AETHER SCIENCE PAPERS: NO. 9
This paper was published in Physics Essays 1 pp.72-76 (1988)
A THEORY OF PROTON CREATION
Copyright © Harold Aspden, 1987
ABSTRACT
The hitherto unknown role of the muon in physics is now shown
to be connected with the processes of proton creation in a
primordial muon field. It is possible to deduce not only the
mass of the proton in relation to that of the muon, but also the
mass of the muon quantum which creates the proton. The advance
reported depends upon the discovery of an equation which shows
that the merger of a muon pair followed by energy minimization
can serve to nucleate further particle synthesis by muon merger
to give a unique particle some 8.8989795 times the mass of the
muon quantum involved. This leads to the creation of a proton
having a mass that is a little greater than 1836.152 times the
electron mass, in good accord with the measured value.
INTRODUCTION
The primordial processes governing proton creation appear to
involve a concentrated muon field and a critical threshold at
which muons can combine with a degenerate electron state to form
a proton and an electron.
Contrary to the expectation that the mysteries of proton
creation will be resolved by quantum chromodynamics, the
indications from the simple theory outlined below are that the
proton really owes its existence to the quantum electrodynamic
features of a vacuum field in which muon activity is prevalent.
Both the muon/electron mass ratio and the proton/electron mass
ratio become calculable from this theory. Hitherto the role of
the muon in physics has been a mystery. Now it seems that
without the muon, the hydrogen atom as the form from which all
matter in the universe is derived could not exist. Whatever
hidden function the muon may now perform in quantum field theory,
it seems that it has exercised a primary role in matter creation
at a time when the field equilibrium now prevailing was precluded
by excessive field energy concentration.
THE ENERGY CORRELATION
As the author reported in 1984 in Physics Today [1] there is
a very simple energy correlation between the muon and the proton.
This later led to an equation representing the proton creation
process [2, 3] and now forms the basis of a self-contained theory
which requires what may be termed the ‘equilibrium’ phase of a
locally-concentrated muon field.
The simple energy correlation formula recognizes that an
energy quantum Q associated with the electric charge e suggests
a bounding radius x containing that charge, where:
Here k is a constant and the equation applies to charges of
different bounding radii nucleating energy quanta having
different values.
The energy correlation function concerns two such charges of
opposite polarity necessarily separated by the sum of the their
bounding radii. Thus two energy quanta P and Q would have a
total energy P + Q less the Coulomb potential energy of the
interaction between the charges, which gives us, from (1), the
total energy expression:
This extremely simple physical statement offers a very
interesting and unique correlation between P and Q if it is
assumed that P is constant and Q can adjust so that the total
energy is at a minimum equilibrium value. Then we find that:
Applying this with the proton and muon in mind, suppose that
two oppositely charged mouns come together to form an energy
quantum Q nucleated by a charge -e with a separate energy quantum
P taking up the balancing charge +e. Then if equation (3) has
any relevance to this situation we can estimate the value of the
constant k. The numerical connection is that:
The question then is whether this result is just an
interesting curiosity arising from a mere mathematical
coincidence, that is one of the many traps by which Nature
misleads us. However, bearing in mind that we have no accepted
explanation for the quantities 1836 and 207 (the proton/electron
and muon/electron mass ratios), this is a lead we cannot dismiss
without further exploration.
On this course, it is first noted that the k = 2/3 factor has
a physical basis. It was used in classical physics in connection
with an electron formula used by Abraham and also by J. J.
Thomson. Their derivation of the expression has been rejected
in the light of the theory of relativity, but evenso there is a
pure electrostatic derivation that avoids the electromagnetic
argument and so overcomes the relativistic objections [4].
Accordingly, the k = 2/3 expression has a sound physical basis
and is not arbitrary.
The next very important question is that of explaining how the
proton can be ‘created’ from the muon field, if it is Q that is
the variable and P the constant in the derivation of equation
(3). The solution of this problem baffled the author for more
than ten years and the solution, as summarized in references [2,3], advances our argument in a very positive sense.
THE PROTON EQUATION
Suppose that the merger of a muon pair in the muon field
operates to create a minimal energy complex (Q:E), where Q is the
constant energy quantum nucleated by a charge -e and E is a
variable quantum nucleated by +e. Some energy will be dissipated
in this process, because the energy of (Q:E) in its minimal state
is less than that of two muons.
Now, given such a muon field containing neutral systems (Q:E)
imagine that n other muons of mixed polarities are absorbed by
the (Q:E) unit. Take n as odd and, as we are looking at proton
creation, rather than antiproton creation, suppose that
oppositely charged muon pairs are involved plus one positive
muon. Now, suppose that the action separates E from Q and allows
the creation of P in a (P:Q) complex with Q, subject to the
condition that there is complete energy balance in this process.
We have then a system which comprises three energy quanta
nucleated by charge and could determine P if we know n. Note
that we have not said that (P:Q) is in a minimal energy state,
so P is not determined by Q from equation (3). However, the
final step in the argument is to say that the whole energy of the
(P:Q) and E system consolidates to form a single particle of
positive charge which we say is the proton. Now, whether this
final phase takes the form of a three-quark system or a single
charge or retains the (P:Q) plus E configuration, or alternates
between such different states, is irrelevant to our calculation
of the proton energy quantum. The data just presented allows P
and n to be uniquely determined.
The process is represented as:
As a conserved energy statement, this is the proton equation.
To solve the equation we write Q as 2μ and note that, from the
argument leading to (3) with k = 2/3:
The form of this expression can be verified by combination of
equations (2) and (3).
In energy terms, the process of equation (5) becomes:
First, we solve this, ignoring the part involving n. We find
that:
This tells us that the proton rest-mass energy has to be
8.8989795 times whatever the energy of the μ quantum is in the
primordial muon field. However, more than this, there is
something very special about the proton equation which makes the
process of its creation unique. Note that in deriving equation
(8) we have not used the fact that n is an odd integer.
Obviously, one can imagine all kinds of reactions between muons
in the muon field and can devise more elaborate processes which
might involve multiple interactions between intermediate
products, leading to numerous particle forms. Yet we know that
the proton has a special characteristic by virtue of its
exclusive existence as the positively charged elementary particle
that is stable. Therefore, there is something else to consider
and this appears to be the effect of n in equation (7). If, and
only if, the energy of P matches exactly the quantity on the left
hand side of the equation, with n odd, then we can have perfect
energy balance in the creation process and so single out the
proton for its unique role.
Like the contracted Riemann tensor in General Relativity
theory, the proton equation with its n term makes it the unique
equation that can give physical account of the phenomenon under
study. The reader may verify by inspection that when n is 7 the
expression:
thus conforming with the solution found for P/μ in equation (8).
In other words, since the initial (Q:E) system requires two
units of μ it takes nine units of μ to create a proton and the
proton then has a rest-mass that is 8.8989795μ. However, the
magic of the proton equation is the way in which it gives this
unique result without generating surplus energy from the
coalescence with the 7 muons fed into the mininal energy dimuon
complex.
THE MUON MASS
The next ‘problem’ confronting our argument is that when we
put the real muon mass into this expression, we get a
proton/electron mass ratio that is too high. The ratio is 1840
and not 1836. This would be near enough to gain an initial
acceptance if it came by derivation from QCD theory, but we are
following a independent avenue in physics and can still be
suspected of exploiting mere numerical coincidences.
Accordingly, more has to be offered.
The route followed by the author has been to consider the
possibility that the muon ought, ideally, to have a form that
involves its energy equivalence to an odd number of electron or
positron energy quanta. In effect, this says that if the proton
can be created from 9 muons, maybe the muon could be created from
207 electrons and positrons. An independent exploration on this
theme went a little further by saying that if the primordial
negative muon comprised a positively-charged energy quantum of
207m units, where m denotes the electron unit, then in its stages
of formation it could have two satellite electrons to make it
negative overall. Then the negative Coulomb interaction energy,
on the principles outlined above, could reduce the total energy
from the resulting 209m units and hopefully lead to the observed
quantity, which is, according to the latest CODATA values,
206.768262(30).
Following this theme and involving a resonant interaction, it
has been shown elsewhere [5] that the calculated value of μreal, meaning the real muon sensed in particle experiments, is given by:
This gives a mass in electron units of 206.7683, which fits well
with that actually measured.
Onward analysis of the resulting states of the real muon [6]
gave reason for believing that the real muon involves active
transitions between states in which it is effectively a 205m and
207m system in a cyclic sequence, the average state giving the
resulting mass calculated from equation (10).
The relevance of this to the proton question is clear.
Critics should not be misled by knowledge of the measured value
of muon mass when looking at the primordial processes by which
the proton formed from μ states. All we then need to know is
that such μ states could be either μ = 205 or μ = 207 in units
of electron rest-mass energy.
THE THRESHOLD EXCITATION LEVEL
We proceed now without even assuming that μ has such specific
values. The assumption taken from the real muon analysis is that
μ can be either of two adjacent odd numbers. Our task is to
deduce these from first principles and determine their relative
incidence to find a mean value μ that can be used to determine
the equilibrium mass of the proton.
The primordial muon field from which the protons emerged is
assigned an effective energy density ρ such that:
where d is the side of the average space cube occupied on average
by the random migration of the muon pairs in their repeated
mutual annihilation and recreation activity.
It is now supposed that when the proton is created from the
merger of 9 muons the action comes together within a sphere of
characteristic radius b. Take N as signifying the volume of this
sphere of radius b and, with a denoting the characteristic radius
bounding a normal electron charge, write:
Guided by equation (1) regard this sphere as bounding what we
may term a ‘degenerate’ electron state hidden in the vacuum field
and having its effects screened by a neutralizing effect in the
sub-quantum vacuum world. This allows us to suggest that an
equilibrium state setting the threshold N occurs when the energy
m’ associated with density ρ inside this sphere of radius b is
related to the electron unit m in the ratio a/b:
From this, (11) and (12):
N is odd and what this expression means is that the 9 muons
will pool their energy to create N electrons and positrons which
then condense back into the forms leading to the process given
by equation (5). The object of this is to involve the
controlling threshold parameter N as an adjustable characteristic
somehow intrinsic to the field, but yet determined by the
processes under study. Indeed, the theme we follow is that if N
exceeds a certain value then the protons can be created, but if
N equals or is just below that value then the proton creation
process is halted.
This proposal really amounts to the following proposition.
Suppose that N has a value in the equilibrium field now existing
and in which we do not see proton creation activity. Whatever
the physical form of the N unit we can imagine that it involves
something that is at zero or near zero potential in the
equilibrium field. This N unit plays a basic role in determining
certain fundamental physical constants, as we measure them today.
Now, imagine that in the proton creation phase the field was
violently disturbed by effects which developed extraneous
potentials. The N unit could then find itself in a sub-zero
potential state so far as its action in characterizing those
physical constants is concerned, inasmuch as the extraneous
potential would make up the potential difference. In other
words, the physical constants could have been affected during the
proton creation phase. However, the one lead we have is that N
as it now applies to the equilibrium field is likely to have been
marginally lower than that which permitted proton creation.
This allows us to write the approximate formula:
From (13) and (14):
If d/a can be determined, then N can be estimated and μ is
then deduced so that P can be calculated.
THE FINE-STRUCTURE CONSTANT
To find d/a the muon field is imagined as having the
characteristic of a linear oscillator resonating at the
characteristic Compton frequency m/h associated with the
electron. The space system bounded by the sphere of radius b
will have an inertial mass determined by hydrodynamic principles
as half the mass of the energy m’ bounded by the sphere. For a
dynamically balanced oscillation of a juxtaposed system involving
unit displacement from a centre of balance we can then write:
Replace m’/m by b/a or (N)-1/3 (using N here as that now
applicable in the equilibrium field) and write m as 2e2/3a,
according to equation (1) with k as 2/3, to obtain from (16):
We then see that without any knowledge of μ there are two
equations (15) and (17) containing two unknowns N and d/a plus
the fine-structure constant 2πe2/hc, which is known with high
precision and which itself, as a dimensionless quantity, has no
generally accepted explanation in physics.
Merely for initial estimation purposes put hc/2πe2 as 137,
which is approximately the measured value. Then equations (15)
and (16) used to eliminate d/a give:
from which, using (14) μ is a little above 205.
Quite remarkably, therefore, relying essentially on the
natural property of field medium associated with electron
characteristics we have been led to evaluate the approximate
energy quantum of the muon state.
THE PRECISE PROTON MASS
The definitive value of N is then most likely to be 1843 as
the odd number defining the threshold condition. This is just
below the lowest possible m’ value permitting the union of 9
muons having the low μ = 205 state, since 9 times 205 is 1845.
This value of N determines d/a with precision in its relation to
the fine-structure constant. From (13) and (17), therefore, we
can eliminate d/a to obtain:
and:
To test the theory for the proton mass using equation (8),
note that the measured value of hc/2πe is usually quoted as
being between l37.0359 and l37.0360 and equations (8) and (l9)
then tell us that P is between 1836.1519 and 1836.15460, whereas
the latest 1986 CODATA value is 1836.152701(37).
This is unquestionably an encouraging result, bearing in mind
the very simple sequence of argument used and the fact that no
quantities other that the fine-structure constant have been
brought into the derivation.
However, the theory does go further than this, provided that
we are willing to probe the nature of the photon and accept an
argument which leads to the derivation of d/a as 108π. This is
something beyond the scope of this paper, but is of record
elsewhere [7, 8]. Note then that equation (17) would lead to the
formula:
The author believes that this is the value of the
fine-structure constant applicable in the true free space
equilibrium field and that, even now, the field energy activity
associated with the presence and motion of matter does have a
minor effect on the factors determining the constants. However,
using this result the value of P is found to be 1836.152317
according to the theory and assuming that the proton is virtually
a point charge system. In fact, its quark structure has a finite
form and that could account for a correction of a few parts in
ten million. Accordingly, it is submitted that the theory
presented above gives a self-contained physical argument for
interpreting the creation processes of the proton.
Finally, it must be said that although the proton theory
presented has been evolving for several years and has been
touched upon in several published papers, the earliest being in
1974 [9] and the principal one being the 1975 reference [10],
this presentation is wholly original in deriving the proton mass
by argument developed from the complete proton equation (5).
This represents a breakthrough which should make the author’s
methods much easier to understand. What has been avoided,
compared with earlier treatment, is the tortuous analysis by
which the m’ quanta were regarded as near to zero potential sites
in a dynamic lattice. Such argument which concerned the photon
involved notions alien to modern methods in quantum mechanics
and, though the author still defends that case, that plus the
non-adherence to QCD techniques, made it difficult to be led to
the proton mass calculation. Hopefully, the new and direct
account presented above will be more in tune with the receptivity
of those interested in the subject.
REFERENCES
[1] H. Aspden, Physics Today, 37, p. 15 (November 1984).
[2] H. Aspden, Hadronic Journal, 9, 129 (1986).
[3] H. Aspden, Spec. Sc. Tech., 9, 315 (1986).
[4] H. Aspden, Am. J. Phys., 53, 616 (1985).
[5] H. Aspden, Lett. Nuovo Cimento, 38, 342 (1983).
[6] H. Aspden, Lett. Nuovo Cimento, 39, 271 (1984).
[7] H. Aspden & D. M. Eagles, Physics Letters, 41A, 423 (1972).
[8] H. Aspden, Lett. Nuovo Cimento, 40, 53 (1984).
[9] H. Aspden, ‘The Chain Structure of the Nucleus’, (Sabberton,
Southampton), p. 17 (1974).
[10] H. Aspden & D. M. Eagles, Il Nuovo Cimento, 30A, 235 (1975).
