Posts Tagged cordus

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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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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Table of nuclides: An explanation of the nuclides from Hydrogen to Neon

This application of the Cordus theory offers a descriptive solution for the relative lifetimes of all the nuclides of Hydrogen to Neon.

Cordus theory for Table of Nuclides

Cordus theory for Table of Nuclides

More specifically, the theory is able to explain why any one nuclide is stable, unstable, or non-existent. Consequently the theory also explains the drip lines, which are the margins of stability to the table of nuclides. It also explains the gaps in the series and sudden changes in stability across a series. This is achieved by identifying a unique set of rules -a mechanics- for the nuclear polymer. This is based, as with all the rest of the Cordus theory, on a non-local hidden-variable (NLHV) design.

The chart of the nuclides as per the Cordus theory is shown below.

Table of Nuclides (PDF file)

This is a large diagram and may look blank: you will need to pan and zoom to see it. The paper containing this diagram has been submitted to a journal for peer-review. A copy is available on the vixra physics archive.

This theory also explains several other trends in the table of nuclides, which we may discuss another time. Other theories, including quantum chromodynamics (QCD), binding energy, shell model, liquid drop model, and semi-empirical mass formula (SEMF) can explain some of the features of the table of nuclides, but tend to be limited to mathematical representations of binding energy, with little real explanatory power. In contrast this Cordus theory offers explanations where these other theories are at a loss.

So it appears that the nuclide landscape may be explained by morphological considerations based on a NLHV design.

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Explaining the Nuclides

HI! He Lithely Bellowed Boringly, Car Nicely On Fire Nearby.

The first ten elements take us from Hydrogen to Neon. However they have many nuclides, about 140. (Nuclides, or isotopes, are nucleus variants with different numbers of neutrons).

There are many unsolved problems in this area. How are the protons and neutrons arranged in the nucleus? What makes some combinations of protons and neutrons stable, and others not? Why do the series start and stop where they do? How does the strong force bind protons and neutrons in nuclear structures? How do point particles make up a nucleus with volume?

All this continues to be a mystery, a century after Rutherford’s discovery of the nucleus. Current theories for this area, e.g. magic numbers, QCD, and the SEMF, don’t have answers, despite having working at the problem for half a century or more.

The whole thing needs a total re-think at the fundamental level, and we propose starting with what it means to be a ‘particle’.  Quantum mechanics (QM) is built on the assumption that particles are zero-dimensional points. What if quantum mechanics was wrong? What are the alternatives?

One option is to assume that particles really do have internal structures. This is called a hidden-variable solution.  However trying to find a workable version has been an insurmountable difficulty, and most people in physics have given up trying. We have had some success in this, in the form of the Cordus theory. This is a non-local hidden-variable (NLHV) design. Even so, explaining the nuclides from first principles, whether with QM or a NLHV design, is a formidable task that has not been solved.

Consequently, we plan to approach it in stages. Here’s where we have got to:

STAGE A: Create a theory for how the strong force works. [DONE] In the Cordus theory this corresponds to a synchronous interaction. As a bonus, we also get force unification. Read the journal paper here

STAGE B: Elucidate how the synchronous interaction applies to proton and neutrons. [DONE] Surprisingly, it turns out that there are two versions, not just one, of the this force. We worked out how this would affect the bonding of protons and neutrons. This gave us an explanation  of what the neutron is doing in the nucleus. As a bonus, we also got the nuclear structures of the hydrogen nuclides. And as a further bonus, we were able to explain why both 1H0 and 1H1 are stable. So that is ‘Hi!’ sorted. Read the preprint here

STAGE C: Discover how larger collections of protons and neutrons join together. [DONE] Unexpectedly, the theory suggests the protons and neutrons form a nuclear polymer. Generally this is a closed loop. We find the design capable of accepting three-nucleon assemblies, in the form of Bridge neutrons. As a bonus, we find the nuclides of Helium. So that is Hi! ‘He..’ done.   Read the preprint here

That’s all the progress to report for now.

STAGE D: Predict the nuclide structure. Interpret the trends in the table of nuclides. [WORK IN PROGRESS] H and He are easy nuclides. After this it get tougher. We are working on it and hope to report back shortly.

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Will time end, Why, and When?

Illustration of spacetime curvature.

Illustration of spacetime curvature. (Photo credit: Wikipedia)

The answer to that question depends on what theory you adopt for *time*. In the particular case of the Cordus theory, time is caused by matter, i.e. time is an emergent property of matter, especially discoherent matter.

This is a very different proposition to practically every other  theory of time. The main other theory is to link SPACE and TIME together in the SPACE-TIME concept. This also means that such theories are locked into a concept where time is a continuous variable, and is a dimension. Therein lie a lot of deep problems: first that a continuous or ratio variable is not easy to break into discrete units, and hence the difficulty of reconciling the *time* concepts in general & special relativity with quantum mechanics; second that a dimension implies something that can go backward or forward, and it is not at all apparent that time actually does that, and no one really knows why.

The Cordus theory is different in that it proposes that *time* is the interaction of cause and effect between two pieces of discoherent matter. It provides a natural explanation for the tick of time, rooted in what might generally be considered the de Broglie frequency of matter, and for the one-way direction or arrow of time. The Cordus theory also predicts that time does not work this way for coherent assemblies of matter, which may be falsifiable.  (Coherent matter is a very specialised state of matter that includes superfluids and Bose-Einstein condensates, and is not something that is typically encountered at the macroscopic level of our daily existence).

With that in mind, what does the Cordus theory say about the end of time? Well, with time being a property of matter, it implies that time emerges with matter at genesis, and shares the same fate. Therefore time as we know it will cease when the universe does.

Just how the universe will end is another question altogether. One option is that it will continue to expand, and eventually just wimp out (heat death), in which case Cordus theory predicts time would just slow down to a crawl too. The other option is that the universe collapses in on itself, in which case Cordus theory suggests time would speed up and then suddenly stop altogether. There is a third option, which no-one believes, which is that the universe is static. That seems ruled out by the red-shift.

Those outcomes are unimaginably far into the future, and there are more proximal existential threats to worry about. More interesting to us in the present epoch of the universe, is another curious prediction of the Cordus time theory. This is that there is no time (as we know it) outside the universe, i.e. beyond the cosmological boundary (DOI: This  means that there is no time in the void into which the universe is expanding. Likewise for a being outside the universe (God) there need be no time either (atemporal). There are some interesting philosophical implications of this. We will leave that discussion for another day.

Read more about the Cordus theory here:

Pons, D.J. (2013) What really is time? A multiple-level ontological theory for time as a property of matter. vixra, 1-40 DOI:

Pons, D.J. and A.D. Pons (2013) Outer boundary of the expanding cosmos: Discrete fields and implications for the holographic principle vixra (1303.0017), p. 1-26, DOI: Available from:

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Which perspective of time is correct: the absolute clock of quantum mechanics or the spacetime of general relativity?

Neither, but in some ways both are adequate for their purposes.  According to the Cordus theory, time at the fundamental level is created by the local frequency of oscillation of the particule. That effect occurs internal to the particule concerned. Such particules include the electron, proton, etc. Since frequency and energy are related, this has the side effect of making time, as perceived at the particule level, speed up or slow down depending on the energy of the particule.

As a separate effect the arrow of time arises from the irreversibility in the interactions between particules.We explain how that irreversibility arises, but the explanation is a bit long for here.

Thus time is locally generated, and Cordus suggests the QM  idea of an absolute clock is only partlycorrect. Also, Cordus suggests that time is a patchwork at the cosmos scale, not a continuous spacetime, thereby not accepting this feature of GR either. However both QM and GR turn out to be approximately correct, at least at the level of detail that concerns them, which is submicroscopic and macroscopic respectively

English: Cordus model of the photon

English: Cordus model of the photon (Photo credit: Wikipedia)

The Cordus theory provides a more primitive mechanics for time that accommodates the thoroughly different models of QM and GR.

Read more here:

Pons, D.J. (2013) What really is time? A multiple-level ontological theory for time as a property of matter. vixra, 1-40 DOI:

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Reality and apparent simultaneity

One of the long-standing philosophical questions is whether there is a reality to what humans experience. One of the famously controversial ways to looking at this is the holographic principle, which proposes that everything we experience in 3D is merely a holographic projection of 2D information on the outside surface of the universe.

That raises a second question, which is how my experience of reality is connected and coordinated with yours. This introduces time into the problem. Special relativity (SR) has a principle, in the form of the relativity of simultaneity, that says that the order in time of two spatially separate events cannot be determined  absolutely, but instead depends on the motion of the observer. Thus it is impossible to order two events in time if they occur in different places (hence difference frames of reference).

In our Cordus theory of time, we examine some of these questions. We look at the question of how multiple bodies interact, and how the coordination arises. We have already identified that there is no master clock, but if that is lacking then we still need a coordination mechanism. There is a connectedness of phenomena that are at different geometric locations. It seems that spacetime is continuous, because it seems that it is possible to coordinate the two phenomena in time. We show that the two phenomena are linked, because they share the same fabric.

According to this new perspective, any communication between two objects is a result of photons, or massy particules, or fields, and these cause positional constraints on the other, i.e. the geometric location of the reactive end is affected by the communication. A phenomenon that occurs in one volume of matter, be that combustion, noise, motion, etc,  thereby communicates that to other matter around it. Consider one volume to be my body: my speaking transmits forces to the volume of air immediately around me, which in turn propagates the dynamic displacement throughout its bulk, so that the membrane in your ear is displaced, and you hear the sound.

In general the phenomenon is that one volume of matter causes an effect in the second. The interactions at the most basic level all require frequency cycles, so this causes temporal causality.  Thus we infer:

It is not a master clock that accomplishes the temporal connectedness of phenomena that are at different geometric locations, nor does it require continuity of spacetime per se. The piece-wise communication, via discrete field interactions of the fabric, between adjacent volumes of space (matter and fabric) applies spatial consistency to time.

Any one particule A receives discrete forces (fields) from all the particules (many Bs) in the observable universe. Space within the universe is therefore filled with a mesh of  discrete fields in transit, which in the Cordus theory is termed the fabric.

Fabric time is the mutual interconnectedness of matter particules spread over three-dimensional space. This occurs via the fabric, comprising discrete field forces for electric-magnetic-gravitational interaction. Not strictly a time, this is rather  a coordination of events across space.

In this theory the fabric, and the EMG fields it carries, causes a connectedness between particules. They respond together, even if in a slightly delayed manner as their separation increases. There is therefore a coherence and smoothness to the interaction between particules, mediated by the fabric. The resulting interaction stitches together three-dimensional domains of space (matter and vacuum-fabric) into a macroscopic collated time. This level of time passes more slowly, due to the many tiny delays required for particules to react to each other, given the dissimilar-frequency and phase-differences between the particules.  This, Cordus suggests, is where the arrow-of-time arises,  and what general relativity perceives as spacetime. This is also the macroscopic level of physical time, and hence where our perception of time first arises.

This Cordus concept of 3D fabric affirms the general relativity perspective of spacetime.  It also provides an ontological answer to one of the earlier questions: it suggests that spacetime has a quasi-substantial status (comprises discrete force) but has no universal time-signature per se, and mainly represents merely the relationships between bodies.

Read more about the Cordus time theory here:

Pons, D.J. (2013) What really is time? A multiple-level ontological theory for time as a property of matter. vixra, 1-40 DOI:

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