⬇ Download PDF: Aether Science Paper: 1988c
Physics Essays
volume 1, number 2, 1988
A Theory of Proton Creation
H. Aspden
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 that creates the proton. The advance reported depends upon the discovery of an equation that 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 8.898 9795 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 uith the measured value.
Key words: proton mass calculation, fine structure constant, muon pair annihilation, hadron creation
1. 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.
2. THE ENERGY CORRELATION As the author reported in Physics Today,’”) there is a very simple energy correlation between the muon and the proton. This report led to an equation representing the proton creation process”) and now forms the ‘basis of a self-contained theory that requires the “equilibrium” phase of a locally concentrated muon field.
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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:
Q = he’/x. (1)
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 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. This gives us, from Eq. (1), the total energy expression:
(P:Q) = P+ Q— PQ/R(P + Q). (2)
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:
Q/P + 1 = 1/V/(R). (3)
Applying this with the proton and muon in mind, suppose that two oppositely charged muons come together to form an energy quantum Q nucleated by a charge ~e with a separate energy quantum P taking up the
H. Aspden
balancing charge +e. Then, if Eq. (3) has any relevance to this situation, We can estimate the value of the constant &. The numerical connection is that:
2(207)/(1836) ~ (3/2) — 1 = 0.225. (4)
The question then is whether this result is just an interesting curiosity arising from a mere mathematical coincidence, 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 even so, there is a pure electrostatic derivation that avoids the electromagnetic argument and so overcomes the relativistic objections.) 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 Eq. (3). This problem baffled the author for more than ten years; the solution, as summarized in Refs. 2 and 3, advances our argument in a very positive sense.
3. THE PROTON EQUATION
Suppose that the merger of a muon pair in the muon field operates to create a minimal energy complex (Q:F), 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:F), imagine that other muons of mixed polarities are absorbed by the (Q:E) unit. Take n as odd and, because 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 Pin a (P:Q) complex with Q, subject to the condition that there is complete energy balance in this process. We have then a system that 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 Eq. (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:
mu + (Q:E) min > (P:0) + E> P. (5)
As a conserved energy statement, this is the proton equation. To solve the equation we write Q as 2u and note that, from the argument leading to _ Eq. (3) with k = 2/3:
(Q:E) min = [¥(6) — 3/2]9. (6)
The form of this expression can be verified by combination of Eqs. (2) and (3). In energy terms, the process of Eq. (5) becomes:
np + 2[ (6) — 3/2Ju = P+ Y — 3(2Pu)/2(P + 2p)
+ 2[V(3/2) — Ip = P. (7) First, we solve this, ignoring the part involving n. We find that: Pip =4 + 2V(6). (8)
This tells us that the proton rest-mass energy has to be 8.898 979 5 times whatever the energy of the » quantum is in the primordial muon field. However, more than this, there is something very special about the proton equation that makes the process of its creation unique. Note that in deriving Eq. (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 that 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 Eq. (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 80 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:
n+ AV(6) — 3/2} =4+ 2VO (9) thus conforming with the solution found for P/ in Eq. (8).
In other words, since the initial (Q:) system requires 2 units of jt, it takes 9 units of u to create a proton; the proton then has a rest-mass that is 8.898 979 5. 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 minimal energy dimuon complex.
4, 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 an 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,
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A Theory of Proton Creation
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, 206.768 262(30).
Following this theme and involving a resonant interaction, it has been shown elsewhere”) that the calculated value of 41,.,), meaning the real muon sensed in particle experiments, is given by:
treat = 209 — (9/4)207/[207 + VB]. (10)
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”) 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 Eq. (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 p states. All we then need to know is that such p. states could be either pw = 205 or »p = 207 in units of electron rest-mass energy.
5, THE THRESHOLD EXCITATION LEVEL
We proceed now without even assuming that ys has such specific values. The assumption taken from the real muon analysis is that » 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 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 p such that:
p = 2pm/d’, (11)
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 in units of electron volume, and, with a denoting the characteristic radius bounding a normal electron charge, write:
N = (b/ay. ; (12)
Guided by Eq. (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 subquantum vacuum world. This allows us to suggest that an equilibrium state setting the threshold N occurs when the mass m’ associated with density p inside this sphere of radius 5 is related to the electron unit m in the ratio a/b:
m’/m = a/b; m’ = (4/3)nb°p. From this, (11), and (£2): (N)*3u = (3/8n)(d/a)>. (13)
The N unit 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 Eq. (5). The
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object of this is to involve the controlling threshold parameter N as an adjustable characteristic somehow intrinsic to the field but 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 that developed extraneous potentials. The N unit could then find itself in a subzero 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:
N ~ 9p. (14) From (13) and (14): (N)”3 = (27/8md/a)>. (15) If d/a can be determined, then N can be estimated and p is then deduced so that P can be calculated.
6. 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 center of balance we can then write:
Bn(e”/d?) = (m’/2?2nm/hy. (16)
Replace m’/m by a/b or (N) |’? (using N here as that now applicable in the equilibrium field) and write m as 2e”/3a, according to Eq. (1) with & as 2/3, to obtain from (16):
(hc! 2ne’P(N)!3 = (d/a)>/54n. (17)
We then see that without any knowledge of p, there are two equations, (15) and (17), containing two unknowns N and d/a plus the fine-structure constant 2ne”/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/2ne” as 137, which is approximately the measured value. Then Eqs. (15) and (17), used to eliminate d/a, give:
2N = (27)(137) ~ 1849(2) (18)
from which, using Eq. (14), p is a little above 205. Quite remarkably, therefore, relying essentially on the natural property
H. Aspden
of field medium associated with electron characteristics, we have been led to evaluate the approximate energy quantum of the muon state.
7, 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 p = 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:
pp = (81/4)(he/2me?)?/(1843) (19) and: (d/a)’ = 54n(he/2me?)(1843)!/3. (20)
To test the theory for the proton mass using Eq. (8), note that the measured value of hc/2ne’ is usually quoted as being between 137.0359 and 137.0360. Equations (8) and (19) then tell us that P is between 1836.1519 and 1836.154 60, whereas the latest 1986 CODATA value is 1836.152 701(37).
This is unquestionably an encouraging result, bearing in mind the very simple sequence of argument used and the fact that no quantities other than 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 that leads to the derivation of d/a as 108m. This is something beyond the scope of this paper but is of record elsewhere.”®) Note then that Eq. (17) would lead to the formula:
he/2ne* = 108n(8/1843)!/° = 137.035 9148. (21)
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 1836.152 317 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 and the principal one being in 1975, this presentation is wholly original in deriving the Proton mass by argument developed from the complete proton Eq. (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 that concerned the photon involved notions alien to modern methods in quantum mechanics and, though the author still defends that case, that plus the nonadherence 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.
Received on 21 December 1987.
Résumé
Jusqu’a présent, la physique n’expliquait pas le réle des muons; on peut maintenant montrer quiils sont impliqués dans la formation des protons dans le champ primordial qu’ils constituent. Il est possible de déduire non seulement la masse du proton en fonction de celle du muon, mais aussi la masse du muon quantique qui permet la formation du proton. Ce progres a pu étre réalisé a la suite de la formulation d’une équation montrant que la fusion d’une paire de muons suivie d’un état d énergie minimal peut servir a la nucléation d’autres particules. Cette synthése de particules résulte de la fusion de muons aboutissant a la formation d’une particule unique ayant environ 8,898 979 5 fois la masse du muon quantique concerné. Cela conduit a la formation d’un proton ayant une masse légérement supérieure @ 1836,152 fois la masse de Wélectron, ce qui correspond bien 4 la valeur mesurée,
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A Theory of Proton Creation
References 1. H. Aspden, Phys. Today 37, 15 (1984).
. H. Aspden, Hadronic Journal $, 129 (1986).
. H. Aspden, Spec. Sc. Tech. 9, 315 (1986).
. H. Aspden, Am. J. Phys. 53, 616 (1985).
. H. Aspden, Lett. Nuovo Cimento 38, 342 (1983).
. H. Aspden, Lett. Nuovo Cimento 39, 271 (1984).
. H. Aspden and D.M. Eagles, Phys. Lett. 41A, 423 (1972).
. H. Aspden, Lett. Nuovo Cimento 40, 53 (1984).
. H. Aspden, The Chain Structure of the Nucleus (Sabberton, South- ampton, 1974), p. 17.
10. H. Aspden and D.M. Eagles, Nuovo Cimento 30A, 235 (1975).
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H. Aspden
Department of Electrical Engineering University of Southampton Southampton S09 5NH U.K.
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