Presentation to University of Canterbury Mathematics Department (17 Sept 2015)

Title: Conceptual framework for a novel non-local hidden-variable theory of physics: Cordus theory

17 Sept 2015, 15h00, venue Ers446

Content: As per

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How does the synchronous interaction, or strong nuclear force, attract nucleons and hold the nucleus together?

The Cordus theory of the synchronous interaction is key to the concept of the nuclear polymer.

How does the strong force work?

Conventionally the strong nuclear force is proposed to arise by the exchange of gluons of various colour. The theory for this is quantum chromodynamics (QCD). This force is then proposed to be much stronger in attraction than the electrostatic repulsion of protons of like charge, hence ‘strong’. Rather strangely, the theory requires the force to change and become repulsive at close range.  This is to prevent it from collapsing the protons into a singularity (single point). Quite how this change operates is not explained, and the theory as a whole also cannot explain even the simplest atomic nucleus, let alone any of the features of the the table of nuclides. So there is a large gap between the colour force of QCD and any realistic explanation of atomic structure. QCD, gluons, and the strong attraction-repulsion force have no proven external validity: the concepts don’t extend to explain anything else.

It is time to attempt a different approach. Remember, it is necessary to explain not only how the quarks are bonded, but also how the protons and neutrons are bonded, and onward to explain why any one nuclide is stable/unstable/non-existent.  That means seeking explanations to the bigger picture, rather than creating a narrowly-focussed mathematical model of one tiny part of the problem.

What holds protons and neutrons together in the nucleus?

Here is our progress so far. First, note that conventionally the strong nuclear force overcomes the electrostatic repulsion of protons. In contrast the Cordus theory proposes that the protons and neutrons are locked together by  synchronisation of their emitted electrostatic forces. These forces are proposed to be discrete.  This is a radically different mechanism that has nothing to do with the electrostatic force.

‘The Cordus theory proposes that the strong force arises from the synchronisation of discrete forces between the reactive ends of different particules. The emission directions represent the particule’s directional engagement with the external environment, and so two particules that co-locate one of each of their reactive ends need to share this access, and this is proposed as the basis for the synchronicity requirement. This causes the emission of the particules’ discrete forces to be interlocked. The discrete forces cause the reactive ends to be pulled into (or repelled from) co-location and held there. Hence the strong nature of the forces, its apparent attractive-repulsive nature, and its short range.’


The Cordus equivalent of the strong force is a synchronous interaction between particles,  Figure: CM-06-01-01

The Cordus equivalent of the strong force is a synchronous interaction between particles,
Figure: CM-06-01-01

 What is the synchronous interaction?

Second, note that the conventional idea is that the strong force is one of a set that also includes the electrostatic, magnetic, and gravitational forces (EMG). In contrast the Cordus theory proposes that the  electrostatic repulsion force is inoperable inside the atomic nucleus. So there is no need for a ‘strong’ force to ‘overcome’ the  proton  electrostatic repulsion. You can either have the EMG forces or the synchronous interaction, not both. The factor that determines which operates is whether the assembly of matter is discoherent or coherent.

‘Unexpectedly, the Cordus theory predicts that this synchronous force only applies to particules in coherent assembly. In such situations the synchronicity of emission means also that the assembled particules must energise at the same frequency (or a suitable harmonic), and either in or out of phase. Thus the synchronous interaction is predicted to be limited to particules in coherent assembly relationships, with the electro-magneto-gravitational forces being the corresponding interaction for discoherent assemblies of matter.’

This is a radical departure from the orthodox perspective, which otherwise sees the strong and electrostatic forces as operating concurrently. The Cordus theory predicts that the interaction between neighbouring protons in the nucleus is entirely synchronous (strong force) and that there is no electrostatic repulsion (at least for small nuclei).

What determines nuclide stability?

Third, the Cordus theory proposes, by logical extension, that the synchronous interaction makes two distinct types of bond, differentiated by same vs. opposed phase (cis- and transphasic) of the reactive ends. This concept does not exist in conventional theories of the strong force which are based on 0D points.


Figure CM-06-03-01B

Figure CM-06-03-01B


What is the nuclear polymer structure of the atomic nucleus?

By logical progression, this concept lead to the conclusion that protons and neutrons are bound together in a chain, or as we call it, a nuclear polymer. This proves to be a powerful concept, because with it we are able to explain nuclide structures. The following diagram shows how the principle is applied to some example nuclides.


Figure CM-06-03-02-01-4

Figure CM-06-03-02-01-4


More information maybe found in the following references. They are best read in the order given, rather than the order published.

Dirk Pons,

19 July 2015, Christchurch, New Zealand


[1] 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:

[2] Pons, D. J., Pons, A. D., and Pons, A. J., Nuclear polymer explains the stability, instability, and non-existence of nuclides. Physics Research International 2015. 2015(Article ID 651361): p. 1-19. DOI:

[3] 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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Internal structure of the atomic nucleus: Nuclear polymer

Our previous work has shown that it is possible to explain the existence of the nuclides H-Ne, specifically why each is stable/unstable/non-existent. This is achieved under the assumption that the protons and neutrons are rod-like structures. Previous work in the Cordus theory has shown how the discrete fields of these particules would interlock by synchonising their emissions. Hence the STRONG NUCLEAR FORCE was explained as a SYNCHRONOUS INTERACTION of discrete field emissions.

Now we have published the details of these mechanics. See citation below. The theory predicts the nuclear morphology, i.e. the types of shapes that the protons and neutrons can make in their bonding arrangements. It turns out that this is best described as a NUCLEAR POLYMER. Thus the atomic nucleus is proposed to consist of a chain of protons and neutrons. In the lightest nuclides this chain may be open ended, but in general the chain has to be closed. It appears that for stability the proton and  neutron need to alternate, and this explains why neutrons are always needed in the nucleus above 1H1. The theory also predicts that the neutrons can form CROSS-BRIDGES, and that these stabilise the loop into smaller loops. This also explains another puzzling feature of the table of nuclides, which is why disproportionately more neutrons are required for heavier elements. In addition the theory predicts that the sub-loops of the nuclear polymer are required to take specific shapes. This paper explains all these underlying principles and applies them to explain the hydrogen and helium nuclides.

The significance of this is the following. First, this is the first published theory of why individual isotopes are stable or unstable, or even non-existent. By comparison no other theory has done this, neither the binding energy approach, the semi-empirical mass-formula (SEMF),  the various bag theories, nor quantum chromodynamics (QCD). Second, this has been achieved with a hidden-variable theory. This is a surprise, since such theories have otherwise been scarce and hard to develop. The only one of note has been the de Brogle-Bohm theory of the pilot wave, and that certainly does not have application to anything nuclear. So the first theory to explain the stability features of the table of nuclides for the lighter elements is a non-local theory rather than an empirical model, quantum theory, or string theory. That is deeply unexpected. It vindicates the hidden-variable approach, which has long been neglected.

Ultimately any theory of physics is merely a proposition of causality, and while any theory may be validated as sufficiently accurate at some level, there is always opportunity for further development. The Cordus theory and its nuclear mechanics implies that quantum mechanics is a stochastic approximation based on zero-dimensional point morphology of what the Cordus theory asserts is a deeper structure to matter.

Of course there is still much work to do. Showing that a hidden-variable theory explains these nuclides is an achievement but is not proof that the theory is valid. In the future we will need to expand the theory to the larger table of nuclides. If it can explain them, well that would be something. Also, it would be interesting to devise a mathematical formalism for the Cordus theory. Doing so would provide another method to explore the validity of the theory.

Dirk Pons, 9 July 2015, Christchurch

Pons, D. J., Pons, A. D., and Pons, A. J., Nuclear polymer explains the stability, instability, and non-existence of nuclides. Physics Research International 2015. 2015(Article ID 651361): p. 1-19. DOI: (open access) or (open access)

Problem – The explanation of nuclear properties from the strong force upwards has been elusive. It is not clear how binding energy arises, or why the neutrons are necessary in the nucleus at all. Nor has it been possible to explain, from first principles of the strong force, why any one nuclide is stable, unstable, or non-existent. Approach – Design methods were used to develop a conceptual mechanics for the bonding arrangements between nucleons. This was based on the covert structures for the proton and neutron as defined by the Cordus theory, a type of non-local hidden-variable design with discrete fields. Findings – Nuclear bonding arises from the synchronous interaction between the discrete fields of the proton and neutron. This results in not one but multiple types of bond, cis- and transphasic, and assembly of chains and bridges of nucleons into a nuclear polymer. The synchronous interaction constrains the relative orientation of nucleons, hence the nuclear polymer takes only certain spatial layouts. The stability of nuclides is entirely predicted by morphology of the nuclear polymer and the cis/transphasic nature of the bonds. The theory successfully explains the qualitative stability characteristics of all hydrogen and helium nuclides. Originality – Novel contributions include: the concept of a nuclear polymer and its mechanics; an explanation of the stability, instability, or non-existence of nuclides starting from the strong/synchronous force; explanation of the role of the neutron in the nucleus. The theory opens a new field of mechanics by which nucleon interactions may be understood.


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Variable decay rates of nuclides

Our previous work indicates that, under the rules of this framework of physics, the neutrino and antineutrino (neutrino-species) interact differently with matter. Specifically that (a) they interact differently with the proton compared to the neutron, and (b) they are not only by-products of the decay of those nucleons as in the conventional understanding, but also can be inputs that initiate decay. (See previous posts).

Extending that work to the nuclides more generally, we are now able to show how it might be that decay rates could be somewhat erratic for β+, β-, and EC. It is predicted on theoretical grounds that the β-, β+ and electron capture processes may be induced by pre-supply of neutrino-species, and that the effects are asymmetrical for those species. Also predicted is that different input energies are required, i.e. that a threshold effect exists. Four simple  lemmas are proposed with which it is straightforward to explain why β- and EC decays would be enhanced and correlate to solar neutrino flux (proximity & activity), and alpha (α) emission unaffected.

Basically the observed variability is proposed to be caused by the way neutrinos and antineutrinos induce decay differently. This is an interesting and potentially important finding because there are otherwise no physical explanations for how variable decay rates might arise. So the contribution here is providing a candidate theory.

We have put the paper out to peer-review, so it is currently under submission. If you are interested in preliminary information, the pre-print may be found at the physics archive:

This work makes the novel contribution of proposing a detailed mechanism for neutrino-species induced decay, broadly consistent with the empirical evidence.

Dirk Pons

New Zealand, 14 Feb 2015


You may also be interested in related sites talking about variable decay rates:

See also the references in our paper for a summary of the journal literature.


UPDATE (20 April 2015): This paper has been published as DOI: 10.5539/apr.v7n3p18 and is available open access here

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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 neutrino induced decay of nucleons

Most things in physics are symmetrical. This is evident in action-reaction forces and the conservation of momentum and energy. Particle interactions are generally also symmetrical. At least the Standard Model of particles predicts that particle interactions are symmetrical when charge, parity and time (hence CPT) transformations are all applied.

Which makes our latest findings all the more curious. In ‘Asymmetrical neutrino induced decay of nucleons’ ( we predict that the neutrino and antineutrino behave differently in their interactions with the proton and neutron. There are two parts to this prediction. First we predict that the neutrino and antineutrino (neutrino species) can cause (induce) decay. The conventional interpretation is that they are merely outcomes of the decay process, and are not involved in the input side at all. Second, we predict that the neutrino species induce decay differently with the proton and neutron (nucleons), hence asymmetrical decay. In contrast the conventional interpretation is that nucleon decay is purely random, that the mean lifetimes are constant, and that decay is not affected by the external environment.

This prediction is made on theoretical grounds by a logical extension of the Cordus theory, specifically by using its mechanics for discrete fields. This predicted asymmetry is novel and unorthodox. There is nothing in physics that disallows such an asymmetry, but neither is there any reason to expect it. We were therefore surprised that this asymmetry emerged. It was not something that we were actively seeking, but rather it was a supplementary exploration while we were searching for answers to the asymmetrical genesis problem. We have addressed the genesis situation elsewhere, and can explain how the universe came to be made up of more matter than antimatter (CP violation). The present paper takes a similar approach, in that it uses the same Cordus mechanics, but the starting point is different.

The problem is that the operation of neutrino detectors shows that nuclide decay rates can be affected by loading of neutrino species. However the underlying principles of this are poorly understood. The purpose of this paper was to develop a conceptual solution for the neutrino-species interactions with single nucleon decay processes. Single nucleons, i.e. a single proton or neutron, are a simplification of the more complex situation inside the nucleus of large atoms. The starting point was the non-local hidden-variable (NLHV) solution provided by the Cordus theory, specifically its mechanics for the manipulation of discrete forces and the remanufacture of particle identities. This mechanics was applied to the inverse beta decays and electron capture processes for nucleons. These are situations where the neutrino or antineutrino is supplied as an input, as opposed to being an output as in the conventional decays.

Our findings are that Inverse decays are predicted to be differentially susceptible to inducement by neutrino-species. The inverse β- neutron decay is predicted to be susceptible to neutrino inducement (but not to the antineutrino). Correspondingly β+ proton decay is predicted to be induced by input of energetic antineutrinos, but not neutrinos. Hence a species asymmetry is predicted. The inverse electron capture (EC) is predicted to be induced by pre-supply of either a neutrino or antineutrino, with different energy threshold requirements in each situation. The neutrino induced channel is predicted to have the greater energy barrier than the antineutrino channels.

We also have a third prediction. This is that one unified decay equation can be written to express β- neutron decay, β+ proton decay, and electron capture. Furthermore, that this equation applies to the conventional forward decays and the induced decays proposed here. The originality here is the proposed new methodology for predicting the outcomes of decays and particle transformations. If valid, this provides a simplification in the representation of the decay processes. An interesting little rule in the unified decay equation is that transfers across the equality result in inversion of the matter-antimatter species (hand).

What would be the implications if all this was valid? Well, the theory predicts the existence of a number of induced decays with asymmetrical susceptibility to neutrino-species. The results imply that detectors that measure β- outcomes are measuring neutrinos, and β+ antineutrinos.   A novel prediction is made, that neutrino-species induce decay of nucleons, and that the interaction is asymmetrical. Hence also, that different decay types are affected differently by the input of energy and neutrino-species. A detailed explanation is provided of how this occurs at the level of the internal structures of the particules.

This is an unorthodox theory and an unexpected set of predictions. Whether or not this theory is valid we do not yet know, but it does make specific predictions that no other theory makes, which is interesting. None of these are contemplated from conventional theories of quantum mechanics, the standard model, or supersymmetry. This might seem a weakness, but is actually a good position to be in for concept development. If a theory can predict something specific that other theories cannot, then then that differentiates the theory. In this case the predictions are also testable. Consequently this gives a way to for the future to show whether or not it is valid (falsifiable). For the moment we simply state that it is a logical extension of the Cordus theory, and the outcomes are curious enough to be worth reporting.


[1] D.J. Pons, A.D. Pons, A.J. Pons, Asymmetrical neutrino induced decay of nucleons Applied Physics Research, 7 (2015) 1-13. or

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