upon inspection of equations [10b] and [10d] we observe what at first
glance appears to be a dilemma, both the electron and the proton have
the same density at a distance from the *point* center equal to the
radius of the electron.
This poses a question: If there are 1836 times more quanta in a proton
than in an electron, the one light second diameter volume of the proton
must have a much greater mean density; how so, then, at equal radii both
particles have equal densities (mass and energy)?
Answer: The radius of the electron is the radius of the centermost
quantum of the particle. We now imagine adding 1836 times as many quanta
to the electron transforming it to a proton. The quantum that was the
center of the electron is no longer the center. The additional quantum
content has introduced a great many more quanta *inside* the electron
radius thus creating a new - much smaller -- center.
Succinctly, the quantum that was the center is no longer the center -- not
that it has moved outward -- a new *smaller*, denser center of additional
quanta was created. So, whereas the electron radius is of the center in
an electron, this same distance is somewhat to the exterior of the radius
within the proton.
The ratio of the new center radius to that of the old center radius is
1:1836. This is measured from the true point center. This factor to the
fourth power is the ratio of the densities, both mass and energy.
ELECTRONS
Although high energy photons are particle-like the electron is the
threshold to the true particle state.
PAIR PRODUCTION: photon <=====> electron
Experimentally, a high energy photon (1.022 MeV +) upon arriving in the
vicinity of a heavy nucleus (which merely acts as a backstop) may transform
into an electron-positron pair (evidencing the *matter/antimatter*
composition of the photon.) each particle consisting of a mass of .511 MeV.
Excess energy manifests as kinetic energy of the particles.
1.022 MeV is equivalent to 1.637346 x 10^-6 erg. From the equation
E
--- = nu
h
we get a frequency of 2.47122 x 10^20 cycles/sec, the minimum frequency
for pair production. Therefore, it consists of that many quanta, each of
mass m_q. Thus the mass of the photon is 1.821793 x 10^27 gr, which,
divided by two gives 9.10896 x 10^-28 gr, the mass of the electron and
positron.
Thus we see a high energy photon composed of sufficient quanta to equal
two electron masses alter its mode by collision thereby changing into
a concentric, more stationary state containing only one center.
However, it also contains opposite spins that, in the new concentric mode,
are mutually exclusive. Thus the newly formed particle must undergo fission,
one half being of negative spin, the other half positive. Any excess
energy manifests as kinetic energy.
Here we see the process of agglomeration bridge the gap between the radiant
mode (photon) and that of the true prticle by simply altering to the
concentric mode.
The reverse proces also exists, an electron-positron pair merging to
form two photons.
This is an example of the much vaunted "Annihilation" of matter that
takes place when matter and antimatter meet. The opposite spins are
disruptive, causing the particles' composition to dissasociate and
assume the radiation mode where matter-antimatter spins are compatible.
Thus, we see there is no annihilation of matter, just an alteration in
form. Mass and energy are thereby conserved.
SPIN, CHARGE AND MAGNETIC MOMENT
To avoid confusion in assigning spin this author uses the conventonal
clockwise (CW), counterclockwise (CC) notation. The direction is, of course,
in relation to an axial vector. It is assumed the "observer" is peering in
the direction of the vector. By this means we identify a particular spin
regardless of spatial orientation.
The quantum and therefore the electron, proton and neutron have spin.
In a three dimentional manifold, a given direction of spin *but not the
notation* may be reversed by rotating the axis 180 degrees. In that case
we term it "contra" spin as opposed to "opposite" spin which is a reverse
spin in respect to the axial vector.
The question arises, what *is* electric moment and why are there two kinds?
Why are the opposite charges exactly equal when the masses of the particles
carrying them are unequal?
Also, *what* is magnetic force?
In these pages we will attempt a physical explanantion employing the
philosophy that *any* attempt is better than none.
Let us aproach the characteristics of spin in the most literal sense and
see how far we can progress.
Our particles are considered spherical. Since they have mass and spin we
write the standard equation for angular momentum
(where theta is a fraction of a radian)
(iota omega will, for convenience, be IW)
(r_q = 1/2 LS)
[10g]
theta
IW = 2/5 m_q r_q^2 * -----
sec
This for a solitary quantum.
Taking spin angular momentum to be 1/2 h-bar as developed by P.A.M. Dirac,
the angular momentum of the individual quantum is
LS^2 theta h
IW = 2/5 m_q ----- ------ = 1/2 h-bar or -----
2^2 sec 4 pi
theta 10
(where ----- = .7957745 or ------ = omega_q )
sec 4 pi
For n quanta we write IW as
r_q^2 n theta
IW = 2/5 (n m_q) ------- ----------
n^2 sec
We obseve the angular momentum to be conserved even though mass is added
for n cancells out.
Pictorially, the addition of mass (quanta) increases the angular moment
whereas this same addition reduces the effective radius which increases
the angular velocity. These parameters offset each other to a nullity.
Thereby we see that any fermion will maintain the constant spin momentum
of h/4 pi.
We note that for the solitary quantum, I = 1/10 the coefficient of h, and
1 10
W_q = -------- rad/sec = ----- rad/sec
2/5 pi 4 pi
We also note that since the spin angular momentum is constant, it is
therefore the spin angular momentum of the individual quantum, and thus
we regard it as the *absolute minimum spin agular momentum*.
It could be be assumed the absolute spin angular kinetic energy would
be given by the classical
[ /_ = angular ]
IW_q^2
/_ E_k = ----------
2
However, the 2 exists in the divisor to average out acceleration times
time so that the distance in E_k = F*d is obtained.
Where there is no acceleration, as in the production of photons, the 2
is absent (for the photon E_k = m_phot c^2). It is so postulated for
angular kinetic energy, and so we similarly write
theta^2
/_ E_k = IW_q^2 = I ---------
sec^2
which yields 4.195748 x 10^-28 erg and is the rotational analogue to
E = mc^2.
It may also be written analogously to E_k = m a d:
(where d = theta)
theta
/_ E_k_q = I -------- theta
sec^2
theta
However, it should be noted that the acceleration ------- is fictional.
sec^2
This fictional acceleration determines the minimum torque as
L_1 = Ia which is analogous to F = m a.
We might also state the absolute minimum torque in the form
/\ P /\ (IW)_q
F = ------ as L_1 = ------------, and equal to 5.272533 x 10^-28 dyne cm.
t t
As quanta agglomerate and their effective radii become smaller, there is an
increase in angular velocity. We note two things: (1) the increments in
velocity are due to the conservation of momentum -- *not* to an applied
force, and (2) the inner quanta spin faster than the outer quanta.
We now consider an illustration of our spinning fermion and shall regard the
resultant parameters in a slightly different manner than customarily done.
_
q unit in cgs scale
is statcoulomb
c e
For electron = ----- statC
10
_
q
/|\
|
|
- -
--- ---
- -
- -
mu <---- --- -------------- --- ----<<
S - N
- IW -
--- ---
- -
We assert that the spin creates angular momentum and that the spin angular
momentum in turn creats the magnetic moment. This is quantified as
IW
----- = F = mu
/\ t
P
To obtain t we note F x t = P and therefore t = --- .
F
Where P = IW, F = mu_B, and the Bohr magnaton is given as
9.27467 x 10^-21 ampere-centimeter^2, we find t = 5.684874 x 10^-8 sec.
This figure shall emerge again, shortly.
_
h q
The Bohr magnaton is given as ------------ and for purposes here is
4 pi m_e c
considered the theoretical magnetic moment of the electron.
Whereas IW is considered a polar vector its resultant is not so considered.
In a pragmatic vein, we consider magnetism to be a current or "wind" of
qantum substance and as such capable of applying force. This current is
equatorial -- as in the illustration. Consequently, it consists of closed
loops which we observe. The north, south denotations reflect those made
on the macroscale and are arbitrary.
Normal to the equatorial magnetic current we observe the polar vector q
which is the electric force. This is usually given as a fraction
(1.602 x 10^-19) of a coulomb in SI units rather than the g.c.s. which
is utilized in this work. In this scale, the basic electric charge is the
statcoulomb, being the charge required to create one dyne of force at a
distance of one centimeter. Thus the basic electric charge is
4.803618 x 10^-10 statcoloumb. To differentiate it from the standard e,
_
we use the symbol q, the bar signifying that the charge is minimum and
negative.
_
The Bohr magnaton is given in terms of q utilizing the statcoulomb.
Thus, so far we have considered three basic parameters of a spinning electron,
_
IW, mu_B, and q. We shall now observe a fourth. For the moment we will regard
it as "modular momentum".
The electron consists of n = 1.235608 x 10^20 quanta, each of which oscillates
(expands and contracts) once per second. The velocity of oscillation is c.
Therefore, the momentum of *each* quantum is m_q c or
2.210082 x 10^-37 gr cm/sec.(P_1). Thus the total oscillatory (or modular)
momentum of the electron is nP_1 or
1.235608 x 10^20 x 2.210082 x 10^-37
= 2.730796 x 10^-17 gr cm/sec = m_e c
(m_e = mass of electron)
Magnetic moment is circular in form and is related to electric moment
which is a linear vector. By the same token angular momentum is circular
in form and is related to "modular momentum" which is a linear vector
(and in this case equal to m_e c .)
The modular momentum may be considered linear in the sense that the radii
of expansion/contraction is linear. The force is most effective where the
circularity is maximum and the density the greatest, i.e., the polar
region. Thus the force is a polar vector.
There becomes apparent immediately a series of interesting relationships:
First, we note that of the four parameters, two are momentum, m_e c, and
_
IW -- one linear the other rotary. The remaining two, q and mu_B are
considered force fields, one linear and the other rotary. Upon examination
we see that (See illustration below.)
y
(i) the ratio between momenta is the same as the ratio
between forces.
(ii) the ratio between the linear momentum and its charge
_
q (force) is the same as the ratio between angular momentum
and its force, mu_B
Therefore, we are induced to the conclusion that the forces are a direct
manifestation of momentum -- two types of momentum, two types of charge,
all in direct proportion and configuration.
With a graphic display, the relationships become perspicuous:
9.274670 x 10^-21 4.803618 x 10^-10
_
Forces: mu_B q
|
|
5.684874 x 10^-8 sec
|
\|/
Momenta: IW P
5.272533 x10^-28 2.730796 x 10^-17
--------- 5.179287 x 10^10 --------->
Thus
_
mu_B q
-------- :: --- . We see the force to momentum ratios are
IW P equal and are 1.759054 x 10^7 to one.
also
mu_B IW
------ :: ----- . the ratio of forces and the ratio of momenta
_ are equal.
q P
All the relationships of proportionality follow.
The function connecting the forces to their respective momenta is one of
time (F x t = P). {{This is the t obtained above in ascertaining mu_B.}}
Thus we see magnetic moment as the force created by angular momentum, and
electric charge as the force created by modular momentum.
We will now display the momenta and charges in terms of their physical
contants:
_
h q e |c|
----------- -------
4pi m_e c 10
_
mu_B - - - - - - - - - - - - - - - - - - - q
| |
| 4 pi 4 pi m_e |
|- - - - ---- or -------- - - - ->|
| D_e m_q LS |
|_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _|
IW P
h h
----- m_e c or ----
4pi D_e
{where D_e = electron diameter} Note: D_e * m_e c = h
With this array before us we are able to make some very interesting
observations and deductions.
Earlier we queried as to why the basic positive and negative electric
charges were equal when the particles carrying them were of such disparate
mass (1 : 1836). We shall see that the answer is both charges are a
consequence of IW, which of course is constant.
_
We have established that the relationship of q to P and mu_B to IW is
one of time.
_
qt = Ft = mat = mv = P_e (From here forward we
specify electron
parameters.)
and likewise mu_B t_e = IW
(We label this particular time /\t_e for it is specifically of the electron.
_
The question arises, what is th relationship of IW to P_e and mu_B to q?
P_e
Taking ----- we see the result is one of distance -- both linear and
IW
angular:
Eq. (A)
nm_q LS
---------
P_e m_ec sec 4 pi 4 pi
------ = ====== = =============== = n ------- = --------
IW h m_q LS LS sec LS D_e
----- ---------------
4 pi sec^2 4 pi
(We note that 4 pi
= 2 rotations.)
Here we see a ratio between the electron's diameter and its 4 pi rotation.
Since 4 pi equals two rotations, it might be clearer to state the ratio as
2 pi
---- . Thus we have a direct relationship of one revolution to the radius.
r_e
Observing our graphic display we see the following relationships:
Eq. (B)
_
q IW
mu_B = ------- = 9.274671 x10^-21
P_e
This is the relationship for the electron. We now ask, what is the
relationship for the proton and calculate mu_N, proton magnetic moment.
We do this by substituting the proton mass in place of that of the electron.
Eq. (C)
+ +
q IW q IW
Mu_N = ------- = -------- = 5.050825 x 10^-24
P_N m_p c
+
q h
By the standard model Mu_N is given as ---------- which yields
4 pi m_p c
the identical result.
Thus we have
+
Mu_N - - - - - - - - - - - - - - - - - q
| |
| 4 pi |
| -------- ------- ---------> | t_p = 1.043896 x 10^-4
| D_p |
IW |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ | m_p c
(or h/D_p)
These variations, of course, are all in the ratio of the electron to proton
mass.
Rewriting equation B and C we have
_ mu_B P_e
q = -----------
IW
and
+ mu_N P_N
q = ------------
IW
We now perceive the answer as to why particles of such disparate mass
as the electron and proton have quantitatively the same (although opposite)
charge, IW is constant and mu_B P_e = mu_N P_N.
As to the charge being opposite, it is well accepted that this is due to
the reverse spin, although it is not quite clear. This subject shall
be dealt with later.
_
Another obvious conclusion is that the polar vector q is the motive force
for the *electron* current, I. When a wire is moved accross magnetic lines
the magnetic moment of the quanta (grouped into electrons) aligns with the
magnetic field thus orienting the electric moment to be unidirectional,
_
creating a current. We note the *left* hand rule applies as q is in the
opposite direction of the current**
--------------------------------------------------------------------------
**
"Current" direction is customarily given as opposite to the direction
of electron flow. In this work it is considered to be in the *direction*
of eletron flow and termed *electron current* vs *electric* current.
It seems inapropos to carry on a tradition, a misconception born in the
dawn of understanding.
---------------------------------------------------------------------------
We now examine magnetic moment from a different view:
Examining equations (B) and (C) we observe that mu_B is inversely
proportional to the mass of the particle -- and since the radius is
inversely proportional to mass, then mu_B is directly proportional to the
radius.
This should not be surprising inasmuch as we attribute mu to an equatorial
wind or current and we would expect the radius of the particle to affect
this; the less the radius, the less the magnetic flux -- and the diameter
of the nucleon is so much less than that of the electron.
There is an overriding minor variation which will be discussed more fully
in the next section.
We note some relationships by way of confirmation:
Eq.(A) may be written as
IW 4pi = P_e D_e
h h 4pi
Substituting (IW = -----), we have ----- x ----- = h = P_e D_e
4pi 4pi 1
As all parameters are constant this holds for protons, neutrons and photons.
An interesting note:
nm_q LS LS
h = P x D = --------- x ---- = m_qc x LS = P_1 LS
sec n
where P_1 is *absolute minimum* momentum.
Of special interest -- toward verification -- is the photon.
Lamda = wavelength = distance, D = c/nu.
P = momentum = h nu/c
Eq. (D)
h nu c
PD = ------ x ----- = h
c nu
We note that the measurements for the above equation are accurately
determined empirically. Thus if the relation h = PD is true for the
photon -- and the theoretical considerations are consistent for radiation
through particle, then we can assume that h = PD is true for particles;
which means our concept of quantum spheres and the method of determining
diameter, momentum and mass is verified. This is the foundation supporting
the rest of the theory.
h
We also note that the Compton wavelength is given as ---- =
mc
h LS
------------------- and is equal to D = ---- . Both expressions hold for
particle momentum n
particles *and* photons (where D = lambda).
The considerations for momentum and h carry for energy also.
In consideration of P c = E we write
h nu c
------ --- = E
c 1
Subst.: (nu = n/sec) We reiterate,
Eq. (E)
m a d t n
---------- = n mad = n h_0 = n(m_q c^2) = (nm_q)c^2 = m_ph c^2 = E_k
t
We note that since relativistically a particle of ponderable mass m
cannot attain c the only mass that can is the mass of the photon
(considered a particle of radiation). Therefore, Eq.(E) is necessarily
an expression of the conversion of mass to radiant energy.:
The photonic mass h nu/c^2 was incorporated into the elevated electron
from which it was ejected upon dropping to a lower energy level. When
incorporated in and part of the electron, it can be considered rest mass.
Therefore h nu/c^2 rest mass is converted to h nu/c^2 photonic mass.
( h nu/c^2 = nm_q)
EQUATORIAL VELOCITY
For the solitary quantum, the equatorial velocity V_1 is
theta
V_1 = ------- r_q .
sec
The minimun velocity is 1.1928366 x 10^10 cm/sec = .3978874 c .
This can be shown to be constant for any fermion:
theta r_q
For a particle of n quanta W = n --------, and r = ------ .
sec n
Thus equatorial velocity for a particle, V_p is
theta r_q theta
V_p = n ----- x --- = ----- r_q = k
sec n sec
We note n cancels leaving only the constants.
Since the equatorial velocity is constant and minimum we denote it as V_1.
This velocity is appreciably close to that of light.
Although quanta are very tenuous, given the high equatorial velocity,
it can readily be seen why magnetic flux is appreciable.
MACROCOSMIC MAGNETIC FLUX
With quanta grouped into electrons, the magnetization of a bar magnet
may be schematically represented thus:
( + indicates electric vector pointing downward through page. )
( * indicates electric vector pointing upward from page. )
( The *left* hand rule applies.)
<-
.
. .
. .
| . .------------------------------------------------. . .
\|/ . | <- <- <- <- | .
. | ( + ) ( + ) ( + ) S( + )N | . .
| -> -> - > -> | .
|- - - - - - - - - - - - - - - - -| .
S |- - - - - - - - - - - - - - - - -| . N
. | -> -> -> -> | . .
. | ( * ) ( * ) ( * ) S( * )N | . .
/|\ . | <- <- <- <- | .
| . |________________________________________________| . .
. .
. .
.
<-
End view ->
q
q q
q q
q q
q
<-
ATTRACTION, REPULSION AND ANTIMATTER
Let us regard a matter/antimatter pair of particles:
_
q
/|\
|
|
- -
--- ---
- -
- IW -
<---- --- -------------- --- ---<<<
- _ -
- e -
--- ---
- -
+
q
/|\
|
|
- -
--- ---
- -
- IW -
>>>-- --- -------------- --- ---->
- + -
- e -
--- ---
- -
We note the distinction is a *reversal* of spin, i.e., the q forces
are unidirectional whereas the spins are opposing. Opposite spins or
antiparallel spins, say of electrons, may be achieved by acquiring an
180 degree orientation, *but the q forces are then opposing.*
Thereby lies the uniqueness of spin REVERSAL versus *opposite* or
*counter* spin. We reserve the meaning of REVERSE spin to be in reference
to parallel q forces.
Next, let us suppose two particles -- or two photons -- approaching each
other or separating with their spin orientations at approximately
90 degrees (as an extreme case)
__
/|
/
- - /
--- ---
- / -
- / -
-- / --
- / -
- / -
--- ---
/ - -
\ / \
\ \ - -
\ --- ---
\ - \ -
\ - \ -
\ \ --
_\| - \ -
__ - \ -
|\ --- ---
\ - - \
\ \
\ _\|
\
\
\
\
\
\
Let us constantly be conscious that in actuality "particles" are huge
spheroids of 1 LS diameter. Thus *in approach* the two particles become
entangled -- at first in their extremely rarefied zones -- and through
mutual influence must eventually re-orient in relation to each other such
that their equatorial planes are parallel. Thus there are only two possible
resultants, parallel or antiparallel spin. Therefore, we posit that all
particles whose cores are in close proximity are aligned equatorially
in parallel or antiparallel spin.
The entanglement phenomena accounts for empirical experience of non-locality,
diffraction, and other wave/particle phenomena and may manifest with
particles separating.
We now examine the dynamics of merging *full diameter* (1LS) particles.
It will be found to be complex, *very* complex -- and surprising.
Therefore, the methodology employed here will be crude but hopefully
sufficient to correctly display the results with a fair degree of
accuracy.
To ilustrate the complexities we display the approach and merging of two
particles of parallel spin.
(It may augment the illustration if one
connects the "dots".)
PHASE I
^^^^^^^
spin -->
.
/|\ . . |
spin | . Zone 2 . \|/
. .
. . .
. . -> -> . .
Zone 1 ---> . . <- <- . .
. . . | spin
. . \|/
/|\ . .
| . Zone 2 .
. .
.
<--
Zone 1 is a counterforce region, and increasing. Only rarefied regions of
the particles are involved.
.
. .
. -----> .
._______________.
. .
. <----- .
. .
.
Diameter is dividing line for current vectors. (drawn straight instead of
curved -- ASCII restriction)
End of PHASE I, start of PHASE II
^^^^^^^^^^^^^^ -->
.
Zone 2 --> . .
. .
._______._______.
/|\ .. --> --> . . |
Zone 1 -----> | .. <-- <-- . \|/
._______._______.
Zone 1 is the volume common . .
to intersecting spheres . .
*limited to the volume between .
their axes.
<--
Zone 1 at maximum. The surface of each sphere reaches the diameter (axis)
of the other.
The extremely rarefied region of each particle is involved with the very
dense region of the other. Thus zone 1, at maximum, is not very influential.
We note, also, that the volume of zone 1 at maximum is somewhat less than
the rest of the spheres.
spin
-->
.
Zone 2 -----> . . Zone 1 commences to diminish
. . . and denser regions becoming
.__._________.__. involved.
Zone 1 ---------> .. --> <-- ..
._______________ . Zone 2 increasing, includes
. . . . all volume extraneous to
. . . that between axes.
. .
.
<--
spin
.
. . .
.. --> ..
._____________._.
Zone 1 --> .______________.. <--
Zone 2 --> . .
. . <-- . .
. . .
.
Merged volume of Zone 2 increasing rapidly . Denser regions becoming
involved.
END OF PHASE II
^^^^^^^^^^^^^^^
The Zone 2 force will become stronger until the *effective* surfaces are
nearly engaged and an equilibrium with the Zone 1 countereforce *approached*,
i.e., the attraction force of Zone 2 approaches equilibrium with the
repulsion force of Zone 1. However, the repulsive force dominates and the
reaction is considered one of repulsion.
----------------------------------------------------------------------------
In these illustrations it sometimes becomes a bit difficult to visualize
the interactions of the zones for spin and contraspin events. The reader
can make a workable moving model quite easily by taking two circular
pieces of tissue paper or tracing paper, draw curved lines representing
the currents, and then simulate a merger by superimposing the circular
pieces -- sliding one past the other, simulating a merger.
To simplify the confusion of arrows that results, it is sufficient to
draw them so:
spin
-->
..
. --> --> .
. --> --> --> --> .
. --> --> --> --> .
. --> --> --> --> --> .
.________________________.
. <-- <-- <-- <-- <-- .
. <-- <-- <-- <-- <-- .
. <-- <-- <-- <-- .
. <-- <-- <-- .
. <-- <-- .
..
/|\
|
merger contact and direction
We thus simplify the flow of each hemisphere. By superimposing the tissues
and observing them through a light, one *approximates* the dynamics.
Spin and contra-spin are achieved simply by "flipping" one of the tissues.
---------------------------------------------------------------------------
Although the volume of Zone 1 reduces to a comparatively minute quantity
the repulsive q force is very strong as the region is extremely dense.
The cores are close together and q increases inversely as the square
of the distance.
The reason that q varies inversely as the *square* of the distance rather
than the fourth power( as does density) is not understood except that it
no doubt is influenced by the following.
As Zone 1 approaches terminus its volume approaches the configuration of a
disk having a virtually constant radius which is LS/2 or r_q. The cores
lie along the center of the intersect planes of the disk shaped zone and as
they approach each other the volume becomes *directly proportional* to d,
the distance between cores. The force is proportional to the volume and
the density of that volume. In addition the influence of Zone 1 is also felt.
We now summarize a *contra* spin merger.
The contra spin merger is the same except the charges are reversed -- Zone 1
is attractive while Zone 2 is repulsive. However, the attraction of
Zone 1 proceeds to the point where the repulsion of Zone 2 reaches an
equilibrium with it. Thus the particles are not drawn into contact by the
attraction force but establish a balanced position. In the case of photons
they will each continue on their course because the density is such that
they do transit each other -- and because they are constructed in a
sequential (wave) pattern.
The contra-spin merger can be illustrated simply by "flipping" one of
the tissues.
Below is a graph that *roughly* aproximates the conditions.
(apologies for the graph but ascii is ascii. However, connecting the "dots"
on a print out helps tremendously.)
r_q
_______________________________________
| | |
| PHASE I | PHASE II |
| | |
| | |
| | |
| | * |
| | |
| | |
| | * |
increase | | | antiparallel spin
| | |
| | * |
| / | - |
| / | - * |
| / | - |
| / | - |
| / | A ^|
| / | - ^ #|
| / | * - # |
| / | ^ _# R |
|/ ^ | # _ |
`-^--^---------- --*#------------------
time
Referring to the graph:
The abscissa is time as the particles merge. The ordinate is increase --
in both volume and force. The (/) (-) (*) lines are volume, the (^) and
(#) lines are force (labeled A and R for attractive and repulsive).
There is a verticle bisect labeled r_q, radius of the quantum (1/2 LS).
It is at this point (distance between particle cores) that Zone 1 reaches
its maximum volume and commences to decrease. This is labeled Phase I
Phase II commences as Phase I ends.
Zone two (*) commences growth to become virtually the entire *united* volume.
In Phase I, as Zone 1 grows from its inception to full volume, the force
it generates is shown by either the A curve or the R curve depending on
spin orientation (parallel or anti-parallel).
In Phase II, as the volume of Zone 1 *decreases* the force continues to
*increase*, as the central -- dense -- cores are approaching proximity.
In phase II as the volume of Zone 2 increases the second force increases.
It is opposed to that of Zone 1 but always lesser.
We note that in the antiparallel event the attractive force A is at all times
greater than R the repulsive force. Therefore the antiparallel situation
is considered one of attraction.
*Conversely, in the parallel spin situation the dominant curve is labeled
R and we have a repellent condition.
Thus we see the proton and electron (hydrogen atom) are held in an
attractive electromotive force which is varied depending on the spin
direction.
An alteration of electron spin from parallel to antiparallel results in an
energy drop in the form of a photon of 21.11 cm wavelength.
Referring to the merger mechanics we see that in the parallel case the
repulsive force dominates. Thus the proton and electron maintain a more
distant relationship than than that of a proton and electron with
antiparallel spins, which is predominantly attractive.
The energy difference of the two levels is 9.41 x 10 ^-18 erg. There has
been observed from deep space a radiation of wavelength 21.11 cm and it
is hypothesized that the origin is free hydrogen atoms, the electrons of
which "flip".
* * *
Of interest is the magnetic moment of the "bare" proton and neutron vs
the magnetic moment of the *nucleonic* proton and neutron.
The moment mu_e of the electron is is
_
h q
-----------
4 pi m_e c
The only variable is mass. One would suppose, therefore, that the proton
magnetic moment would be
+
h q
-----------
4 pi m_p c
which yields 5.050824 x 10^-24
But this is not the case. This quantity is mu_N, the *nuclear* magnetic
moment or "nuclear magnaton".
The moment of the "bare" proton (mu_p) and neutron (mu_n) is more than
mu_N by a factor of 2.792845 for the proton and -1.913 for the neutron.
There are explanations given for the differential of the "bare" magnetic
moment from mu_N but this author has yet to find an explanation for the
difference between the "bare" proton and neutron, i.e., the factor 2.79
for the proton vs -1.913 for the neutron. That the factor for mu_n is
given a minus sign indicates a reverse spin, confirming experiment showing
the neutron to have a negative envelope. This leads to the following
explanantion.
If one examines the above graph they will find the key to the riddle.
The neutron consists of a combination of one proton and one electron.
Thus we have contra spins and the union is one of attraction. The electron,
being of larger diameter, *encases* (as opposed to *orbits*) the proton.
The reverse spins are opposite and *this tends to neutralize the
core-proton magnetic moment* -- succeeding in mitigating it so that the
net neutron factor is only 1.91 mu_N instead of 2.79.
The electric moment -- a core situation the vector of which is polar -- is
quite different. There the close proximity works so as to effect a full
nullity of charge and the neutron is thus neutral electrically.
Experiments sending free neutrons through a magnetic field found them
reacting in such a manner as to indicate that although they are totally
neutral electrically, the neutron is electrically negative on the surface
and positive toward the core; the maximum negativity occurring at
1 x 10^-13 cm from the center (whereas, the present theory shows the radius
of the proton to be *less* at 6.6 x 10^-14 cm).
A question arises: If we have an electron and a proton, why do we not have
a hydrogen atom?
The answer seems to be that for some reason during the original formation
of the pair there was enough energy available to supply a binding energy and
thereby effect a more closer union than that of the hydrogen atom.
There are several factors to note: (a) The *effective* radius of the neutron
is 6.6 x 10^-14 cm whereas the experiment mentioned above gave 1 x 10^-13 cm
as the maximum radius of the "negative envelope", much closer to the core
than an electron *in orbit*.
(b) The extra energy in the formation that was assumed to be present is
substantiated by the additional mass of the neutron over that of the
hydrogen atom -- a mass that accounts for the energy of beta decay and
its concomitant antineutrinos.
(c) The magnetic moment of the neutron, being less that that of the proton
indicates that the spins of the neutron's constituent electron and proton
are antiparallel. This antiparallelism would mitigate the magnetic moment.
However, a perusal of the graph shows the antiparallel state to
be *primarily* attractive -- which is the state we would expect in order
to induce and maintain the close association. Further, we note that the
magnetic moment of the two constituent particles are opposed and posit as
a consequence there is an eventual erosion of Zone 1 caused by the
opposition of Zone 2. Observing the graph once again we see that this would
mitigate the status of the pair reducing the attraction status such that the
equilibrium is upset. The consequence of this would be to *trigger* a
disruption of the close association caused by the exclusion principle.
The extra energy incorporated during the formation, which we may call binding
energy, is then released as antineutrinos impelling the electron and proton
so far apart that a hydrogen atom cannot be formed. We have here, of course,
a description of beta decay of the *free* neutron.
The interaction of nuclear protons in close association with the nuclear
neutrons in some way defuses or alters the magnetic moment trigger,
probably by forming Zone 1 attractive associations with the outer electron
casing of the neutrinos thereby defusing the disruptive activity.
We also note that the magnetic moment is a weak force in comparison to the
electric force (which in this case is nullified) and this would explain
the inordinately long lifetime required to achieve disruption (decay) which
is approximately 9 x 10^2 seconds in the free state.
As if all the above were not complex enough, we have one more force to
contend with that superimposes itself over the entire process just
described (and may be *the* factor in nucleonic neutrino stability).
That force is the nuclear force.
Earlier it was discussed that particles consist of concentric quanta and
that as one proceeds from the exterior to the interior the quanta rotate
at an ever increasing rate.
Thus we have a vortex with an accompanying vortical current and a resultant
vortical force directed toward the center. And so with the addition of
this force we see the quantification of particle mergers as *very* complex.
We will now analyze this force.
THE NUCLEAR FORCE
To the time of this writing the nuclear force has remained an enigma.
Very little of a concrete nature is known about it except for some
basically inexplicable empirical data.
We shall attempt here a physical explanation that is admittedly of a very
general and approximate nature. However, it seems a good beginning and
commensurate with the rest of this work --- which purports to be nothing
more than a blueprint, the details to be filled in by others.
A most cogent reference is a remarkable text [[[[ Physics, K.R. Atkins,
John Wiley & Sons, Inc. 1966, Chpt. 30 ]]]] most noteworthy because
of its clarity, simplicity, and unerring aim at essentials. Most of the
guidelines (clues) were obtained therein:
The clues:
(See illustration)
(a) "The radius of the proton is believed to be 8 x 10^-14 cm."
(b) "It is not known exactly how the nuclear force varies with
distance between nucleons, although it is quite certain that it
does not vary inversely as the square of the distance ..."
(c) "When two nucleons are farther apart than 10^-12 cm the nuclear
force is negligible."
(d) "As they are brought closer together, to distances less than
10^-12 cm, the force is attractive and increases rapidly --
more rapidly than 1/R^2."
(R = radius)
(e) "At a distance of about 2 x 10^-13 cm, the force becomes much
stronger than the electrostatic repulsion between two protons
at the same distance apart."
(f) "At distances below about 5 x 10^-14 cm, the attraction probably
changes into a strong repulsion."
(g) ". . . the two neighboring nucleons settle down at a distance
1.9 x 10^-13 cm apart, where the attractive force is still large."
(h) "To an accuracy of about 1% the force between two protons is the
same as the force between two neutrons or the force between a
proton and a neutron. This is called charge independence of the
nuclear forces."
(i) ". . . in the case of two protons there is an additional
electrostatic repulsion, but at a distance of 1.9 x 10^-13 cm
this in fact is less than 1% of the nuclear force."
(j) In addition, the work explains the mass defect of the deuteron
showing it to be 3.96 x 10^-27 gr. This establishes the binding
energy to be mc^2 or 3.559072 x 10^-6 erg.
(k) "The nuclear force does seem to depend on whether the two
nucleons are spinning in the same or opposite directions.
It is much weaker when they are in opposite directions."
With these fairly well established quantities and characteristics we
proceed with our own posits and deductions:
In view of statement (i) we take the nuclear force to be approximately
+
100 times the electromagnetic force q at 1.9 x 10^-13 cm. Thus, where the
+ q^2
statcoulomb q is 4.803618 x 10^-10, ------ = 6.391896 x 10^6 dynes at
d^2
that distance.
We then perceive the nuclear force, F_n, to be 100 times that or
6.391896 x 10^8 dynes (approx). This gives us a quantitative location
on the illustrated curve:
[[[[also from PHYSICS, K.R. Atkins, John Wiley & Sons, Inc, Chpt. 30]]]].
Strength of nuclear force
| Average distance between nucleons in nuclei
attraction |
|
** |
/|\ * |
| |*
| * |
| | *
| * |
| | *
| * |
| | *
| * | *
| | *
0 |------|------||------|------|------|------|----*-|-----*|--*---|------|
| * 1 2 3 4 5 6 7 8 9 10^-12
| * 10 ^-13 cm cm
| *
| * Distance between nucleons
| *
| *
\|/ *
*
*
repulsion
Variation of a nuclear force with distance (qualitative)
Likewise, we observe on the curve that at approximately 9 x 10^-13 cm
+
F_n approximately equals q. We also note that the greatest rate of change
(maximum) of the increasing curve is approximately 3 x 10^-13 cm.
In statements (a) and (f) we see a parallel: (a) "The radius of the proton
is believed to be 8x 10^-14 cm." (f) "At a distance below about
5 x 10^-14 cm the attraction probably changes into a strong repulsion."
(This statement is not accurately reflected in the graph.)
INTERPRETING THIS IN VIEW OF THE PRESENT THEORY:
The effective radius for the proton given by the present theory is
| (see appendix)
1/2 LS | where LS = light second and
r = -------- = 6.61 x 10^-14 cm | n = number of quanta in particle
n | = particle frequency
|______________________________
(developed prior in this work)
Thus at 2r or 1.32 x 10^-13 cm the nucleons would be in *effective
contact* with each other. We note that the effective surface is not
definite --but a zone. ---
****************************************************************************
It is shown earlier that the density of a particle falls off as the
*fourth* power of the distance from the center. Consequently, there is
no surface as such but a zone, a condition somewhat analogous to the
"surface" of a star.
****************************************************************************
As the two surface zones meet we would expect the attractive force to no
longer increase and that as the nuclei attempted to merge -- what this
theory sees as the Pauli exclusion principle (adopted from the classic:
two bodies cannot occupy the same space at the same time) would manifest
and the mutual attraction would be transformed to mutual repulsion.
This is what the curve shows. At almost exactly 1.32 x 10^-13 cm the
^^^^^^^^^^^^^^^^^^^^^^^^^^^^
curve changes from attraction to repulsion and increases negatively in
an asymptotic manner.
* * *
It was shown earlier that as one progressed from the outer region
of a particle toward the core the quanta spin velocity, quanta to quanta,
increased but the *equatorial* velocity, V_1, of each quantum remained
constant.
However, the increasing *angular velocity* as one approaches the core
establishes a vortex condition. It is this vortex that creates the
vorticle force drawing ambient quanta into the particle (see gravity)
and also draws nucleons to each other. This is the strong or nuclear
force.
The question arises, how do we quantify this vortical force? I found a
dearth of information on the subject. What there is deals with
hydrodynamics and aerodynamics. Furthermore, the descriptions are
essentially cubic -- or Cartesian.,i.e., a circularly moving surface
in conjunction with a height or depth. None seemed applicable to the
present situation which is *spherical*. In addition the substance
here is neither liquid or gas.
Consequently, the author was left quite out on a limb as to how to proceed.
However, one light shown in the dark; a statement was made in one text
that vorticity is a function of the circularity divided by the area within
the curve or streamline. Thus vorticity increased toward the center as the
area reduced.
Applying that to the present problem indicated that the vorticity
(vortical force) could be arrived at by taking the circularity to be
the equatorial velocity (invariable) and instead of the enclosed *area*
we should utilize the enclosed *volume*.
(where phi = vorticity)
V_1
This gives us phi = -------- . The volume is determined by 4/3 pi r^3.
volume
Thus for the *full* proton (diameter = 1 LS) the vorticity is
1.192836 x 10^10
phi = ------------------- = 8.45512 x 10^-22
4/3 pi (1/2 LS)^3
This is the vorticity 1/2 LS from the center.
Note, we give vorticity as a force, yet the dimensions of velocity/volume
are not those of force. How, then, can we consider phi a force?
By way of analogy let us regard the surface of the earth, say at the
equator. Because of the rotation every body on the surface regardless,
of mass, is undergoing an acceleration toward the center of the earth.
*This acceleration is the same for all bodies regardless of mass.*
If we regard force as m x a , and a is constant but m varied, then
we conclude the centrepital force varies directly as the mass. We see
the situation as one where larger masses have larger forces working on
them and smaller masses smaller forces. Thus for all bodies the centrally
directed acceleration is equal. *Therefore, we may discuss force in
terms of acceleration without regard to mass.* We assume this
characteristic for the vortex.
There is an ancillary view of the analogy. In the case of the earth,
we have various masses at the surface placed in the influence of
its gravity field. In the case of the nucleus, we have ambient masses
(other nuclei) placed in the influence of the vortical force. Both can
be expressed by centripetal acceleration.
In summary, phi = vorticity = centripetal *acceleration*
and phi x m = force
*We may regard mass as unity as it does not alter acceleration.*
Therefore, phi correspnds to F
Thus we discuss force in terms of vorticity, i.e., acceleration
without regard to mass.
We restate and simplify the equation for phi:
theta 10
(where V_1 = ------ r_q) and theta = -------
sec 4 pi
[Eq. D]
V_1 (theta/sec) r_q theta
phi = ------ = ---------------- = ------------------
Vol [4/3] pi r_q^3 [4/3] pi r^2 sec
Thus at the *full* radius of the proton
phi = 8.455122 x 10^-22 gr cm/sec^2 (dyne)
This is the vortical force *at the very extremity of the proton.*
r_p = r_q = 1/2 LS)
As a given mass is drawn toward the center, the volume reduces
v_1 (/\ = delta)
Therefore, /\ phi = ----------
/\ vol
We now consider two protons in proximity. The phi of each then interacts
with the other. Thus we have, analogously to Coulomb's law,
(where F_n = nuclear force)
phi phi phi^2
F_n = ----- x ----- = -----
d^2 d^2 d^4
We observe from Eq D that the vorticity or force varies inversely as
the *square* of the distance from the center. therefore , with
*interacting* protons the variation is inversely proportional to the
fourth power of the distance, d, between centers. This is not surprising
in as much as the density of the nucleons also increases inversely as
the fourth power of the radius.
Thus as a general statement:
(r_q = r_p because the outer limit of the proton is determined by
the maximum expansion of the component quanta. *Not* to be confused with
the *effective* radius which is the radius of significant density.)
theta^2
--------------------------
phi^2 ([4/3] pi )^2 r_q^4 sec^2 k
Nuclear force F_n = ------ = ========================== = -----
d^4 d^4 d^4
k = 7.148909 x 10^-43
+
We now construct a table making comparisons between q and F_n at
key distances. Notice how closely they follow the above graph.
+ |
q^2 |
--- | 6.4 x 10^6 2.6 x 10^6 9.2 x 10^5 2.4 x10^5
d^2 |
=============================================================================
(d) 1.9 x 10^-13 3 x 10^-13 5 x 10^-13 9.9 x 10^13
=============================================================================
|
phi^2 |
--- | 5.5 x 10^8 8.8 x 10^7 1.1 x 10^7 7.4 x 10^5
d^4 |
|
(continued)
1.9 x 10^5 1.0 x 10^5 1.0 x 10^3 9.2 x 10^-1
=============================================================================
1.1 x 10^-12 1.5 x 10^-12 1.5 x 10^-11 5 x 10^-10
=============================================================================
4.9 x 10^5 1.4 x 10^5 1.4 x 10^1 1.1 x 10^-5
Thus we see that at 1.9 x 10^-13 cm the electrostatic repulsion is 1.16%
of the nuclear force [see (i)]. At 1.5 x 10^-11 cm, F_q is approximately
71 times stronger than F_n, and at 5 x 10^-10 cm, it is approximately
83,600 times as strong.
PARTICLE-ANTIPARTICLE
We assemble our particles in an orderly fasion, i.e. we group them in
particle-antiparticle pairs:
/|\
-------> indicates spin | indicates electric moment vector
+ _ + _
q q q q
/|\ /|\ /|\ /|\ /|\ /|\
| | | | | |
-------> <------- -------> <------- -------> <-------
positron electron proton antiproton neutron antineutron
+ _ + _
e e p p
antimatter matter matter antimatter matter antimatter
RH LH RH LH RH LH
( At this juncture we use the RH, LH notation simply because, being
anatomical, it is more graphic.)
Inspection immediately reveals that the determining factor for
matter-antimatter is spin -- given conditions where
* the polar vectors are unidirectional and
* mass is identical
reverse spin creates opposite charge which in turn creates an antiparticle.
There is an interesting situation in the disruption of an electron-positron
pair. We have two particles of opposite charge and equal mass that *should*
disrupt each other immediately upon contact. That does not happen.
Instead they orbit each other for a brief period, and for that period of
time are considered a quasi atom called positronium.
What is of interest is the lifetime of positronium for the antiparallel
spin case, 1.25 x 10^-10 sec, and the parallel spin case, 1.39 x 10^-7sec.
Thus we see the parallel spin case as being over one thousand times longer.
In observing the the merger chart we see that in the parallel case the
*repulsion* force is the stronger until equilibrium. It, therefore, is
not suprising that this predominance would tend to keep the particles
apart and thereby slow the ultimate disruption. Of course the reverse
is true for the antiparallel case.
PHOTONS - LIGHT WAVES
As shown earlier all free qaunta groups are drawn into one spin orientation
or the other. Thus photons and their composite waves consist of quanta of
both spins with the resulting electric and magnetic moments 90 degrees to
each other.
The magnetic flux comprises the magnetic wave component. The electric wave
component (q) has an orientation of 90 degrees to that. One half of the
q vectors point "up", the other half, "down". This combination comprises
the electric wave component.
-->
..
. ~ .
* _ * . ~ . mu
* q * . ~ .
* /|\ * . ~ .
* | * . ~ .
-----*-------------------*----------|---------*--------> wave direction
. ~ . * \|/ *
. ~ . * + *
. ~ . * q *
. ~ . * *
. ~ . mu
. .. .
<--
Thus we have in combination an electromagnetic wave considered to be of the
transverse type, each component field normal to the other and traveling a
ray vector normal to both.
The composition of the electromagnetic (e m) wave, or more specifically,
the photons is not simple and will therefore require some analysis.
We have in effect great quantities of quanta emitted in a linear fashion
with the ability to merge and exist co-spatially. These quanta also have
parallel and antiparallel spin as well as opposing electric moments.
Their co-spatiality and and perfect elasticity results in the phenomenon
of superposition creating the familiar wave characteristics of the
electromagnetic spectrum.
Making the assumption that counter rotating groups of quanta will pair off
in all possible combinations, we now ascertain the possible combinations
in order to discuss photon characteristics.
However, there is a matter of more general nature that needs be addressed
before we proceed,
In the less dense *linear* state of electromagneticc propagation the quanta
chain will string together compatibly, but in the more dense concentric
condition of matter the group will separate into positive and negative
(positron, electron) states. This is the familiar "pair production" event.
We project that more massive matter-antimatter particles would be produced
should the incident photon be of suffcient frequency.
We note here a startling under-stressed phenomenon: *One half of each photon
consists of antimatter* -- or more exactly, of *antimatter quanta*,i.e.,
reverse rotating quanta. Thus there is far more antimatter in the universe
than heretofore estimated.
In the radiation mode matter and antimatter not only exist harmoniously but
do so for billions of years.
This matter-antimatter relationship shall be clearer as we proceed with
the analysis of the quanta combinations forming photons.
Returning to the assumption that counter rotating groups of quanta will
pair off in all possible combinations, we now ascertain the possible
combinations in order to discuss photon characteristics.
We will see that photons must statistically consist of both positive and
negative electric moments -- with the concomitant magnetic moments. Thus
photons consist of two halves or "couplings", i.e., 50% of one kind,
50% of another -- co-spatially existent, and electrically and magnetically
neutral.
There are four -- and *only* four possible combinations of the rotating
quanta couplings.
(1) Antiparallel: Left-Right ( A || - LR )
(2) Antiparallel: Right-Left ( A || - RL )
(3) Parallel: Right Right ( || - RR )
(4) Parallel: Left-Left ( || - LL )
It is apparent immediately that the antiparallel couplings, both Left-Right
and Right-Left are *indistinguishable* from each other, whereas the parallel
couplings -- both LL and RR *are* distinguishable as LL is a left rotating
photon and RR is a right rotating photon.
Therefore, of the four possible couplings
2 are A ||
1 is L
1 is R
Put another way the photon make-up (spin-wise) of *non*polarized light is
50 % A || (i.e., no spin effect)
25 % LH
25 % RH
Yet at the base (individual quantum) level the spin/anti spin ratio
is 50%-50%.
A schematic representation may clarify:
= = = = = = = = = = = = = = = = = = = = = = = = =
Photons are actually co-spatial but composition is shown separately, i.e.,
*the two types of quanta (shown horizontally) are contained co-spatially
in a single spheroid photon.*
50 % ANTIMATTER, 50% MATTER
_ +
q q
/|\ /|\
| |
PHOTON --> <--------- + ---------> = no net spin (A || LR)
Plane Polarized
+ _
q forces q q
parallel /|\ /|\
| |
spins opposed ---------> + <--------- = no net spin (A || RL)
A 180 degree rotation of the axis of plane polarized photons has no altering
effect as A|| LR photons are indistinguishable from A|| RL photons.
+
q
/|\
|
---------> + ---------> = spin R (|| RR)
|
\|/
_
Circularly q
Polarized
_
q forces opposed q
/|\
|
spins parallel <--------- + <--------- = spin L (|| LL
|
\|/
+
q
Rotating the axis of circularly polarized photons converts them from LH
spin to RH or vice versa.
In summation, in an unmodified non polarized beam, the mix is 50% all
A||, 25% L and 25% R spins. Nonetheless, en toto the composition is
50% "matter" quanta and 50% "antimatter" quanta, i.e., LH and RH spins.
= = = = = = = = = = = = = = = = = = = = = = = = = =
the following is an excerpt from "LIGHT" by R.W. Ditchburn, Blackie & Son Ltd.
London, p 639. The author is one of the foremest authorities on light.
" ... These results suggest a very simple 'picture' in which photons are of
two kinds -- one without spin representing plane polarized light, the other
either with right - or left-hand spin representing circularly polarized
light."
After a short discussion on the superposition of states, he goes on to say,
"... While the resolution occaisions no difficulty in the mathematical
formulation of Quantum mechanics, it shows the inadequacy of the simple
concept (above). If circularly polarized light 'consists' of particles with
spin, it cannot be regarded as a mixture of two sets of particles neither
of which have spin. In a similar way, if a photon, corresponding to a plane
polarized light is essentially a particle with some axis which defines its
plane of polarization, it cannot be regarded as the 'resultant' of two
particles which have their axes in different planes. These and many other
considerations show that the word picture suggested (above) does not
completely correspond with the situation described in the mathematical
equations."
* * *
To this author it seems Ditchburn has made an "either/or" assumption. If he
were to regard the photon composition given in this text he would have
available to him photons consisting *simutaneously* of "... sets of particles
neither of which have spin." -- i.e., A|| elements, and "... two particles
which have their axes in different planes" -- i.e., ||L and ||R.
The A|| couplings can be considered self-antiparticles whereas the ||
couplings are each antiparticle to the other. Thus 50% of the photon
population is particle/antiparticle and 50% self-antiparticle. The over all
effect:
A photon stream contains paticle/antiparticle elements and self-antiparticle
elements. Either can be revealed by proper influence on the stream.
50% of the elements have spins of one orientation, the balance, the opposite,
_
i.e., there are spins equally of + 1 h/2 pi. Combined, they produce
zero spin.
The thesis displayed above is reinforced by experiment using circularly
polarized light where the angular momentum of the photon was transferred
to a suspended half-wave plate and the motion measured.*
----------------------------------------------------------------------------
*
LIGHT, R. W. Ditchburn, Blackie & Son Ltd., London. p 561.
Experiment reference: GEIGER & BOTHE : Z. PHYSIK, 1925, B.D. 32, p 639.
-----------------------------------------------------------------------------
That the photon contains equal quantities of matter/antimatter quanta is
irrefutably evidenced by the phenomena of pair production.
MINIMUM MOMENTA
As a matter of corroboration, we develop another approach to spin angular
momentum, showing the the results to be identical.
/\ P
Just as there are two approaches to force (F = m a and F = ----- )
/\ t
we perceive two approaches to angular ( /_ ) momentum -- spin and orbital.
->
A particle with a linear momentum vector P orthogonal to a point A at a
->
distance d has an angular orbital momentum vector J about the point A
Eq.(11)
given by
-> ->
J = P d
============================================================================
For use below: (in angular motion of a sphere)
/_ m is the center of mass for a *rotating* sphere = 2/5 m
"I" is mass moment = /_ m * r^2
10
"W" is angular velocity in n theta/sec. theta = ---- radian.
4 pi
V_1 = orbital velocity = theta * r_q/sec = k for all particles.
->
P = *linear* momentum vector = /_ m * V_1
d = r
============================================================================
Considering any rotating particle, we regard 2/5 m as a *point mass*
->
(/_ m) located at the *effective* equator. Then /_ m * V-1 = P and
->
P * d = orbital angular momentum (where d = effective radius 1/2 LS/n).
By writing Eq.11 in the form
-> 1/2 LS
J = 2/5 (n m_q) * V_1 ------- ,
n
we see it holds for all particles as n cancels. Further, we see it can be
written for one quantum:
-> ->
J = /_ m_q * V_1 * r_q = P d
->
Comparing the equations for J and (IW) in the primary (single quantum)
form we have
-> ->
J = P d
/_ m * V_1 r_q
| | |
| | |
| | |
| | |
| | |
(IW) I W
/_ m_q r_q^2 theta/sec
->
Thus we see J = (IW)
That the parameters utilized produce consistent results tends to substantiate
the correctness of the effective surface concept (with its effective radius)
and the equatorial velocity as given.
SOME INTERESTING RELATIONSHIPS
->
We note that for the individual quantum, the linear momentum component P is
->
P_1. This is the *minimum linear component* of angular momentum and is
less than P_1. In short there are two absolute minimum linear momenta. One
is linear momentum (m_q c) and the other is a linear momentum *component*
of angular momentum (/_ m_q theta r_q /sec). [Note, theta r_q is the
orbital sector subtended by theta.]
Some interesting relationships follow:
[ where /_ P_1 = absolute minimum (IW) or (IW)_q ]
[a] [b]
P_1 /_ P_1
----- = 2 pi --------- = r_q
-> ->
P_1 P_1
[c] [d]
h h bar
----- = 1 LS ------- = 1 LS
P_1 ->
P_1
In variation we note:
->
for [a] P_1 2 pi = P_1 minimum linear momentum
->
[b] P_1 r_q = /_ P_1 minimum angular momentum
[c] P_1 1 LS = h minimum linear unit of action
->
[d] P_1 1 LS = h bar minimum angular unit of action
In another view divisibility by 2 pi, i.e., one revolution in radians, or
an angular frequency of one gives us
h P_1 ->
------ = h bar , ------ = P_1
2 pi 2 pi
By way of analysis we we perceive the *meanings* of these equations on the
basis of the *individual quantum* :
[a] Minimum angular momentum component for one revolution expressed as
2 pi radians is equal to the minimum linear momentum (m_q c).
->
P_1 2pi = P_1
[b] Minimum angular momentum component traversing an orbital arc equal
to the radius of the quantum produces the angular momentum of the
quantum (considered a minimum where /\ t = 1 sec).
The multiplicand, r_q, is *not* the radius. In angular notation one
radian is subtended by an *arc* equal in length to the radius. In
this case r_q refers to the length of the arc. Thus
->
P_1 r_q = /_ P_1 = /_ P_q
[c] The minimum *linear* momentum applied accross the diameter of the
quantum (1 LS) yields one h. This is a strictly linear event.
P_1 LS = h
[d] The minimum angular momentum component applied accross the diameter
of the quantum yields h bar (h/2 pi)
->
P_1 LS = h/2 pi
The minimum angular momentum component applied through a circumference with
a radius of 1/2 light second (r_q) for one revolution produces h/2.
->
P_1 2pi r_q = h/2
The same applied for *two* revolutions produces one h.
The equation may be rewritten
->
P_1 4pi r_q = h
or
-> h h
P_1 r_q = ------- = 1/2 ------
4 pi 2 pi
A disturbing question arises: Why does it require *two* revolutions of the
minimum angular momentum component to produce *one* h? Intuitively, it
should be *one* revolution.
LINEAR AND ROTATIONAL ANALOGS
As quanta agglomerate and their *effective* radii become smaller there is
an increase in angular velocity. We note two things: (1) The increments in
velocity are due to the conservation of momentum -- *not* to an applied
force, and (2) the increments are discontinuous, in quantized steps. Each
quantum joining the agglomeration adds one step, viz., n is given in whole
numbers and therefore n theta/sec is incremental.
We observe the following relations to be the rotational analogs of linear
parameters. They are minimals.
Linear parameters are in parentheses. (common usage)
(where "cor" = corresponds to ...)
(d) cor theta = .7957747 radian or 10/4 pi radian.
theta rad
(v) cor W_q = ------ = .7957747 ------
sec sec
(m) cor I = 2/5 m_q r^2_q = |h|/10 gr cm_^2
theta
(a) = acceleration = ------- (pseudo)
sec^2
(P) cor [IW]^q = I theta/sec = 5.272533 x 10^-28 gr cm/sec or h/4 pi radians
/\P /\ I theta/sec theta
(F) = ----- dyne cm cor L. --------------- = L_1 = I ------- (pseudo a)
/\t sec sec^2
|theta|^2
(E_k) = mc^2 cor /_ E_k_q = I |-----| = 4.195748 x10^-28 erg
| sec |
There is no divisor, 2, because there is no acceleration. The situation
is analogous to that of light and mass-to-energy conversion,i.e., mc^2.
/\P /\I theta/s
(E_k) = (Fd) = --- d cor /_ E_k_q = L_1 theta = ----------- theta =
/\t sec
4.195748 x 10^-28
theta h
(h) = (Pd) cor /_ I ----- theta = /_ h = /_ E_k_q sec = ---- theta =
sec 4 pi
4.195748 x 10^-28 madt
We now extend the rotation from theta to one full rotation,i.e., 2 pi rad.
/\I theta/s
(E_k) = (Fd) cor ------------ 2 pi rad = 1/2 h_0
sec
I theta
(h) = (Pd) cor /_ h = ------- 2 pi = 1/2 h
sec
|theta|^2 2 pi
(h) = (E_k t) cor /_ h = /_ E_k_q t = I |-----| x ------- = 1/2 h
| sec | theta/s
10 rad |h| |h| theta^2
Of interest: -------- = theta. Also ----- = I, ---- ------- = /_ E_k_q
4 pi rad 10 10 sec
2 . 5 rad
and - pi theta = 1 rad . . pi = -------- and pi theta = 5\2 rad
5 2 theta
In addition we note there is no innate or universal relation between momentum
and kinetic energy except that it is the cross product of momentum and
velocity in a general way with specificity by application.
Some Examples
Radiation: P c = E_k
Elastic-inelastic (Compton) collision: (Pe' + 2 P_ph') c = E_k
Linear mechanical: (Newtonian) P v/2 = E_k
v
Relativistic: P = gamma m v and P ----- = E_k
1 + R
Note:- The last equation is both Newtonian and relativistic -- as is
Einstein's E_k = (gamma - 1)m c^2. The problem with the latter is at low
(i.e., Newtonian) velocities the term in the parentheses is an extremely
small fraction. For example, if limited to nine decimals, 3 x 10^4 cm/sec
is unregisterable as R, i.e., it registers as 1 (unity).
The equation developed in this theory has no such problem.
* * *
In the first graphic display we observed the relationship between the angular
parameters (IW and mu_B) and the linear parameters (p and q) to be
5.179287 x 10^10. We find a pursuit of these relationships to be of interest.
Utilizing the cross products of proportions we have
| q | | P_e |
(IW) | ------ | = P_e and mu B |----- | = q
| mu B | | IW |
We now state the bracketed ratios *in terms of their physical constants* --
theta
except (IW) for which Eq. (10g) is used: IW = 2/5 m_q r_q^2 ------.
sec
h
Also P_e is written n_e -- .
LS
We note the bracketed terms are conversion factors converting the respective
momenta and forces. (See SPIN, CHARGE AND MAGNETIC MOMENT)
4 pi mc where m = m_e
The first factor reduces to ---------, and n = n_e
h or m_e/m_q
10 n
the second to ----------
LS theta
. 10 n 4 pi mc
. . ---------- = ---------
LS theta h
cross multiplying, 10 nh = 4 pi mc LS theta
thus nh = mc LS
(as 4 pi theta = 10)
mc LS n m_q c LS
or h = ------- = ------------- = m_q c LS = P_1 d
n n
Thus we see h equals the momentum of the electron accross its diameter.
This is true for all particles and the photon, for the general equation is
P * diam = P * d = n m_q c * LS/n = P_1 * LS = h
"n" means it holds for *all* particles, and P_1 and LS are constants.
The same result is obtained from
(in this case IW is written h/4 pi)
( q " " q )
( P_e " " h/D_e )
| P_e | | IW |
mu_B | ----- | = IW and q | ------ | = P_e
| q | | mu_B |
(where D_e = LS\n) ( where mu_B = hq/4 pi m )
n h mc
The first factor: ------- second factor: ----
LS q q
LS q mc
Thus n h = ----------
q
and since m = n m_q, we have n h = LS n m_q c
or h = LS P_1
Also we can write the above equation as
n h q = LS q m c
LS q m c
therefore, h = ----------- = D_e m c = D_e P_e
n q
(LS/n = D_e)
THE ELECTRON
Given the mass of the electron (m_e) as 9.108953 x 10^-28 gr'
m_e
---- = n_e, the number of quanta in an electron.
m_q
As each quantum creates a pulse, n_e cor nu_e = 1.235608 x 10^20 .
n_q E_q (n_e m_q)c^2 m_e c^2 E_i n_e
Thus -------- = ------------- = ------- = ----- = ----- = nu_e
h h h h sec
(where E_i = rest or internal energy)
Since the mass of the free electron is n_e m_q, the momentum is
P = (n_e m_q) gamma v. (where v = velocity)
The effective diameter of the electron is
1 LS 1 LS m_q
D = ------ or ---------- = 2.426275 x 10^-10 cm.
n_e m_e
EMPIRICAL VERIFICATION
In the concentric mode the oscillating quanta are analogous to an oscillating
electromagnetic cavity the *resonance radius* of which is given as
2.41 c
a = ---------
2 pi nu
Following are two results for calculating the radius of the electron. The
first (r) is by the present theory, the seconf (a) is by utilizing the
resonance cavity expression above.
1 LS
r = --- ---- = 1.213137 x 10^-10 cm
2 n
a = 9.306301 x 10^-11 cm
Acceptably close.
The same comparative relationship holds for the proton and neutron
(and photon).
The closeness of the results are reassuring. What is most certainly
ascertained here is that the electron of radius r does oscillate in
resonance as does the proton and neutron. What is not ascertained is whether
there is an exclusiveness or uniqueness to these radii, or whether
resonance is available to particles of any other size. In this respect,
more consideration must be given to the standing group wave aspect of
particle pulsation and its relationship to resonance.
Ideally, it should be found that in the concentric pulsating
expansion/contraction wave mode there are only two numerical configurations
that establish a stable resonating standing group wave. These would be
n = 1.235608 x 10^20 of the electron and n = 2.268909 x 10^23 of the proton,
the only stable and therefore only true particles in the universe.
The photon, though stable, should not be considered a true particle as it
is essentially a sequential group wave having radiation characteristics
following the Bose-Einstein statistics, whereas the electron and the proton
follow the Pauli exclusion principle.
In fact since particles and photons are both comprised of quanta we are
justified in proclaiming that there exists in nature *two forms* of
matter -- *ponderable* and *radiant*.("Plasma" may possibly be considerd
a third state of matter, man made. There is also the question as to whether
the interior of stars may not be considered natural plasma.)
There is a precedence in ponderable matter for this classification of
states, namely, "solid", "liquid", and "vapor". The molecule H_2O exists
as the constituent of all three states. This is analogous to the quantum
being the constituent of matter and radiation.
THE PROTON
Given the mass of the proton (m_p) as 1.672649 x 10^-24 gr, then
m_p
----- = n_p = 2.268909 x 10^ 23
m_q
m_p c^2 (n_p m_q)c^2 n_p(m_q c^2) n_p h_0 n_p n_p
n_p cor nu = ------- = ------------ = ------------ = -------- = ---- = ---
h h h h t sec
= 2.268909 x 10^ 23/sec
INTERNAL (REST) ENERGY
E_i = n_p h_0 = n_p(m_q c^2) = (n_p m_q)c^2 = m_p c^2
= h nu_p = 1.503302 x 10-3 erg
(These are of the form n h_0, m c^2, and h nu)
DIAMETER
LS
---- = 1.321307 x 10-13 cm
n_p
r = 6.606535 x 10^-14 cm
a = 5.068050 x 10^-14 cm
THE NEUTRON
We may think of the neutron as a hybrid composed of a proton and and an
electron plus approximately one and one-half electron mass of quanta as a
binding force. Although this view has been discarded it is the authors
belief there is such verification herein that the structure should be
reinstated.
We note that in the free state the neutron is unstable and will decay in
approximately 918 seconds. Located in the nucleus, in combination with
protons, the stability is permament -- except in heavy nuclei where there
is a surplus of neutrons. There the neutron's tendency to decay begins to
assert itself and "radioactive" decay takes place, although we do note
the products and half-lives are different.
Given the mass of the neutron as 1.6749543 x 10^6-24 gr we may write
m_N
----- = n_N = 2.272037 x 10^23
m_q
m_N c^2 (n_N m_q)c^2 n_N(m_q c^2) n_N h_0 n_N n_N
n_p cor nu = ------- = ------------ = ------------ = -------- = ---- = ---
h h h h t sec
= 2.272037 x 10^23/sec
INTERNAL (REST) ENERGY
E_i = n_N h_0 = n_N(m_q c^2) = (n_N m_q)c^2 = m_N c^2
= h nu_N = 1.505375 x 10-3 erg
(These are of the form n h_0, m c^2, and h nu)
DIAMETER
LS
---- = 1.319488 x 10-13 cm
n_N
r = 6.597440 x 10^-14 cm
a = 5.061073 x 10^-14 cm
NEUTRON DECAY
We determine the difference in mass between the neutron and proton to be
m_N - m_p = 2.305800 x 10^-27 gr .
When a neutron decays by emitting an electron and antineutrino it bcomes
a proton concurrently emitting the 2.3058 x 10^-27 gr.
Of this 9.108953 x 10^-28 gr is the electron, leaving a balance of
1.394905 x 10^-27 gr, or approximately 1.5 electron mass to comprise
the antineutrino.
The rest energy (internal energy) of the antineutrino is
mc^2 = nm_q c^2 = nh_0 = 1.253678 x 10^-6 erg = .783 MeV.
We represent the decay thus:
+ - + -
N --> p + e + 1.5 electron mass
The 1.5 electron mass does not create a particle because it is non-coherent
being the manifestation of the binding energy. Part of this energy
(and mass) is released as the energy accelerating the proton and electron,
the rest forms a quasi particle consisting of quanta traveling through
space *clustered* in close proximity. This "particle" is known as the
antineutrino.
The "size" of the antineutrino is in question (but may be deduced) because
a portion of the .783 MeV is utilized in accelerating the proton, electron,
and the antineutrino itself.
As individual qaunta the contituents of the neutrino possess spatial
orientation in many directions. This nullifies the electric and magnetic
moment. The intrinsic spin, however, persists and serves to conserve
the whole.
charge + - + - 0
N --> p + e + q
spin 1/2 1/2 1/2 1/2
To whatever extent neutrinos permeate the cosmos, they are a factor in
the total mass (or mass density in a steady state universe of unknown
boundaries).
As a result of the above description of beta decay, we perceive the neutron
*not* to be a true elementary particle but a composite of a proton and an
electron. Thus the neutron is electrically neutral because it contains both
charges.
This concept of the neutron is further enhanced by noting that the *free*
neutron is unstable, which in turn suggests there are certain interactions
within the atomic nuclei that keep nucleonic neutrinos stable.
An attractive hypothesis would be that the pre-neutrino not only binds
the electron and the proton to form the neutron but in the atomic nucleus
is at least a part of the binding process of protons to neutrons which
varies the neucleonic forces thus resulting in isotopes and radioactive
decay. It is noted that in a general way the larger the proportions of
neutrons in the nuclei, the greater the instability, viz., nuclei with
an excess of neutrons have a problem similar to that of the individual
neutron, stability. This interrelation of forces might also explain the
excess of nucleonic neutrons per se, which raises a question, why are
there not an exact equal quantity of protons and neutrons in atomic nuclei?
In furtherance of this concept of the neutron we take a closer look which
will display a sightly different and more accurate picture.
Bombarding beryllium-9 with high energy photons yields beryllium-8 plus
a neutron. In other words adding the high energy photon to a proton
creates a neutron.
Thus we perceive a photon -- consisting of one-half RH spin and one-half LH
spin -- entering a proton of RH spin, the RH quanta of the photon being
added to the proton.
The LH quanta become *concentric* to the proton core, encasing the proton,
and maintaining a close proximity to it by virtue of the merger attraction
displayed earlier. The Zone 1 region is predominant and the attraction strong.
While in this state the particle is known as a neutron for the electric
moments are opposed and thus canceled.
However, other than the attractive force there are other forces at work, one
is the Pauli exclusion principle where the proton resonance is overburdened
by the presence of the RH quanta. In addition the proton core and the
electron core are in close proximity in a union that is mostly Zone 2.
Within that zone the repulsive force comes into play, therefore the LH
quanta of the photon are ejected.
The LH quanta, being now concentric, form an electron and antineutrino.
The RH quanta overpopulating the proton could be ejected as a RH circularly
polarized photon.
----------------------------------------------------------------------------
It would be an interesting experiment to bombard beryllium-9 with
sufficiently high energy RH circularly polarized photons and to analyze
the result.
Neutrons should *not* be formed but secondary circularly polarized photons
may be created.
In addition, bombarding beryllium-9 with comparable LH circularly polarized
photons should create neutrons but no polarized photons.
-----------------------------------------------------------------------------
Let us now visualize the dimensions of the neutron. Recalling the curve for
the strong force we consider in conjunction with it the curve for the
electrical charge distribution.
(a)
Strength of nuclear force
| Average distance between nucleons in nuclei
attraction |
: |
: ** |
/|\: * |
| : |*
| : * |
| : | *
| : * |
| : | *
| : * |
| : | *
| : * | *
| : | *
0 |------|------||------|------|------|------|----*-|-----*|--*---|------|
| : * 1 2 3 4 5 6 7 8 9 10^-12
| : * 10 ^-13 cm cm
| : *
| : * Distance between nucleons
| : *
| : *
\|/: *
: *
: *
repulsion
Variation of a nuclear force with distance (qualitative)
Electrical Charge Distribution
(not drawn to scale)
(b)
(+): ?
: \
c : *
h :
a :
r :
g : *
e :
:
: *
d :
e :
n :
s : * * *
i : * *
t : * *
y : * * * *
*-------------------|------------------------|------------------------->
/:\ * 10^-13 cm * |
: * * 2 x 10^-12 cm
Center of *
neutron * *
: *
: * *
:
:
:
(-):
----------------------------------------------------------------------------
Source of (b): THE PHYSICAL SCIENCES: A CONTEMPORARY APPROACH,
Edward F. Neuzel, Bogden & Quigley, N.Y., 1972, p 199
-----------------------------------------------------------------------------
The data displayed confirms in dimensional form the hypothesis of the
neutron structure.
The effective radius is LS/2n_N = 6.6 x 10^-14 cm. We now seek the
effective radius of the "internal electron" , i.e., the concentric LH quanta
before emission. To do this we refer to the above curves ( a and b) and note
on curve (a) that, as determined earlier, the nuclear force dramatically
becomes negatively asymptotic just below 10^-13 cm indicating that this is
the surface *region* of the nucleon, the *region* of nucleonic contact.
Just below 10^-13 cm we perceive the nuclear force at its maximum -- and
also that it changes from the positive direction to negative. Thus
10^-13 cm is a critical region.
Observing curve (b) we see that this same region is the location of the
maximum *negative* charge surrounding the core.
We also note from curve (b) that there is a *positive* electric moment above
the negative, i.e., outward.
Bearing in mind that our composite particle has an actual diameter of one
light second we form the following picture:
Commmencing from the outer extremity (1/2 LS) we experience a charge-neutral
zone. As we approach the core of the neutron we register the positive
(RH) quanta which far outnumber the LH by a ratio greater than 1836 to 1.
As we reach 2 x 10^-13 cm [curve (b)] the positive force commences to
accelerate its increase. At approximately 1.36 x 10^-13 cm the curve is
downward, *changing from positive to negative*. We see on curve (a) that
this is the same locale as the change in the nucleonic force from the
positive direction to the negative. Thus we deduce that the negative (LH)
quanta have their essential location, i.e., essential radius at 10^-13 cm
from the center. In other words the essential radius of the electron
surrounds -- almost touching -- the essential surface of the proton.
Normally the essential surface of the electron would be 1.2 x 10^-10 cm
out -- a difference by a factor of approximately 12,000. Thus the electron
can be considered buried quite deeply within the proton and this would
explain the violent ejection which prevents the electron from orbiting the
proton and forming a hydrogen atom.
We note on curve (b) that after inwardly passing the negative (electron)
shell at 10^-13 cm the curve rises rapidly indicating we are entering the
proton core. Concurrewently, at that same location on curve (a), the strong
force is nullified and the (+) repulsion force becomes asymptotic -- again
indicating we are entering the proton core.
In short, by overview, we see that approaching from the extremity of what
is essentially a proton the positive charg commences to rise but is
interrupted by the negative (electron) envelope and then commences to rise
once again, rapidly, as we enter the interior of the proton core.
In confirmation we note that the magnetic moment of the neutron is given
as -1.9135 mu_n (nuclear magnaton). The negative sign refers to the
condition of the angular momentum *vector* being in the *opposite direction*
of the magnetic moment. We note the electron envelope spins in the
*opposite direction* of the proton. This apparently accounts for the
phenomenon.
NEUTRON DENSITY
The neutron density is confirmed by estimates of the density of neutron
stars.
4
| n_N |
Neutron density = n^4 D_1 = | ----- | D_1 = 1.392477 x 10^15 gr/cc.
| m_q |
m_q
D_1 (primary density) = ------------- = 5.225484 x 10^-79 gr/cc
4\3 pi r_q^3
(r_q = 1/2 LS)
UNCERTAINTY
We now examine the Heisenberg uncertainty relations.
/\ x . /\ P_x r h
/\ y . /\ P_y r h
/\ z . /\ P_z r h
/\ t . /\ W r h
We analyze the first expression (which applies to the others as well):
The cross product of /\ x and /\ P_x is *equal to* or greater than h.
We assume the *minimum* condition of "equal to" h.
We then set /\ P_x to the absolute minimum, P_1. In that case /\ x = 1 LS.
Therefore, *as a minimum*, we have 1 LS * m_q c = h.
Thus we have the momentum (m_q c) of *one* quantum accross the diameter
(1 LS) equal to h.
We have seen this elsewhere. It holds here as further verification of the
physical quantum concept.
The same holds true for /\ y and /\ z as the quantum is spherical.
Let us consider the last expression, where /\ W = kinetic energy.
h
/\ W_min = -------
/\ t
When the maximum diameter of one quantum is 1 LS, it will require one
second for transit. (velocity of free quanta is c)
Therefore, we have
6.625661 x 10^-27
/\ W_min = ------------------ = h_0
1 sec
Thus the minimum kinetic energy is h_0. The present theory gives the kinetic
energy of one quantum as m_q c^2 which is 6.62566 x 10^-27 erg or h_0.
THE HEISENBNERG PHOTON
A photon is composed of an aggregate of n quanta, the effective diameter
1 LS
of which is ------- .
n
Since photons are linearly grouped quanta and always in motion they have no
*exact* location, their best approximated locations being the clustered cores.
Therefore, the /\ x, /\ y, /\ z of Heisenberg is the *effective* size of the
aggregate. That is to say whereas the individual quantum has a diameter of
1 LS , an aggregate of quanta has a very small core the density of which
creates an effective diameter of 1LS/n. However, the group as a whole
attenuates outward to a one light second diameter. The effective diameter
is the wavelength which can be written
LS
-----
LS Dividing both sec c
lambda = ---- parameters by lambda = ======= = ----
n one second: n nu
----
sec
Thus we have an extremely mobile entity which is essentially a group wave
embodying measurable mass as well as measurable electromagnetic
characteristics requiring two distinct type of detectors (material and
electromagnetic) and having no clearly discernable boundaries.
THE HEISENBERG PARTICLE
The photon conditions continue into the realm of particles -- but with
modifications.
(a) The linear wave pattern is exchanged for an oscillating,
concentric standing group wave having resonance.
(b) The group wave core becomes more definite as n increases.
(c) Also, as n increases the mass characteristics become more
predominant, and Newtonian/Galilean mechanics begins to emerge.
(d) The 90 degree orientation and balanced coexistence of electric
and magnetic manifestations that existed in photons is altered,
becoming unilaterally aligned and manifesting as electric charge
and magnetic torque or moment -- still orthogonal one to the
other.
(e) Spin is also separated. Whereas photons tolerate right and left
hand spin quanta, in the condensed concentric mode of particles,
reverse spins become mutually exclusive as matter and antimatter.
In regard to (e) we see this phenomenon manifest in pair production where a
photon of sufficient mass (energy) is converted to an electron and a
positron.
There is no experiment known to this author where a circularly polarized
high energy photon *of singular spin* is used to attempt pair production.
The result should be two electrons or two positrons depending on which
photon is used, i.e., RR or LL.
----------------------------------------------------------------------------
MATHEMATICAL AGENDA
An area to be more exactly defined (mathematically) is the wave composition
of the photon as a secondary wave in a standing group wave.
Another, and most essential requirement, is a showing of the wave mechanics
of the electron and proton. The question to be answered is, why are there
two -- and only two -- quantities of concentric oscillating quanta that
are stable? As a corollary, we ask what is the nature of this stability? How
does a set of free standing concentric oscillating waves set up a resonance
where there is apparently nothing with which to be in resonance?
One supposition might be that in order to have a resonsnce there must be two
boundaries. In the instance of a tube and driven air column there is the
open end of the tube and its closed end. Analogously, in the case of the
particle it would be the outer limit of expansion and the inner limit of the
repulsing density of the core.
There should be a showing that quantities of quanta other than the stable
two exist briefly in a semi resonant state (exhibiting charge, spin, etc.)
quickly attaining a resonant state of a lesser configuration. Thus we
experience the phenomenon of "elementary " particles and their "decay" to
stable particles, electron, proton, photon, and nuclei neutrons.
And as a cap to these questions: What is the wave nature of the proton
electron union forming the neutron -- and the mechanics of the interaction
between that union and the other protons and neutrons in the nucleus?
There remains much to be done.
----------------------------------------------------------------------------
GRAVITY
We are faced with the question, what is the mechanics of action at a
distance? In other words if space is truly empty, how can one body exert
a force on another - especially at great distances?
The standard model proposes "virtual" particles which, in the case of
gravity is given a name (graviton) and not much more. In the case of the
electromagnetic force the virtual particle is the photon, for the strong
force it's the pi meson.
The present theory has a different view. The electromagnetic force is a
symbiotic one consisting of two components, electric force and magnetic
force.
It is the electric force that binds the electrons to the nucleus and
repels the nucleons from each other. If we were to peer at an electron
or proton from the *polar* perspective, we would see the inner core quanta
rotating faster than the outer. These same rotating core quanta are
sequentially expanding and contracting, supplying two forces -- a magnetic
force sweeping circularly and transverse to the polar axis, and an electric
force parallel to the polar axis.
Peering at a particle from the equatorial view one would perceive the
equatorial "wind" and as one came closer to the core they would also
perceive the velocity as being constant, though increasingly dense. This
is the magnetic force -- and much weaker than the electric.
In conjuction with these two forces is the merger dynamics illustrated above.
The electron and proton having opposite spins attract, drawing their nuclei
into close proximity where the polar electric forces cancel each other
leaving the composit neutral electrically and dynamically stable.
Two protons or two electrons having parallel spins the merger dynamics
repels, the polar electric forces also repel maintaining their identity,
i.e., the composite maintains its negative or positive electric charge.
We here discuss the gravity force. It will be found to be related to the
strong force inasmuch as the vortical force of fermions comes into play.
There is a major difference. Whereas in the case of the strong force the
vortical force draws in whole particles, in the case of gravity it draws
individual quanta. But we are getting ahead of ourselves.
* * *
Consider the hypothesis that not all quanta in a material body are confined,
and that some escape to be free, radiating outward in all directions at the
speed of light.
We may consider this as analogous to the sublimation of solids.
It is yet to be determined whether this process is affected quantitatively
by extremes of temperature. Beyond that we may assume that all matter,
regardless of physical or chemical composition, emmanates individual quanta
at the same rate, viz., the emmanation is a function of fermion particles
regardless of how they are grouped. Further, the rate of emmanation as a
certain percentage of the total mass, is constant. [Be aware that this is
an *assumption*. It may well turn out that there are conditions of state of
matter, temperature or masssiveness that alter this rate -- and in turn
alter the force of gravity. However, for the present, we proceed on this
assumption.]
Not only do we assume that a portion of a given mass is radiated as solitary
"gravity quanta" but that the portion is constant. Collaterally we also
assume that all grouped quanta in a body simultaneously absorb the available
quanta in their vicinity. (Recall that free quanta have a diameter of one
light second.)
We now consider the absorptive process. "Absorption" is not a wholly accurate
term because by the present hypothesis the gravity quanta are not absorbed
so much as they are *drawn* into the body with such great rapidity as to
*also_draw_the_absorbing_body_toward_the_quanta*, i.e., towards the emitting
body. Since this process is mutual, there appears what is interpreted as a
"mutual attraction" and "action at a distance".
The question arises, what is the nature of this drawing force? In the case
of the strong force it was demonstrated that protons and neutrons developed
a vorticle force that mutually drew neighboring nuclei together. It is this
same vorticle force that draws ambient quanta into the nuclei. As all nuclei
draw simultaneously the more nuclei present the faster ambient quanta are
ingested.
Let us now quantify the over all gravitational process.
The assumed mechanism can be shown to be commensurate with the mathematical
expression for gravity interaction as shown under *standard* conditions:
G (m_1 x m_2)
F = ---------------
d^2
STANDARD CONDITIONS
m = mass = 1 gr
d = distance between the
centers of mass
= 1 cm
G = gravity constant
We now quantify the sublimation of matter. To do this we discuss
gravitational force in terms of energy. It is evident that F x 1 cm = E_k.
Thereby, a body having a force F exerted on it, will possess a kinetic
energy of the same coefficient as the force when it moves 1 cm. By
designating the quantity as dyne-centimeters, we keep this relationship
constantly in mind.
Since potential and kinetic energy are interchangeable and conserved in a
closed system, it matters not whether we consider the energy associated with
the bodies under consideration as potential or kinetic, what is essential is
that we consider the *energy* and *recognize_that_it_is_created_by_the_
force_G*.
Having ascertained the energy existent between two bodies, we can
immediately determine the *equivalent mass* from the familiar m = E/c^2 .
[This is of the same genre as radiation where E = mc^2.]
We assert *that* mass to be the *mass equivalent of G*.
(1) Contemplating the standard condition,
G 1 x 1
F = ----------- = 6.672 x 10^-8 dyne
1^2
(2) If the weights join, i.e., travel 1 cm, we have
F x 1cm = E = 6.672 x 10^-8 dyne centimeter (erg)
E
and ----- = m
c^2
therefore, the mass equivalent of G is
6.672 x 10^-8
S = ---------------- = 7.423597 x 10^-29 gr .
c^2
Thus we conclude that the mass of the energy between the weights is
7.423597 x 10^-29 gr *and is the quantity sublimated from 1gr*. And so we
term this sublimated mass, S.
The reason for taking S as the sublimation of *one* gram instead of two
is that the force resulting from S is *common to both*. That means each
weight draws that amount from the other, which in turn means each one
gram mass sublimates S (7.423597 x 10^-29 gr) to be absorbed by the other.
The correctness of this is displayed in the worked example at the end of
this section.
Since S is stated for *one* gram then we can say that it represents the
*portion* of mass sublimated for *any* mass. Thus m x S is the total mass
sublimated from any body. We designate that m_S, "mass sublimated".
m E
Next we note that by n = ----- = --- we can ascertain the number of
m_q h_0
quanta comprising the 6.672 x 10^-8 erg (or 7.423597 x10^-29 gr).
This turns to be 1.006994 x 10^19 quanta.
We now ask, if 1.006994 x 10^19 quanta produce 6.672 x10 ^-8 erg, then
what part of an erg would *one* quantum produce? That is to say, how much
potential energy exists between one quantum one centimeter from one gram?
(This is equivalent to being an ambient quantum the surface of which is in
contact with the drawing mass.) We write
1.006994 x 10^19 quanta 1
------------------------- :: -------
6.672 x 10^-8 erg x erg
and we see x = h_0 .
Thus we show that in the standard (or ambient) case 1_q = h_0 and
G is thus quantized:
1.006994 x 10^19 h_0 = |G|erg. and
|G|erg
-------- = G dyne .
1 cm
Thus 1.006994 x 10^19 quanta correspond to G dyne or 6.672 x 10^-8 dyne .
Therefore, 1 quantum cor |h|dyne. That is, one ambient quanta will produce
|h| (6.625661 x 10^-27) dyne *per gram* absorbing it.
It is assumed that bodies radiate individual quanta, i.e., gravity at the
same velocity as any other radiation -- c.
The mass loss would also be the same: E/c^2.
PRIMAL QUANTITES
"Standard conditions" is a *special case*. More importantly, it utilizes
unity which is a mechanism to easily arrive at definite quantites otherwise
obscured. However, we recognize it *is* a *special* case and therefore we
seek a more fundamental reference. We shall term the parameters of this
reference "primal" quantities.
We ask if 1 q is drawn to 1 gr by |h| dyne, then what is the primal force
!F between two quanta one centimeter apart?
We find our answer, of course, by dividing |h| dyne by the number of quanta
in the absorbing gram.
|h| dyne
Thus !F = ========== = 4.884463 x 10^-74 dyne
1 gr
-------
m_q
-----------------------------------------------------------------------------
Note:- Henceforward we will refer to sublimated quanta as "gravity quanta",
"free quanta", or "ambient quanta" and assign them the symbol, Q.
"Ambient quanta" are specifically gravity quanta that are in proximity to
an absorbing body.
-----------------------------------------------------------------------------
We now seek the time t_a (standard conditions) for Q to be absorbed.
Since the drawing force of absorption is a function of the time for
absorption we derive such from
d
F = m a = m -----
t^2
thus t = sqrt [ m d/F ]
Therefore primal time for absorption: !t_a = sqrt [ m_Q 1 LS/!F ]
= 2.127139 x 10^18 sec.
Note, this is also equal to sqrt [1/|P_1| ].
For *any* mass nm_q, the time t_a to absorb an ambient quantum is
inversely proportional to the number of quanta comprising the mass.
Eq. [7-a]
t_a = sqrt [ m_Q 1 LS/!F n ]
Since m_Q LS/!F is a constant equal to !t^2, we can write
t_a = sqrt [ !t^2/n ] or !t/sqrt [ n ]
1 gr
We apply Eq. 7-a to the standard condition where n = ------ .
m_q
The result is t_a = 5.7755 x 10^-6 sec. This cannot be obtained from
the equation for t.
We note t_a can also be written sqrt [ 1 cm/c ].
Example:
With what force will a 1 gr mass attract another 1 gram mass
at a distance of 1 cm? (It will be shown later how and why that
varies with distance between objects.)
F = m a
LS
= m_Q ------- = |h| dyne = F for one Q quantum.
t_a^2
We now calculate the quantity of Q emanating from one 1 gr mass to be
drawn into the other.
1 gr x S = portion sublimated (in grams)
1 S
----- = nQ = 1.006994 x 10^19
m_q
Total force: F = |h| nQ
which for standard conditions is G.
We now derive primal acceleration, !a.
From a = F/m we have !a = !F/m_q = 6.625661 x 10^-27 cm/sec^2
where we observe the coefficient to be the same as that of Planck's
constant. In fact, many such interesting quantities and relationships
emerge.
Primal velocity !v can be obtained from v = a t
!v = !a x !t = 1.40937 x 10^-8 cm/sec
For distance d = v t
Thus !d = !v x !t = one light second
We might consider one light second as primal in the sense that it is the
diameter of one solitary Q, the primal particle of the universe.
Tables showing some common parameters for STANDARD, PRIMAL, AND MINIMAL
conditions are now displayed.
----------------------------------------------------------------------------
It will be noticed that there is a plethora of familiar constants, i.e.,
the coefficient of the constant appears but has mismatched dimensions. The
frequency with which these quantities appear is practically incestuous.
We will display these quantities in their symbolic form but bracket the
mismatched coefficient symbol; thus we remain aware of the tight
interrelation of a relatively few basic quantities and at the same time
emphasize the simplicity, rhythm, and beauty of the universe. It is this
simplicity and rhythm that forms a fractal-like construction of the universe.
-----------------------------------------------------------------------------
STANDARD CONDITIONS
(Two one-gram masses one centimeter apart)
F = G = 6.672 x 10^-8 dyne
(where nQ = m x S/m_q)
F_Q = force per gravitic quanta = G/nQ = |h| gr cm/sec^2 = |h| dyne.
E_Q = F_Q x 1 cm = h_0
a_Q = F_Q/m_Q = |h|/m_Q = c^2/sec
m_Q = m_q
(where sub-a signifies absorption)
From a*t^2 = d, where d = LS and a = c^2/sec
we set t = sqrt[ d/a ] . Thus
t_a = 5.7755 x 10^-6 sec = sqrt [ 1/c ]
v_a = a_Q t_a = LS/t_a = 5.190763 x 10^15 cm/sec
d_a = a_Q t_a^2 = LS = diameter of Q.
An other aproach to F_Q :
/\ P
F_Q = ------ .
t_a
Where /\ v = a_Q t_a
and /\v m_Q = /\ P
/\ P 3.826651 x 10^-32
-------- = F_Q = ------------------- = 6.625661 x10^-27 dyne
t_a 5.775500 x 10^-6
PRIMAL CONDITIONS
(where n = number of quanta in one gram)
!F = F_Q/n = |h|/n = m_Q !a = 4.884463 x 10^-74 gr cm/sec^2
c^2
-------
a_Q sec !F
!a = === = ================= = ---- = |h| cm/sec^2
n n m_Q
!t = sqrt [ m_Q LS/!F ] = 2.127139 x 10^18 sec
!v = !a !t = LS/!t = 1.409370 x 10^-8 cm/sec
!d = !v !t = !a !t^2 = LS
!E = E_Q/n = h_0/n = 4.884463 x 10^-74 erg
!m = m_Q = 7.37203854 x 10^-48 gr
m_Q is considered primal as it is the least mass in the universe. One
LS is considered primal as it is the diameter of the primal particle.
MINIMAL CONDITIONS
The minimal condition, signified by the subscript 1, is a function of the
natural, i.e., *uninfluenced emission* of quanta. It is a result of the
internal (potential) energy of the quantum solely.
LS
Action = h = m a d t = m_q ------- LS 1 sec
sec^2
c LS h m a d t
a_1 = ---- = ------ = ------------ = ---------
sec sec^2 m_q LS sec m d t
h h
t_1 = 1 sec = ----------------- = ---
m_q LS LS h_0
-----
sec^2
h
P_1 = m_q c = ---- = 2.210082 x 10^-37 gr cm/sec
LS
/\ P_1
F_1 = --------- = m_q a_1 = 2.10082 x 10^-37 gr cm/sec2
sec
E_1 = F_1 LS = h_0
h
v_1 = c = --------
m_q LS
LS h
d_1 = ---- = LS = -------
1 m_q c
The parameters h, F_1, P_1, and E_1 (or h_0) are *absolute* minimums.
EXTRAPOLATIONS
The following operations summarize the extrapolations from the primal
condition to the standard condition. As the latter is simply a special
case of a spectrum of possibilities we may then expect these operations
*to hold generally* by extending the mass parameter n.
(Where n = 1 gr/ m_q, i.e., the number of quanta in one gram.)
PRIMAL STANDARD
!F n nQ = G dyne F = G
!F n = |h| dyne F_Q = |h| dyne
!a n = c^2/sec a_Q = c^2/sec
!t/ sqrt [ n ] = t_a t_a = 5.7755 x 10^-6
!v sqrt [ n ] = v_a v_a = aQ t_a = 5.190764 x 10^15
!d = v t = !v !t = LS d = 1 LS
!E n = h_0 E_Q = F_Q 1cm = h_0
!F n nQ G
S = ---------- ----- = S
c^2 c^2
* * *
Before proceeding to a worked example it may be well to display a few key
shorthand notations.
Q = 1 nascent or gravity quantum.
S = 7.423597 x 10^-29 gr = portion of mass sublimated per gram per sec.
mS = portion of a body, in grams, sublimated per second as Q.
NQ = mS/m_q = number of Q per second sublimated by a body of mass m.
n_q = m/m_q = number of quanta comprising a body. Usually given as n
when the mass is known.
nm_q = mass of a body
N_q = n_q * nQ = total *interacting* quanta. Represents the number of
quanta in an absorbing body (n_q) multiplied by the number of
nascent quanta, nQ.
m S
nQ = ------- = number of Q emitted by a mass that are available
m_q d^2
at a distance from that mass.
A WORKED EXAMPLE
We shall concern ourselves with the gravitational attraction of the moon (M)
and the earth (E) for which some of the parameters are known. There is one
disadvantage which is that these parameters are approximate (at least as
given here). However, for purposes of illustration, they shall suffice.
(where m = mass, d = distance, r = radius, a = acceleration (at Earth's
surface 45 degrees from the equator).
m_E = 5.98 x 10^27 gr
m_M = 7.36 x 10^25 gr
d_E-M = 3.8 x 10^10 cm
r_E = 6.37 x 10^8 cm
a_E_sur = 980.665 cm/sec^2
Step (1)
We ascertain by *standard form* the gravitational attraction
between E and M , which we write F_E-M.
Gravity can be expressed either as a force or in terms of acceleration.
Eq. 7-b
G m_E m_M
F = ------------- = 2.033611 x 10^25 dynes
d_E-M ^2
F
From a = --- we obtain
m
a_E = 3.400687 x 10-3 cm/sec (acceleration of E toward M)
a_M = 2.763058 x 10^-1 cm/sec (acceleration of M toward E)
We note that whereas F is common to both bodies, the acceleration of each
is different being inversely proportional to its mass.
Step (2)
Next we calculate the force by which *one* quantum, Q, is pulled to Earth.
Eq. 7-c
G m_Q m_E
F_Q-E = -------------- = 2.941337 x 10^-27
1^2
One centimeter is used as the distance separating the quantum and Earth
merely to maintain unity. The significance of the parameter d exists because
we have the condition of gravity quanta expanding along the expanding surface
of an imaginary sphere; thus quanta available for absorption diminish in
numbers inversely proportional to d^2.
However, this condition is nonexistent in the situation considered
here -- which is one free quantum in proximate contact with a multiplicity
of others comprising a body. Here the force G governs without respect to
the distance between centers of mass, viz., we have one fully expanded
quantum in contact with a condensed multiplicity of quanta (Earth) and
since contact *is* established, d is considered unity(1 cm).
Step (3)
We calculate nQ, the number of nascent quanta from the moon that *are_in_
the_vicinity_of_Earth*, i.e., *ambient* quanta
m_M
------ S
m_q
nQ = ============ = 5.132600 x 10^23 Q
d^2
Step (4)
By utilization of F = !F nQ nq_E we have
F = 2.033611 x 10^25 dynes which agrees with Eq. 7-b.
Step (5)
Time required for E to absorb one Q:
t_Q = !t/sqrt [ nq_E ] = 7.468597 x 10^-20 sec
Step (6)
The acceleration of Q to Earth is
a_Q-E = !a nq_E = 5.374559 x 10^48 cm/sec^2.
d LS
or, where a = ----, a_Q-E = -------
t^2 t_Q^2
Step (7)
We note v_Q-E = a_Q-E * t_Q = 4.014042 x 10^29 cm/sec
Utilizing the primal form: v_Q-E = !v sqrt[ nq_E ] yields the same.
Utilizing the form E = mv^2 we have E per Q drawn to Earth as
m_Q v_Q-E^2 = 1.187822 x 10^12 erg.
E
By F = --- (where d = 1 LS) we then have
d
F_Q-E = 3.962147 x 10^1 dynes, and
F_Q-E nQ = 2.033611 10^25 dynes.
Step (8)
By way of verification:
/\ P (v_Q-E m_q) - 0
F_Q-E = ------ = ----------------- = 3.962145 x 10^1 dynes, and
t t_Q
F_Q-E x nQ = 2.033611 x 10^25 dynes, in agreemenrt with Eq.[ 7-b ].
We now calculate the acceleration of a body at the surface of the Earth:
m_E S
NQ = -------- = 6.02 x 10^46 Q
m_q
6.02 x 10^46 Q
----------------- = nQ at the surface.
(r_E^2) (6.37 x 10^8)^2
!a nQ = a
|h| nQ = 983.3 cm/sec^2
Given : 980.665 cm/sec^2 (at latitude 45 deg.)
A CAVEAT
Another example exists here as to why the mathematics of physics -- even
this simple mathematics -- is to be regarded with great caution.
Our equation for the gravitational interactions of bodies is
F = !F nQ nq
where
|h| m_1 S
!F = ======= nQ = ---------
1 gr m_q d^2
-------
m_q
m_2 G
nq = ----- S = -----
m_q c^2
Thus
|h| m_1 S m_2
F = ====== ---------------
1 gr m_q d^2 m_q
------
m_q
G
( Subst: S = ----- and |h| = |m_q c^2| )
c^2
|m_q c^2| m_1 G m_2 m_q G m_1 m_2
F = ----------------------------- = ----------------
1 gr c^2 m_q d^2 m_q d^2
Thus we see that by writing the equation in its simplest form, we obtain an
erroneous conception of the mechanics.
THE QUANTIZATION OF GRAVITY
Gravitational action is not customarily thought of in magnitudes on the
order of c because the response of ponderable bodies results in
velocities extremely small compared to that of light, nor is it thought
of in terms of typical quantum magnitudes because it is such a weak force
that determinations of micro proportion are difficult or considered
insignificant.
However, the concept here is that the mechanics of gravity in its
*initiating* form employs free quanta traveling at c, and the dimensions
of which are on the order of c. Absorption velocity must necessarily be
of *greater* magnitudes.
Thus we see gravitational action as initiating on the quantum mass level
but altered by the factors nQ and nq to magnitudes we usually associate
with gravity.
Whereas one usually thinks of quantum magnitudes as being very small, in
gravitational mechanics we are dealing with a broad spectrum commencing with
the large dimensions of *indvidual* quanta having micro mass which are
modified by large numbers of quanta to evolve into what appears as a
mechanics of macro proportions only.
QUESTIONS
We persue some inevitable questions regarding the sublimation of mass. We
propose here that all bodies radiate gravitational quanta which represent
7.423597 x 10^-29 or one part in 1.347056 x 10^28 per second.
The question arises, is this loss detectable? Probably not because (a) it
is so miniscule, and (b) each body also receives ambient quanta from other
bodies which compensates for the loss. Thus the individual quanta may be
thought of as the "virtual" or exchange particle of gravity (although the
mechanics is different).
Other questions: Is the sublimation rate variable for any reason? For
example, would near absolute temperatures affect the rate? If not, what
would? And, is any of this detectable with present day technology?
In summary, in regard to the basic questions of gravity the present theory
has ascertained or explained quantitatively *and* qualitatively
(a) action at a distance -- and its corollary
(b) mutual attraction
(c) the gravity "virtual" particle or "gravity wave"
(d) rate of quantum absorption and force engendered
(e) portion of mass radiated as gravitational quanta.
What we are in need of is a more exact picture of the mechanism of
absorption.
At this juncture we picture a continuum of free quanta aproaching a body
at c and being drawn in at an increased velocity proportional to the
number of quanta comprising the body. Thus the conclusion is that *all*
quanta of the body simultaneously draw on each and every ambient quantum,
the more quanta (mass) comprising the body, the faster the draw and
consequently the greater the force.
As a given quantum is drawn in it must, being indivisible, be eventually
pulled away from other absorbing quanta and become an integral part of a
single fermion.
But what is the cause or mechanism of absorption, and how do we quantify it?
At base we believe the mechanism must be the vortex described for the
strong force. This is the most logical prospect.
However, taking the vortex force as 8.455122 x 10^-22 dyne as given at the
full radius of the proton, and applying it to an ambient quantum, the
resultant is found to be too great, i.e., greater than gravity by five
orders of ten.
Of course there are differences. The strong force operates between two
nuclei extremely close to their centers whereas the gravity situation has
many fermions spread over a wide range absorbing inactive ambient quanta.
In addition these quanta are impacting at c. This c has to be to be
absorbed and then surpassed before a force can be exerted in the direction
from which the quanta are arriving.
In addition, in the final stage the absorbed quantum is drawn in many
different directions and, because it is indivisible, finally absorbed by
only *one* fermion. All these conditions must result in a reduction of
force. However, it is extremely difficult to quantitatively assess them.
REGARDING CURVED SPACE AND THE PRESENT THEORY OF GRAVITY
Apparently the universe consists as a cluster of galaxy clusters.
We know that galaxies rotate -- and so do virtualy all things in cosmology
and on the quantum particle level.
Thereby, we ask: Does the universe rotate?
If so, we ask
(a) What is the effect of rotation as to centrifugal force?
(b) How would rotation affect Doppler readings?
(c) Does light from distant sources undergo the Coriolis effect?
(d) Do gravity quanta suffer the coriolis effect?
(e) If so would that not create the illusion that space is curved?
V. Vergon
1980 - 1995
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