Archive for category Matter-antimatter

Mnemonic for the beta decays and electron capture

In our paper [1:] we anticipate a unified decay equation. It describes all three conventional decays: β- neutron decay, β+ proton decay, and electron capture (EC). These are the decays of the individual proton or neutron.

Here is a handy Mnemonic for remembering all these decays, based on this equation: pie with icing equals nuts with egg below and a dash of vinegar

Pproton + 2y + iz(energy) <=> nneutron + eantielectron or positron + Vneutrino
pie with icing equals nuts with egg below and a dash of vinegar


Then rearrange this to suit. Remember to invert the matter-antimatter species when you move a particle across the equality (species transfer rule). Note that we use underscore to show antimatter species, and this is the same as the overbar with which you may be more familiar. (We don’t use overbar because it is a confounded symbol  used in other contexts such as h-bar. Underscore is a fresh and clearer way to designate antimatter species. It is also a visual reminder that this mechanics needs to be understood from within the NLHV framework of the Cordus theory, i.e. we are not talking about the usual zero-dimensional point particles of quantum mechanics here. Underscore is also easier to print and therefore use.)

The equation as written is focussed on the proton decay, which is β+. It is called beta plus because it gives a positive charge output in the form of the e hence ‘+’.

β+ proton decay: p + 2y => n + e + v

For electron capture just move the e across the equality to the p side and change it to plain ‘e’ instead.

Electron capture (EC): p + e => n + v

For neutron decay, move both the e and v across the equality, changing them to e and v. It is called beta ‘minus’ because the output is the negatively charged electron.

β- neutron decay: n => p + e + v


Remember that electric charge and matter-antimatter species hand are not the same thing. This is an easy area in which to get confused. Electric charge (+/-) refers to the direction in which the discrete forces of the electric field travel, and may be outwards or inwards from the particle. The matter-antimatter species hand (m/m) refers to the handedness of the discrete field, which in the Cordus theory corresponds to the energisation sequence of the field (somewhat like the firing order of a three-cylinder internal combustion engine) which also has two variables.

The mnemonic works for all three conventional decays providing you remember the species transfer rule, but I’m not convinced of the soundness of the dietary advice!


  1. Pons, D. J., Pons, A. D., and Pons, A. J., Asymmetrical neutrino induced decay of nucleons Applied Physics Research, 2015. 7(2): p. 1-13. DOI: or


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Unified decay equation for individual nucleons

The original Cordus conjecture [1] was a broad conceptual work, and we did not foresee that assuming a two-ended structure for particles would ultimately lead to highly specific predictions for many other phenomena, including nuclear processes as here. Now the theory predicts that neutrino-species can induce decay, and do so asymmetrically [2]. That paper also predicted an underlying orderliness to the decay processes, in the form of a unified decay equation for individual protons and neutrons (nucleons).

Nucleons decay by β- neutron decay, β+ proton decay, and electron capture. These decays proceed by the emission of a neutrino species in the output stream. This is the forward direction. There is also a predicted inverse decay, where the neutrino-species is supplied as an input. The theory also predicts that the inverse decay can be induced, depending on the particle identities.

It is proposed that all these decays can be expressed in a single equation, the unified decay equation, given by:

p + 2y + iz <=> n + e + v



n             neutron

p             proton

e             electron

e             antielectron

v              neutrino

v              antineutrino

y              photon

z              discrete force complex (a type of vacuum fluctuation)

2y           a pair of photons

i               quantity, e.g. of photons

<=>        indicates the decay is bidirectional

The equation can be rearranged. However, and this is important, there is a species transfer rule. Thus particles other than photons change matter-antimatter hand when transferred over the equality. One also has to be sensible about mass when predicting which side the photons are required.

For example, this equation may be rearranged to represent β-, β+, and EC in the conventional forward directions:

β- neutron decay: n => p + e + v

β+ proton decay: p + 2y => n + e + v

Electron capture (EC): p + e => n + v

Furthermore, by representing the equality as bidirectional we can show both the conventional (forward) and proposed neutrino-species induced decays in simple equations. For example:

p + e + v <=> n

with β- in the ‘<=’ direction, and antineutrino induced electron capture represented by ‘=>’.

It is simple to represent additional decays such as:

p + n <=> e + v + iy

Many other applications are possible. This simple mechanics of manipulating decay equations permits an efficient representation. The many different decays can all be represented in one equation. The equation holds for the conventional decays even if its reliability for the induced decays still needs to be validated.

So instead of trying to remember the three conventional decays (β-, β+, EC), simply remember one unified equation p + 2y + iz <=> n + e + v


  1. Pons, D. J., Pons, A. D., Pons, A. M., and Pons, A. J., Wave-particle duality: A conceptual solution from the cordus conjecture. Physics Essays, 2012. 25(1): p. 132-140. DOI: or .
  2. Pons, D. J., Pons, A. D., and Pons, A. J., Asymmetrical neutrino induced decay of nucleons Applied Physics Research, 2015. 7(2): p. 1-13. DOI: or


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Asymmetrical genesis

A solution to the matter-antimatter asymmetry problem

Problem: Why is there more matter than antimatter in the universe?

A deep question is why the universe has so much matter and so little antimatter.  The energy at genesis should have created equal amounts of matter and antimatter, through the pair-production process, which should have subsequently annihilated. Related questions are, ‘Why is there any matter at all?’ and ‘Where did the antimatter go, or how was it suppressed?’

While it is not impossible that there might be parts of the universe that consist of antimatter, and thereby balance the matter, neither is there any evidence that this is the case. Therefore it is generally accepted that the observed matter universe is more likely a result of an asymmetrical production of matter in the first place. Thus something in the genesis processes is thought to have skewed the production towards matter. But it is very difficult to see how physical processes, which are very even-handed, could have done this.

This is the asymmetrical genesis problem. There are two sub-parts, why there are more electrons than antielectrons around (asymmetrical leptogenesis) and why there are more nucleons (protons and neutron) than their antimatter counterparts (asymmetrical baryogenesis).

Our latest work explores this problem [1]. The full paper is published in the Journal of Modern Physics (link here), and is open access (free download). A brief summary of the findings is given below.

Solution: Remanufacture of antielectrons

The theory we put forward is that the initial genesis process converted energy into equal quantities of matter and antimatter, in the form of electrons and antielectrons (positrons). A second process, which is defined in the theory, converted the antielectrons into the protons. The antimatter component is predicted to be discarded by the production and emission of antineutrinos. Thus the antineutrinos were the waste  stream or by-product of the process. Having converted antielectrons into protons, it is easy to explain how neutrons arise, via electron capture or  beta plus decay. Thus the production processes are identified for all the building blocks of a matter universe.

Therefore according to this interpretation, the asymmetry of baryogenesis is because the antimatter is hiding in plain sight, having been remanufactured into the protons and neutrons (matter baryons) themselves.

Approach: How was this solution obtained?

To solve the genesis problem, start by abandoning the idea that particles are 0-D points. This is a radical but entirely reasonable departure.  Instead, accept that particles of matter are two-ended cord-like structures [2].

These Cordus particules emit discrete forces, hence discrete fields. The nature of those emissions defines the characteristics of the particule in terms of charge and matter-antimatter species. In turn this defines the particule type: electron, antielectron, proton, etc. This also means that any process that changes the discrete field emission sequence also changes the identity of the particule.

This allows a novel breakthrough approach: we found a way to represent the discrete force structures, and we inferred a set of mechanics that define what transformations are possible under reasonable assumptions of conservation of charge and hand. We calibrated this against the known beta decay processes [3]. We created a calculus to represent these transformation processes: this is called the Cordus HED mechanics. (See paper for details). We call the process RE-MANUFACTURING, as it involves the re-arrangement of the discrete forces including the partitioning of an assembly into multiple particules, and the management of the matter-antimatter species hand (Latin manus: hand). The same HED mechanics is good for explaining other particule transformations like the decays.

Then we used the Cordus HED mechanics to search for possible solutions to the asymmetrical genesis problem. We looked at various options but only found one solution, and this is the one reported in the paper. Thus the HED mechanics predict a production process whereby the antielectron is converted into a proton. The HED mechanics is also very specific in its predictions of the by-products of this process, and this makes it testable and falsifiable.

The antimatter field structure of the antielectron is carried away by the antineutrinos as a waste stream. The antineutrinos have little reactivity, so they escape the scene, leaving the proton behind. This is fortunate since the theory also predicts that the protons would decay back to antielectrons if struck by antielectrons. This would have dissolved the universe even as it formed.

An explanation is provided for why the matter hand prevailed over antimatter during the cosmological start-up process. This is attributed to a dynamic process of domain warfare between the matter and antimatter species, wherein the dominance oscillated and became frozen into the matter production pathway as the universe cooled.

This is an efficient solution since it solves both asymmetrical leptogenesis and asymmetrical baryogenesis.


The genesis production sequence starts with a pair of photons being converted, via pair production, into an electron and antielectron. The Cordus theory explains how [4]. The antielectron remanufacturing processes, described here, convert the antielectron into a proton. The asymmetry in the manufacturing processes arises from domain warfare between the matter-antimatter species, and re-annihilation [5]. Neutrons are formed by electron capture or beta plus decay, for which a Cordus explanation is available [3]. Thus all the components of the atom are accounted for: proton, neutron, and electron. The Cordus theory also explains the strong force, as a synchronization between discrete forces of neighbouring particules [6], and the structure of the atomic nucleus [7]. The same theory also explains the stability trends and drip lines in the table of nuclides (H-Ne) [8]. This is much more than other theories, and shows the extent to which the Cordus theory is able to radically reconceptualise the genesis process.

Production process for the conversion of an antielectron into a proton.



This is a radical theory, since it forces one to think deeply and in a fresh way about foundational physics, how matter, energy, time, space, and force arise.

It is also a disruptive theory. First because it predicts that locality fails, and explains how. Locality means that particles are 0-D points and only affected by the fields at that 0-D location. A Cordus particule continuously breaks locality, at least at the small scale. Many physicists have been suspicious about locality, though have been reluctant to let go of it. The Cordus theory requires us to abandon locality.

The Cordus theory also strongly reasserts physical realism, and pushes back against QM’s denial thereof.  QM gives weird explanations for double-slit behaviour, interferometer locus problems, superposition, and entanglement. The Cordus theory explains all these from the basis of physical realism, and without all the weirdness.   Quantum mechanic’s wave-function is now understood to be merely a stochastic approximation to a deeper and more deterministic reality. That QM gives weird explanations is not because reality is weird, but because QM is only an approximate mechanics for the foundational level. Naturally this is contentious, but such are the debates of science.

Keywords: matter-antimatter asymmetry problem; open questions in physics; baryogenesis; leptogenesis; Sakharov conditions; cosmology; genesis; big bang


  1. Pons, D.J., Pons, A.D., and Pons, A.J., Asymmetrical baryogenesis by remanufacture of antielectrons. Journal of Modern Physics, 2014. 5: p. 1980-1994. DOI:
  2. Pons, D.J., Pons, A.D., Pons, A.M., and Pons, A.J., Wave-particle duality: A conceptual solution from the cordus conjecture. Physics Essays, 2012. 25(1): p. 132-140. DOI:
  3. Pons, D.J., Pons, A., D., and Pons, A., J., Beta decays and the inner structures of the neutrino in a NLHV design. Applied Physics Research, 2014. 6(3): p. 50-63. DOI:
  4. Pons, D.J., Pons, A.D., and Pons, A.J., Pair production explained by a NLHV design Vixra, 2014. 1404.0051: p. 1-17. DOI:
  5. Pons, D.J., Pons, A.D., and Pons, A.J., Annihilation mechanisms. Applied Physics Research 2014. 6(2): p. 28-46. DOI:
  6. Pons, D.J., Pons, A.D., and Pons, A.J., Synchronous interlocking of discrete forces: Strong force reconceptualised in a NLHV solution Applied Physics Research, 2013. 5(5): p. 107-126. DOI:
  7. Pons, D.J., Pons, A.D., and Pons, A.J. Proton-Neutron bonds in nuclides: Cis- and Trans-phasic assembly with the synchronous interaction. vixra, 2013. 1309.0010, 1-26. DOI:
  8. Pons, D.J., Pons, A.D., and Pons, A.J., Explanation of the Table of Nuclides: Qualitative nuclear mechanics from a NLHV design. Applied Physics Research 2013. 5(6): p. 145-174. DOI:


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Why are neutrinos left handed?

And also, Why are antineutrinos right handed? These questions do not have answers. In quantum mechanics and the Standard model of particles it is assumed that the unique left and right spin properties, also called helicity, are fixed ‘intrinsic’ properties. (For example, see Hyperphysics on left handed neutrinos). These theories cannot explain why: the spin is assumed to just happen to be like this. Obviously this is not ontologically satisfactory. Not that weirdness is any stranger to QM.

It’s not hard to see why QM would have logical difficulties in this area. It assumes that particles are zero dimensional (0-D) points, and no physical interpretation is possible for ‘spin’ in such a model: there simply aren’t enough dimensions in a 0-D construct to accommodate something as complex as spin. It is true that string and  M-theory have sufficient dimensions, about 11 depending on the theory. So in theory it might be possible to to accommodate ‘spin’ in that framework, except that these theories are entirely abstract. They do not map to the physical world.

So if there is an explanation for the peculiar handedness of the neutrino spins, it is beyond the current theories of physics.

And that’s where the hidden sector theories come in. By their very nature they contain internal structures, the ‘hidden variables’. These theories have the potential to give powerful explanations at levels deeper than quantum mechanics can go. However the difficulty is finding suitable candidate solutions. Our Cordus theory is one such design. Technically it’s called a non-local hidden-variable (NLHV) theory.

In our recent work we return to the question of neutrino spin, and have some explanations to offer. These have been published here 10.5539/apr.v6n3p50 based on a development of our earlier work (see vixra). Here’s how we approached it. We started by determining the internal structure of the neutrino (and antineutrino) within this NLHV framework. We did this by reverse-engineering the beta decays. In β- decay, or electron emission, the free-neutron decays into a proton, electron, and an antineutrino:

n => p + e + v

Since we already have the internal structures of the n, p and e, we can infer the structure of the antineutrino. Similarly, in β+ decay, also called positron emission, the proton converts into a neutron, antielectron (positron) and neutrino:

p + energy => n + e + v

This allows the neutrino structure to be determined, since everything else is known. Obviously in doing this we are relying on the hope that the Cordus theory has internal validity.  The result we get is shown in the Figure.

Internal structure of the Neutrino, in the Cordus theory

In turn, this structure offers an explanation for why the neutrino moves: it has incomplete discrete forces and therefore has to borrow discrete fields from the surrounding fabric, and this means moving at the speed of propagation of the fabric fields, which is the speed of light.An explanation for the selective spin direction is that the energisation sequence of the neutrino’s discrete forces causes a rotational spin. The energisation sequence -of which there are only two options- also determines the matter-antimatter species differentiation. So the spin direction depends on the energisation sequence, and the latter also determines the matter-antimatter nature. So a species-specific spin arises. The linear velocity and spin also have a common cause, since it is the lack of discrete forces that causes both the velocity and the spin reactions. Consequently the neutrino takes one hand (left) and the antineutrino the other (right). Which is to say, helicity is species-specific.

So there, in one paragraph, we have a natural explanation for why the neutrino is left handed, and for why the neutrino moves at the speed of light. We also have an explanation for neutrino mass, but I’ll leave that for now. It is covered in the paper, which is open access.

The fact that we have been able to achieve an explanation of neutrino spin shows that the Cordus theory has a good degree of logical consistency and internal validity. However we do acknowledge that it could be coherent but still wrong. Nonetheless given the plausibility of the result, one either has to show why it’s wrong, or consider the consequences of it being correct. As for showing where the theory might be wrong, I’ll leave that to others. I suspect the easiest way to do that would be to show that the electron cannot have the structure we propose. Looking at our paper on pair-production might show weaknesses? On the other side of the equation, if this theory is correct then the implications are radical and unorthodox. Radical because it claims there is a deeper NLHV physics beneath quantum mechanics. Unorthodox because it means that that QM’s premise of particles being 0-D points would be merely a coarse approximation to a deeper reality. This implies that QM would be unsuitable -unfit for purpose- as a basis for new physics at the next level down.

There is no logical reason why particles should be 0-D points: it was merely a convenient assumption of ignorance on the part of the pioneers of quantum mechanics. Now times have moved on and more powerful NLHV designs are available that, by their wide-ranging explanatory power, demonstrate that it is possible to think beyond the cognitively stifling 0-D point premise of QM.

Dirk Pons

18 April 2014






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Internal mechanisms of the annihilation process

The problem

How does annihilation work? What occurs when matter and antimatter annihilate? How does an electron combine with an antielectron (positron) to disappear in a blip of photons? What is the process whereby the photons emerge from annihilation interaction? How, at the fundamental level, does mass-energy equivalence operate? (Mass-energy equivalence is the conversion of matter into energy, and the reciprocal conversion of photons into matter and antimatter, and is quantified by E=mc^2). How can something as substantial as matter be wiped out? Why does annihilation sometimes produce 2 photons, and at other times 3? No-one really knows how annihilation occurs.

A solution from the hidden sector

In our latest paper (10.5539/apr.v6n2p28) we offer an explanation for the annihilation process. This solution uses the Cordus theory, which is a specific non-local hidden-variable design, and is therefore from the hidden sector of fundamental physics (as opposed to quantum mechanics, relativity, or string theory).

This paper explains annihilation as the collapse of the discrete force structures of the electron and antielectron, and their reformation into photon structures.  The process is more one of remanufacture than destruction. The resulting Cordus theory successfully explains para- and ortho-positronium annihilation: the different photons output, the relative difference in lifetimes, and why Bhabha scattering sometimes happens instead.

Curiously, this theory suggests that annihilation is the same class of interaction as pair-creation (nothing new there), and bonding via the strong force. It suggests the mechanisms are common.

For other background reading on annihilation, see Encycl. Britannica, and Wikipedia. One can also represent the inputs and outputs in a simple Feynman diagram. However the difficulty with all these approaches is describing how the annihilation process works. This is where our design offers a solution.


Pons DJ, Pons AD, Pons AJ (2014) Annihilation mechanisms. Applied Physics Research 6 (2):28-46.

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Does the Proton decay?

What is proton decay?

Some theories of physics predict that the proton decays, i.e. it breaks down into other products. There is no experimental evidence that this actually occurs. If it does occur, it is expected to be a very rare event. The life of the proton, according to those theories that predict it to decay, is longer than 10^33. So there is no danger of the atoms in our world suddenly breaking up in an immediate end of the universe scenario.

Still, the question of proton decay is important to the grand unified theories (GUTs), those theories of physics that seek to unify the electric, magnetic, weak, and strong forces (interactions). Their idea is that the proton decays into a positron (antielectron) and pion. Quite how they might decay depends on the theory under consideration, and might involve the Higgs particle or other exotic particles that are not yet observed.

Does the Cordus conjecture have anything to add about proton decay?

Yes, it predicts that hitting it with two antineutrinos should remanufacture it to an antielectron and two photons. This prediction may be testable and falsifiable.

Cordus model of the PROTON. Showing the proposed internal geometry and external fields (which are discrete).

This result also implies that proton decay would not be fundamentally random, but rather a result of a specific coincidence of antineutrinos. In the Cordus model decay is a conditional event, which is an unorthodox position. By comparison conventional explanations consider decay rates to be fixed, and therefore the events are merely spontaneous and random. Read more …

What this means is that the proton could unravel back into a positron and two photons, with the right kind of forcing by antineutrinos. But realistically that is not expected to be a common occurrence given that antineutrinos do not react much with matter.

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Parity violation

One of the paradoxes of physics is why parity is violated. Parity refers to the expected symmetry of behaviour (e.g. equal decay or reaction rates) for a particle and its mirror structure (spatial inversion).  The problem for physics is that while parity is conserved for the electromagnetic and strong interactions, experiments showed it is violated for the weak decay. Combining parity and charge symmetry results in CP-symmetry, but that too is violated in kaons.

The reason for CP violation becomes clear with cordus: the particule has a finite span (the geometric distance between the two reactive ends) and the discrete fields at each end have a direction (charge) and hand (matter-antimatter differentiation) that is consistent for both reactive ends of any one particule.  Nor are the two reactive ends energised simultaneously (except for the photon and even then in opposite directions). Thus a cordus particule is not symmetrical. Therefore mirroring the cordus particule does not result in an identical copy, hence charge-parity violation occurs. Cordus also explains why the CP violation only occurs at small scales: because this is the level at which the span becomes significant.


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