AETHER SCIENCE PAPERS: NO. 11
A THEORY OF PION CREATION
Copyright © Harold Aspden, 1987
ABSTRACT
Pion creation is discussed using the same physical principles
as those involved in a recent Physics Essays paper on proton
creation. The proton-electron mass ratio was deduced
theoretically with part per million concordance with its measured
value. Now it is shown that the theory for the charged pion
gives a pion/electron mass ratio also in precise accord with its
measured value. Other meson creation is discussed, and
particularly the neutral pion, which is dependent upon resonant
interactions that account for its lifetime and mass in a way
which supports the proton creation theory.
INTRODUCTION
In a recent paper [1] the author has shown how the proton can
be created from a concentrated muon field. This was subject to
threshold conditions which applied in an earlier epoch before
what may be considered a state of saturated equilibrium of the
vacuum field was reached.
The paper derives, with part per million precision, the
measured proton/electron mass ratio using techniques which are
simply based upon Coulomb interaction energy and a finite charge
form specified by a formula used by J. J. Thomson. This formula
merely requires the energy E of a charge e bounded by a
characteristic sphere of radius r to be given by:
The author is anxious that this method is not seen as
restricted to this one case of the proton. Other particle forms
should be predicted if the theory is to have any chance of
acceptance and, though the earlier paper did address the
derivation of the muon/electron mass ratio, more needs to be
offered.
The object of this paper, therefore, is to follow the same
argument and present a self-contained account which discusses how
both the charged pion and the neutral pion are created and
explains their decay and why the pion is such an important
by-product of high energy particle collision.
WAVE NODE RESONANCE
There is one important physical principle which affects the
precise determination of pion mass and which was not needed in
the discussion of the proton mass determination. It will be seen
how the physics used in the proton theory will point directly to
a specific particle form that has a mass extremely close to that
of the charged pion. However, pions are short-lived particles
and, contrary to the situation with the proton, their transient
nature in a fluctuating energy field allows them to assume a
simple resonant mass state. The charged pion is particularly
sensitive to interaction with the electrons in a nearby matter
field. The neutral pion has a much shorter lifetime and a dual
sensitivity to field resonance, in that it is affected by the
presence of electrons and a particle which we will term the
‘sub-electron’.
The ‘sub-electron’ was not discussed explicitly in the earlier
proton paper [1], but it was implicit in the argument. There was
reference in that paper to a “degenerate” electron
state. That state is what the author refers to as a
‘sub-electron’. It is believed to be the primary denizen of the
true vacuum. In previous writings the author has usually
referred to this as a ‘lattice particle’, because it featured in
a structured vacuum state resembling in some respects liquid
crystal properties. This ‘sub-electron’ has the property of
being activitated statistically by multiple muon impact to create
the quasi-proton in company with a quasi-electron. The ‘quasi’
term merely means that the creation is abortive in the sense that
it is very short-lived, so that these created particles have a
ghost-like presence, but one which nevertheless can affect other
particle creation processes in high energy matter fields.
The important factor which is brought forward from the proton
paper is the N factor. N was shown to be 1843. Earlier joint
research with Dr. D. M. Eagles gave a less direct justification
for this N = 1843 factor [2], compared with the argument
summarized in the proton paper [1]. However, for the purpose of
this discourse what matters is that the radius of a bounding
sub-electron sphere corresponds to a volume that is 1843 times
that bounding the electron.
By ‘wave node resonance’ we mean a property by which standing
wave oscillations on a charge set up discrete nodes and antinodes
which have a resonant interaction with similar standing waves on
other charges. It appears that such resonance can fine-tune the
rest mass-energy of a fundamental particle. Thus, given a valid
theory which determines the energy package from which a particle
form nucleates, we can appeal to this ‘wave node resonance’ to
give us the precise mass value.
By way of example, in the proton paper [1], it was stated by
equation (10) that the mass of the real muon, as opposed to that
of the migrant virtual muons of the vacuum state, has a
specifically formulated value in electron units of:
If this is evaluated it comes to 206.768 670 4, which is
nearly two parts in a million higher than the measured value.
Now, as was shown in reference [5] of the proton paper or in
reference [3] of this paper, the effect of wave node resonance
between the muon and the electron is to cause the (3)1/2 term in
the above equation to be replaced by 1 + 2π/9. This involves
resonance between surface standing waves on the muon core charge
and the standing wave interaction separating the muon core charge
and the electron.
When this substitution is made in equation (2), the reader may
verify that the real muon mass, in terms of the electron, becomes
206.768 307 8. This brings the muon mass into perfect accord
with that measured.
For this reason the reader is asked to bear in mind that wave
node resonance can also ‘fine-tune’ the mass properties of other
fundamental particles which are short-lived, such as the charged
and neutral pions.
What we can expect from such tuning is that charges have an
integer numerator and denominator ratio for their mass ratio vis
a vis a primary reference charge such as the electron. Charges
such as the real muon of which the bounding charge spheres are
slightly separated may also have a supplementary resonance ratio
applicable to the free standing waves in the space between
adjacent bounding spheres.
THE PROTON EQUATION
As was shown in reference [1], the proton is the product of
a creation process involving muons. If two muons each of energy
μ merge to produce a charge +e of energy 2μ in a Coulomb coupling
with an opposite charge -e of energy μ, we can have perfect
energy balance.
To verify this add 2μ and μ and subtract the Coulomb
interaction energy of the charges. If r is the bounding radius
of the μ charge at which it interfaces with the bounding radius
of the 2μ charge, we see from equation (1) that this latter
charge has a bounding radius of r/2. The separation distance
between the charge centres is 3r/2. As a result, the Coulomb
interaction energy is negative and is 2e2/3r, which is exactly
equal to μ.
The proton equation was developed on the basis that this
neutral entity (2μ:μ) would adjust to shed energy by adopting a
minimum value nucleated on the 2μ energy charge. Thus the μ
component becomes a degraded charge form denoted ε and the energy
of (2μ:ε) can be evaluated as (61/2-3/2)2μ. The proton equation was then written as:
This gave a unique value for P in terms of μ, by requiring P
to be 8.898 979 5 times μ. However, the remarkable factor which
explains why the proton is the primary matter form is the fact
that there is perfect energy balance when n is the odd integer
7.
The proton equation shows us that P can be a charge system
that changes state whilst retaining the same rest-mass energy.
It is sometimes a composite of three charged particles, which
have the values +e, -e and +e, but this does not preclude the
triple quark state with fractional charge forms +2e/3, +2e/3 and
-e/3. The author has reserved his own position on such quarks
and developed this theory without any commitment to fractional
charge. The reason is that the vacuum properties can intercede
in a way which can meet similar criteria, because a neutral state
or double-charge state can be a question of whether a +e charge
or -e charge is free or takes up a ‘sub-electron’ site in the
vacuum lattice. In any event, the quark idea can be interposed
in the proton equation and the author’s theory offers an
explanation for the proton mass which is rather exceptional.
When we extend this ‘mass’ determination method to other
particles, we are similarly not entering conflict with quark
theory, nor shall we get involved in the hierarchical
classification of conventional theory or questions of spin
properties. This is not necessary for the pion property. The
sole objective is, therefore, to examine why pions are such a
prevalent particle form and why they have the mass measured. Our
hope is that the more prevalent the particle in cosmic rays and
in particle physics, the more direct will be its mass derivation
from this theory. For this reason, the pion is the first
candidate for analysis after the proton and the muon, the
electron being assumed as the mass reference.
THE PION CREATION PROCESS
It occurred to the author to consider the effect of merging μ
with the (P:2μ) neutral ‘quark’ aggregation in the proton
equation. The resulting energy is given by (61/2-3/2)P plus μ or, using the P/μ ratio deduced above, (61/2-3/2)P plus
(0.1123724)P, which is:
From the proton/electron mass ratio of 1836.1527 this energy
is nearly 1950 electron mass units shared by three charge
constituents. The step of interest involved considering the
energy of a three-charge in-line particle form which can be
denoted (P:π:π), where π is the energy of the -e, +e components
of the created charge pair coupled to the proton charge +e of
energy P. Here π is a symbol for the energy of the particle in
which we are interested, namely the pion.
A little analysis, working out the energy of P plus 2π
adjusted by the three Coulomb interaction components, clearly
shows that π has about the right energy to be the pion. However,
before developing that analysis, we will digress a little to
examine how a neutral system can be formed. This would require
a charge such as an electron merging with the three-charge
system. The resulting neutral complex of four charges, of nearly
1951 times the electron mass can then be investigated from three
different aspects.
Firstly, it could split into two equal neutral forms, each
comprising two charge components. The mass of each such neutral
form would be about 975 electron units of 0.511 MeV or 498 MeV.
This is the mass-energy we associate with the neutral kaon, which
is an interesting by-product of this analysis.
Secondly, it could involve two charges annihilating to
consolidate the energy into, say, an electron and a unitary
charge Z conforming with the Thomson formula (1). The neutral
entity (e:Z) would, by the resonance criteria discussed above,
have Z as an integer in electron units. To correspond with the
energy supplied, Z is 1951 and this gives a total energy in
electron terms of 1952 less the Coulomb component
3(1951)/2(1951+1) or 1950.501, which is:
Thirdly, the four-charge neutral entity could form as an
in-line system denoted (π:P:π:π), where there are three
identical-energy π particle components associated with the
proton, placed at an inner position owing to this being a least
energy configuration.
The third option appears to be one that forms via the second
as an intermediate step, so that the energy given by expression
(5) creates (π:P:π:π) with a π/P ratio of 0.148 744 12. This may be verified by analysis using the energy terms P + 3π and Coulomb
interaction terms which together comprise -3π/4-9Pπ/4(P+π)-3Pπ/4(2P+π)+3Pπ/2(3P+π).
Again, however, there is a resonance effect in the (πP:π:π)
system which causes π/P to become an integer ratio that very
closely approximates 0.148 744 12. A search for such a ratio
depends upon the degree of approximation that Nature accepts.
However, it is a search that we shall not pursue, because what
we are interested in is the value of the pion mass once it is
free from the proton complex. Then the pion will be affected
more by electron or ‘sub-electron’ interaction.
Note that we have established that π is close to 0.148 744 12
times P, which is 1836.152 7 times the electron mass. Therefore
π is close to 273.117 electron units.
We will defer discussion of the regulating wave resonance that
‘fine-tunes’ the pion mass, until we see how π is freed from its
proton system.
THE PION EQUATIONS
Just as for the proton there is something quite remarkable
about the equations governing pion creation.
What has just been presented shows how we can deduce the
pion/electron mass ratio, but this does not tell us why the pion
is so special. As we have seen, neutral kaons can emerge too
from the type of equation presented.
The remarkable feature is that the (π:P:π:π) system can, in
an energetic environment, deploy energy from that environment to
shed the isolated π and leave a charged entity (π:P:π) which has
precisely the amount of energy needed to reconstitute the state
which led to (π:P:π:π) being created from an added electron. In
other words the system is an ideal catalyst for converting
electrons into pions.
Using the π/P value of 0.148 744 12 which is already deduced,
calculation of (π:P:π) gives (1.062 562 76)P. This can be
checked from the analysis of P+2π-(3π/4)-3Pπ/2(P+π)+3Pπ/2(3P+π). Therefore when the pion is released from the (π:P:π:π) system we are left with a three-charge unit of energy equal to 1951.027 electron units. This can, therefore, shed a
little energy to form the Z charge of 1951 units as before, owing
to the resonant interaction with a nearby electron, and stand
ready to develop back into the resonant (π:P:π:π) system when
that electron comes close enough to merge.
What is so remarkable is the fact that the (π:P:π:π) system,
the (π:P:π) system and the (P:2μ)+μ system all have virtually the same energy. This is an unavoidable fact of physics that could
never have been imagined by mere theorizing. Nature has
exploited this natural coincidence. The proton and electron are
the matter forms favored by Nature, but faced with the unique
particle synthesis conditions associated with the pion, Nature
inevitably creates pions as well. This is what makes the pion
so special and why the pion appears so readily in collisions
involving proton and baryon decay.
The pion equations are very simply:
Equation (6) is intimately associated with the processes of
proton creation discussed in reference (1). Equation (7)
suggests that an electron (or positron) is involved in the
synthesis of the pion system. Equation (8), which is a reversible equation, is the stage in which the energy equilibrium applies as the electron is converted into a pion. The process in equation (9) shows how the pion is liberated to reconstitute the catalyst that recycles to equation (7).
THE PION MASS
The question at issue now is how the free pion is affected by
resonant interaction with the electron-positron fields that are
present in this situation. Note that positive or negative pions
π develop from positive or negative electrons e. There is an
optimum pion resonance state that can then be induced close to
the π mass value of 273.ll7 electron units.
This is one that admits, on a time average, that the pion
preserves some characteristic betraying its origin from the
electron or positron. The charged pion is seen, therefore, as
having a quasi-stable form denoted (π:e:e) for half the time and
the isolated π form for the other half of the time. This means
that it spends half the time in close company with a coupled
electron-positron pair. Similar theory applies in the real muon
model of reference [3].
Note that in the energy calculation using the Thomson formula
and Coulomb interaction, e can be written as 1 and π will be
written as 273, to exploit the integer resonance condition. The
(π:e:e) mass-energy is then π + 2 -3π/2(π+1) -3/2(2) + 3π/2(3π+1), which, with π as 273, is 273.254864. This
mass-energy applies for 50% of the time and the bare π of 273
applies for the other 50% of the time. This is due to vacuum
energy fluctuations associated with the cyclic creation and
annihilation of the electron-positron pair.
On this basis the free pion-electron mass ratio is 273.127432 or 139.5678 MeV. This compares with the Particle Data Group listed measurement of 139.5685 ± 0.0010 MeV and so is well
within the single standard deviation.
The non-resonant estimate of the π value of 273.117 was
equivalent to 139.5625 MeV, which is in error by 6 standard
deviations.
For this reason the author feels that this is a case where
resonance with an electron state is occurring. Moreover a pion
can decay into a muon, which in turn decays into an electron or
positron. This suggests that there is mean presence of a
characterizing half of the electron-positron pair, meaning the
cyclic 50% periods of pair annihilation and recreation. However,
it is inappropriate to speculate further on this aspect in this
work, though it is very relevant to the gravitational
implications of the theory and the extension of the theory to the
wider meson spectrum.
RELATED MESON PRODUCTION
The following equations, which have already been presented
elsewhere [4], will serve to summarize how the principles
discussed in this paper can lead directly to other varieties of
meson creation.
The first three of these processes suggest that protons can,
in fact, decay by degenerating from their transient state in
association with the dimuon unit 2μ. However, their decay
products do eventually find their way into radiant energy, muons
and neutrinos and it is conceivable that some regeneration of
protons does occur by the vacuum maintaining its equilibrium
state.
Note also, from equation (6), that the (P:2μ) + μ component
of equations (11), (12) and (13) can be simply the presence of
a (P:π:π) system.
As then reformulated, equation (13) becomes:
This, together with the pion equations above, shows that in
the energetic systems where protons exist and also baryons which
decay into protons, there should be a prolific presence of
charged or neutral pions in the decay products.
The connection of the pion and these other meson states with
the processes involved in proton creation, as discussed in
reference (1), does therefore open up channels for scientific
exploration which were hitherto out of sight.
THE NEUTRAL PION
Equation (13) or (14) allows us to estimate the mass of the
neutral pion. It is very slightly below the measured value if
the μ terms are the virtual muons of this theory, of mass [(3/8)1/2 – 1/2]P, and very slightly above the measured value if the μ terms could involve real muons.
This, however, is a case where the wave node resonance may be
relevant. The question, however, is whether the resonance
relates solely to the influence of electrons. Here we must be
guided by the decay properties of the neutral pion. The decay
does not involve muons or electrons but merely gamma radiation.
To the author this signifies that the neutral pion is resonantly
coupled with the degenerate sub-electron state of the vacuum
medium, as discussed above.
For this reason, the author chose to examine the wave
resonance and integer relationships applicable between a charged
constituent of the neutral pion and the degenerate electron
state. The latter has an effective energy in electron units
which is smaller than that of the electron by a factor that is
the cube root of N or 1843.
The neutral pion model, envisaged as a charge +e and a charge
-e, was seen in the following perspective. The pion mass is
divided between these two charges set in a vacuum background in
which the degenerate sub-electron state (-e)’ exists in a
neutralizing charge continuum of opposite polarity. See Fig. 1.
Sporadically, the energy exchanges between the pion charges
in this state A cause one charge to expand into a form which
develops a positive version of the degenerate electron state
(+e)’. This leaves the pion energy concentrated in a negative
charge of mass œ in electron units. Possibly this will unseat
the (-e)’ charge from a vacuum lattice site, denoted by the
intersection of the broken lines, and allow œ to take this
(neutral) equilibrium position. This is then somewhat similar
to the Dirac vacuum in which electrons leave vacuum sites to
create positive holes or positrons. In this case we are taking
out a degenerate electron and substituting the pion to obtain
what appears as a neutral system. The two degenerate states
(-e)’ and (+e)’ are shown in Fig. 2.
Now, firstly, it is essential that states A and B prevail for
equal periods of time. This assures that the continuum charge
displaced by transitions between states averages about a zero
mean. Secondly, we note that the ‘degenerate’ sub-electron state
cannot decay, virtually by definition, because it is the lowest
energy state that a negative charge can assume. Therefore, the
decay characterizing the neutral pion is the event when the
target set by the sphere bounding (+e)’ for the migrant virtual
muon activity destroys state B. This results in mutual
annihilation of (-e)’ and (+e)’ and leaves œ to degenerate
directly into the (-e)’ state. The decay occurs directly into
gamma energy.
Thirdly, we can confirm this by calculating the lifetime
involved, because it is known from the proton paper [1] that the
degenerate electron form occupies a volume that is 1 part in
N1/3(2μ) of the cell volume of a migrant muon of opposite
polarity. Also, the activitating frequency of the vacuum is that
of the Compton electron. The state B applies for half the time,
so doubling the lifetime otherwise obtained. The reader has
simply to multiply the Compton electron period of 8.09×10-21 s.
by the quantity (4)(1843)1/3(206) to obtain:
The Particle Data Group [5] report a measured lifetime of:
which supports the theory presented and so helps us in our onward
quest to determine the mass of this neutral pion.
The integer correlation involved in the wave node resonance
is one which depends upon the degenerate electron state. Now,
whatever the resonant mode of interaction between the electron
and the degenerate electron in a true vacuum state, we can assume
that this adjusts if a third party to the interaction is
involved. There are then three interactions which must satisfy
the integer connection at the same time.
For this reason we write the inverse-mass ratios of the
sub-electron, the electron, and the neutral pion charge (denoted φ in Fig. 2) as being A: B: C, where A, B and C are integers.
We know from what has been said about equation (14) that the
neutral pion has a mass approximately 264 times that of the
electron. Thus B/C is approximately 264. Our problem is now to
‘fine-tune’ this by resonance. We also known that A/B is very
close indeed to (1843)1/3. The mathematical task is, therefore,
to step through values of C from unity upwards until we find the
optimum resonance conditions.
The mathematics of this exercise involves multiplying C by 264
and the result by (1843)1/3 to find, in the first step, an
integer B and, in the second step, a nearest integer A. Then A/B
is compared with (1843)1/3 to determine how close the resonance
is in parts per million (δ in the tabulation).
For each C value the analysis must be repeated by stepping the
(264C) product either way in integer steps to be sure that the
closest resonance is found.
By way of example, Table I gives a typical calculation for C
= 9.
| C | B | A | δ |
| 9 | 2375 | 29119 | +10.1 |
| 9 | 2376 | 29131 | +1.2 |
| 9 | 2377 | 29143 | -7.7 |
The middle term is the one deduced from C times 264, but, to
be sure it is the optimum for resonance, the resulting 2376 has
been stepped either way to show that adjacent resonance
possibilities are not favored owing to the greater discrepancy.
Table II shows the optimum resonance found in this way for C
incrementing from unity onwards. In the table it will be seen
that two sets of data are given for C as 5. This is because
there were two very competitive resonance values. What this
really meant was that there would be an extremely strong
resonance when C was doubled. With C = 10 the table shows a
truly outstanding resonance condition, which makes it virtually
certain that the particle interaction would be regulated to
determine mass states in the specified ratios.
| C | B | A | δ |
| 1 | 265 | 3249 | -10.6 |
| 2 | 530 | 6498 | -10.6 |
| 3 | 791 | 9698 | -33.1 |
| 4 | 1056 | 12947 | -7.4 |
| 5 | 1320 | 16184 | +8.0 |
| 5 | 1321 | 16196 | -8.0 |
| 6 | 1585 | 19433 | +4.9 |
| 7 | 1847 | 22645 | -6.9 |
| 8 | 2112 | 25894 | -7.4 |
| 9 | 2376 | 29131 | +1.2 |
| 10 | 2641 | 32380 | -0.004 |
| 11 | 2905 | 35617 | +6.3 |
| 12 | 3167 | 38829 | -7.0 |
Thus, taking the ratio of φ mass to electron mass as B/C we
know that 264.1 is the optimum ratio. There is then one very
minute adjustment to this to obtain the proper neutral pion mass
as measured. When the system in Fig. 2 decays, there will be a
small amount of surplus energy, depending upon how close the two
(-e)’ and (+e)’ charges are positioned. If they are well spaced
this energy will arise from that of one (e)’ sub-electron, that
is the factor B/A in electron units. However, as we must allow
for vacuum energy fluctuations to determine the mean surplus
energy this has to be halved owing to state B prevailing for only
50% of the time. Therefore, B/2A is an upper limit. The lower
limit for this energy surplus is that applicable for touching
charge boundaries of the two degenerate states and this means
offsetting the Coulomb interaction energy. This reduces the
result to B/8A and we should think it more likely that the actual
state of the average neutral pion at the time of decay will sit
closer to the least energy value.
It follows from this that the upper value of the neutral
pion-electron mass ratio is 264.141 but the more representative
minimal energy value is 264.110. The theory, therefore, gives
us a definite rest-mass energy for the neutral pion of between
134.960 and 134.976 MeV.
This compares with a measured value listed as 134.9642±0.0038
MeV and this is, indeed, very good agreement with the theoretical
value.
CONCLUSIONS
The object of this paper has been to provide supporting
evidence for the proton theory presented in reference [1]. This
has taken the form of an extended analysis showing how the same
theoretical principles account for the creation of the charged
pion with a mass-energy of 139.568 MeV and the neutral pion with
a mass-energy of between 134.960 and 134.976 Mev.
Concerning this charged pion theory, it should also be noted
that the author has shown elsewhere [6] how the pion lifetime can
be calculated as approximately 26.1 nanoseconds. The theory was
based on the applicability of equation (1) and the statistical
encounter with the μ energy quanta on which the above mass
calculations are based. The currently listed measured value of
this lifetime is 26.030±0.023 nanoseconds.
Though this research is based on foundations that have been
developing for several years, the author has presented here a
novel and original perspective on the physics of particle
creation. The approach to calculating the masses of the charged
and neutral pions has not been one of manipulation to find the
numbers that worked. That in itself is an irrelevant pursuit.
The author sees the precision measurement of the particle
masses, and the fact that they are universally fixed with
standard precision, as a statement by Nature that there are
specific controls in Nature’s fabric setting the mass ratios.
Nature has therefore challenged us to solve a riddle to find the
basis of that determination of mass. The accuracy with which we
can justify the specific mass by physically-based argument is an
indication of our likelihood of having understood the physics
involved. This accounts for the exploration of the resonance
possibilities that have been discussed.
It is hoped that the reader will find something quite
intriguing in the concerted action that determines the pion form.
The pion equations have a unique characteristic and the fact that
they work so well has to be endorsement for the use of the
Thomson formula and the Coulomb interaction as governing the
particle creation process.
To the author, what is particularly important from the
research presented is the new way in which the degenerate
electron state manifests itself in the neutral pion situation.
That degenerate sub-electron state has long been seen by critics
of the author’s work as a mere hypothesis of an arbitrary vacuum
model. Yet it is fundamental to the Planck quantum of action,
as readers might appreciate from reference [7]. That reference
gives a self-contained derivation of the formula:
which is the reciprocal of the fine-structure constant expressed
in terms of the B/A ratio used in this paper. The formula gives
137.036, in full accord with the measured value.
This photon theory is discussed in detail in a paper in the
recently published record of the NATO Advanced Research Workshop
on “Quantum Uncertainties” [8].
The photon theory is important in that it offers the best
possibilities for tests that can verify the principles involved.
Since we know the precise value of the proton-electron mass ratio
or pion-electron mass ratio, the theoretical derivation of that
exact ratio is, for some reason which this author fails to
comprehend, generally judged as unimpressive. There is a
suspicion that the result is contrived, the intrinsic merit in
the analysis seemingly being irrelevant. Concerning the photon,
however, or rather its formulation in the fine-structure
constant, there is hope that certain minute variations in value
will emerge with increasing precision in the tests.
For this reason, the author has shown how certain predicted
effects can, if found in future measurement, come to verify the
theory involved. This is the basis of a paper entitled ‘Tests
of photon theory in terms of precision measurement’ [9].
Finally, reverting to what QCD has to say about the pion, it
is the view of those expert in that subject that the pion has
long been recognized as the Goldstone mode of broken chiral
symmetry. This has tended to become fundamental to any
acceptable theory of hadron physics. Consequently there is the
view that any route in QCD to justifying the origin of pion mass,
however partial, would be an important step forward since it
would be dealing with the fundamental questions of the nature of
the QCD vacuum and chiral symmetry breaking.
Now, it is conceivable that these words and the terminology
of QCD are really speaking about much the same structure as is
foreseen by the author’s vacuum model. Chiral symmetry breaking
is little different from what may be signified by actions
involving energy exchanges and state transitions in the ether
medium, connected characteristically with the muon field and the
dynamic lattice of the author’s theory.
However, QCD is far from telling us why the pion has the
precise mass listed in particle data and, with the above points
in mind, one must wonder how strong QCD really is when one reads
the following in an expert treatise on the subject [10]:
‘The electroweak theory which which we are now concerned is
a chiral theory. For these theories the fermionic integration
measure is not in general gauge invariant. In consequence the
Shavnov-Taylor identity is violated, and S-matrix elements will
be ε-dependent, because of the appearance of unphysical particles
(e.g. Goldstone scalars) in physical processes. Clearly such a
theory is nonsense, the gauge fixing and ghost terms in the
Lagrangian were merely technical devices to permit the
formulation of quantum field theory, and nothing physical should
depend upon ε, if the theory is to make sense. Thus the gauge
non-invariance of the fermionic measure is a disaster for the
chiral gauge theories in which it appears. It means that these
theories are non-quantisable. Only theories in which this
problem can be evaded can be considered as candidates to describe
reality.’
It is submitted that the author’s theory of the pion does
evade the mathematical nicities of the chiral problem completely
and so stands a better chance of portraying reality.
It would be inappropriate to end without making reference to
a rival theoretical method for deriving basic dimensionless
constants, including and the proton-electron mass ratio and the
fine-structure constant. It is for the reader to compare the
techniques involved and judge the relative merits of the
arguments used. This also involves radical departure from the
conventional QCD methods. This is a reference to a very recent
paper by Noyes and McGoveran [11]. Concerning the pion, this
rival theory is less specific, in quoting the neutral
pion-electron mass ratio (measured as just over 264) as
approximately twice l37 or (274), l37 being the reciprocal of the
fine-structure constant.
REFERENCES
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[3] H. Aspden, Lett. Nuovo Cimento, 38, 342 (1983).
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[7] H. Aspden, Lett. Nuovo Cimento, 40, 53 (1984).
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[11] H. P. Noyes and D. O. McGovernan, ‘An Essay on
Discrete Foundations for Physics’, SLAC-PUB-4528,
Standford Linear Accelerator Center (July l988).
