Time in coherent matter

The Cordus theory proposes that TIME arises from the de Broglie frequency of individual particules. Here’s how. Each time a particule energises, it becomes available to interact with other particules.  The interaction may be via one of the electro-magneto-gravitational forces, or the synchronous (strong) interaction. The interaction occurs via the transmission and receipt of discrete forces. When the particule de-energises, then the interaction no longer applies. The energisation is at the the frequency given by E=h.f. Each time the particule energises it is effectively in existence and able to interact with other matter around it. Consequently the particule only experiences TIME, e.g. the opportunity to move or decay, when in its energised state and emitting and receiving discrete forces. So time flows for for the particule at its frequency.

This also means that anything that CHANGES the frequency of the particule, will change how time flows for the particule. Typical effects that can do this are external, e.g. the particule moves into a stronger gravitational field or moves with relativistic velocity. In these situations it encounters external discrete forces (fabric) faster, and this retards its own emission of discrete forces and hence also slows its frequency, so time flows slower. Hence gravitational and relativistic time dilation can readily be explained. So it is perfectly natural that your feet age slightly slower than your head, since the atoms in the foot are exposed to a sightly greater gravitational field than those in the head (when standing up). The reason this does not rip us apart is that the matter in between is in a discoherent state, and can move to accommodate the strain.

But what about coherent matter?

Coherent matter includes condensed matter (e.g. Bose-Einstein condensates, BECs), superfluids, and superconductors (electron superfluid). The theory explains these as arising from synchronicity of  emission of discrete forces by neighbouring particules. Hence this theory refers to the SYNCHRONOUS interaction, which explains the strong force. In coherence, the multiple particules are in complementary geometric locations and frequency states.  In other words, the particules, which have two ends, share the location of their reactive ends with those of other particules and thus form paired or network structures.

At suitably small scales all matter becomes INTERNALLY coherent. A typical case is the atomic NUCLEUS, and the theory shows how the nuclides may be explained as a chain of protons and neutrons bonded together synchronously. Hence also NUCLEAR POLYMER. Even the individual proton is internally coherent. However, even though particules and nuclei are internally coherent, this does not mean that large assemblies thereof are coherent. An internally coherent particule can exist with an EXTERNAL environment that is discoherent.  Thus matter at our macroscopic level of existence is DISCOHERENT: the metallurgical grains within the steel bar are not synchronised together in their frequency, and the organelles within the biological cell are not locked into frequency and position relative to other structures. Coherence is associated with spatial fixation, whereas discoherent bodies are free to move relative to their environment.

So what does this imply for the operation of TIME IN COHERENT MATTER? Note first that time is determined by frequency in this theory. Note also that in a coherent assembly of matter (‘coherent body’), all the particules are synchronised in frequency.

Thus for a coherent body, e.g. superfluid, the theory predicts that the whole body has one synchronised time frequency (all the particules beat together). Events are therefore synchronised within the coherent body. This is evident in the way these bodies emit synchronised radiation, as partly explains the laser. The theory also predicts that that time (frequency) of a coherent body  does not depend on the number of particules in the assembly. As more matter is added, so it synchronises with the existing coherent body. Also, the theory predicts that the phase (‘spin’) of the particules will also be complementary.

Thus we predict that time will behave strangely in coherent bodies. These specific time-characteristics may be testable and falsifiable.

Dirk Pons

14 October 2014


Read more here:

  1. Pons, D. J., Pons, A. D., & Pons, A. J. (2013). Synchronous interlocking of discrete forces: Strong force reconceptualised in a NLHV solution  Applied Physics Research, 5(5), 107-126. doi: http://dx.doi.org/10.5539/apr.v5n5107  (Open Access)
  2. Pons, D. J., Pons, A., D., & Pons, A., J. (2013). Time: An emergent property of matter. Applied Physics Research, 5(6), 23-47. doi: http://dx.doi.org/10.5539/apr.v5n6p23 (Open access)
  3. Pons, D. J., & Pons, A., D. (2013). Outer boundary of the expanding cosmos: Discrete fields and implications for the holographic principle The Open Astronomy Journal, 6, 77-89. doi: http://dx.doi.org/10.2174/1874381101306010077 (Open access)



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What holds protons and neutrons together in the atomic nucleus?

Big questions, few answers

The nucleus consists of protons and neutrons. The more difficult question is explaining how these are bonded together. How are the protons held together in the nucleus? Why don’t protons in a nucleus repel each other? Since protons all have positive change, they should REPEL each other with the electrostatic force. The atomic nucleus should fly apart, according to classical electrostatic theory.  Yet it does not.

Also, the neutrons have neutral charge, so what holds them in place? For that matter, what are the neutrons even doing in the nucleus? Why does the nucleus not consist only of protons?

There are a number of conventional theories in this area: liquid drop, shell models, and the strong force.

Liquid drop and semi-empirical mass formula

The liquid drop model assumes that the protons and neutrons (i.e. nucleons) are all thrown together without any specific internal structure or bonding arrangements. Think marbles in a bag like this image. It is called the ‘liquid drop’  because it assumes surface tension and bulk effects. Its usual manifestation is the semi-empirical mass formula (SEMF), which is a ‘model’ because it fits coefficients to a type of power series. It represents the general trends in binding energy. On the positive side, it offer an underlying theoretical justification for the various terms. However there are also several criticisms of the SEMF. It is dependent on a very generous power series with no less than seven tuneable parameters: with that number of variables it is not surprising that a fit can be obtained. Unfortunately the fit is poor: It doesn’t model the light nuclides well, it totally fails to represent the extinction of the heaviest nuclides, it doesn’t model the isotope limits (drip lines) well, and it doesn’t accommodate the fact that the nucleons come in whole units. Other criticisms are that the real nuclides show abrupt changes, that the SEMF does not represent.

Shell model

There are also shell models. These are more abstract, being mathematical representations of combinations of protons and neutrons. However the shell models don’t really provide much insight into how the nucleons are bonded. The theory assumes that independent clusters (shells) of protons and neutrons exist. It is based on the mathematical idea of a harmonic oscillator in three coordinates, but it is difficult to give a physical interpretation of this. The theory predicts certain combinations of nucleons are especially stable, hence “magic numbers”. This model also predicts stability for large atoms (hence “island of stability”) beyond the current range of synthesised elements, though the predictions vary with the particular method used. The shell model has good fit for atomic numbers below about 50, but becomes unwieldy for high atomic numbers. The related interacting boson model which assumes that nucleons exist in pairs. However this limits the model to nuclides where p=n, which is an overly simplistic assumption.

Strong Nuclear force

From the perspective of the Standard Model of quantum theory, the protons in the neutron do experience electrostatic repulsion, but the STRONG NUCLEAR FORCE is even stronger and holds the protons together. That force is proposed to be a residual of the strong force that acts at the quark level. Quantum chromodynamics (QCD) proposes that the quarks inside the protons are bonded by the exchange of gluon particles, in the strong force. These gluons are massless particles and three types are proposed, called colours (red, blue, green). Hence the force is also called the colour force. At the quark level this force is proposed to haves some unusual characteristics:

(1) The strong force is strongly ATTRACTIVE at intermediate range, such that it overcomes the electrostatic force.

(2) At short range the strong force is presumed to be REPULSIVE. This attribute is needed to explain why the force does not contract the nucleus into a singularity.

(3) At long range the strong force is CONSTANT, and unlike the electro-magneto-gravitational (EMG) forces, does not decrease with distance. This is called colour confinement.

The colour force is consistent with known empirical data from the jets of material expelled at particle impacts. QCD is a good theory to explain what happens in high-energy particle impacts. But gluons have not been actually observed, only inferred from impacts, so other explanations are still possible.

Ideally the strong nuclear force would say how the protons and neutrons are bonded together, but there is a conceptual chasm in this area. It is unclear how the residual nuclear force (at nucleus level) emerges from the strong force (at quark level), except as a general concept that the gluons leak out. The theoretical details are lacking. Nor is it clear what structure it might impose on how the nucleons are arranged within the nucleus. It is also thought that the residual strong force causes BINDING ENERGY but again the exact mechanism is unknown. QCD is unable to predict even the most basic of nuclear attributes. It does not describe how multiple nucleons interact. It cannot explain the simplest nuclei, the hydrogen isotopes. It does not explain nuclear structure or the table of nuclides.



It is clear from observation that no nucleus exists with multiple protons and no neutrons, so evidently neutrons provide an important role within the nucleus, which is not represented in any of the existing theories.

Logically there should be a conceptual continuity between whatever force binds the protons and neutrons together, to an explanation of the properties of the nuclides. However QCD is stuck at the first stage, and the drop/shell models are marooned at the last stage.

Explaining why any one nuclide is stable, unstable (radioactive) or non-existent is not possible with any of these theories. Nor can existing theories explain why the nuclide series start and end where they do. They also do not explain why disproportionally more neutrons are needed as the number of protons increases (the stability line for p:n is curved as opposed to being a straight line).

If we take any one line of isotopes in the table of nuclides, such as Argon, then there are a number of questions.

Argon Nuclides: Questions

Figure 1: Argon isotopes and key questions. Background image adapted from [1] https://www-nds.iaea.org/relnsd/vcharthtml/VChartHTML.html.


Answers in the Cordus mechanics – a design methodology

The Cordus physics answers many of these questions about the structure of the atomic nucleus. It is the only theory that can explain why any one nuclide is stable/unstable/non-existent, at least from H to Ne. The theory is based on COVERT STRUCTURES. This means that it predicts that particles are not actually zero-dimensional points, which is the standard premise of the conventional theories. Instead, the theory shows that solutions to these deep questions are possible providing one is willing to accept a design where particles have internal  structures. Not just any covert structures either –the Cordus theory goes on to work out, using principles of engineering design, exactly what those structures would need to be. The theory predicts a specific string-like structure, and shows that if particles were to have this structure then many problems in fundamental physics can be given physically realistic explanations. The structure only becomes apparent at finer scales than the relatively coarse level at which quantum mechanics views the world.

What is the covert structure?

The theory predicts that a particle consists of two reactive ends, a small distance apart and joined by a fibril. These reactive ends emit discrete forces into the external environment. This whole structure is called a PARTICULE to differentiate it from a 0-D point particle. The particules react with other particules, e.g. bonding and forces, only at the reactive ends.


Figure 2: Proposed internal and external (discrete force) structures of the proton.


So, what does the Cordus theory say about nuclear structure?

The theory predicts that protons and neutrons are rod-like structures that interact at their two ends. So they have physical size. They join up in chains and networks, to form nuclear polymers. They preferentially bond proton-to-neutron, but will also bond proton-proton or neutron-neutron if there is no other choice. The theory explains how these bonds work, which is by the interlocking of the discrete fields of two or more nucleons. The atomic nucleus is thus proposed to consist of a polymer of protons and neutrons.

Nuclear Polymer Example

Figure 3: The synchronous interaction (strong force) bonds protons and neutrons together in a variety of way, resulting in nuclear polymer structures. These are proposed as the structure of the nucleus.


Some simple geometrically plausible assumptions may be added, in which case the design is able to explain a wide range of nuclides. For example it is necessary to assume that the polymer is generally be a closed loop (exceptions for the lightest nuclides) and there can be bridges across the loop. The polymer is required to take a specific shape, which is to wrap around the edges of a set of interconnected cubes. The cube idea might seem a bit strange, but is merely a consequence of having discrete three-dimensional fields for the proton and neutron. This need not be contentious as QCD has three colour charges.


The results show that the stability of nuclides can be qualitatively predicted by morphology of the nuclear polymer and the phase (cis/transphasic nature, or spin) of the particules. The theory successfully explains the qualitative stability characteristics of the nuclides, at least from hydrogen to neon and apparently higher.

This provides a radical new perspective on nuclear mechanics. This is the first theory to explain what holds the protons and neutrons in the nucleus, what the neutrons do in the nucleus, and why each nuclide is stable or unstable. It also explains why only certain nuclides exist, as opposed to being non-existent. It is also the first to do all this from first principles. Now it is still possible that all this good news is down to a luck chance, that the whole thing is spurious causality. If that were the case, then we would expect to see the theory collapse as it was applied to higher nuclides, or we would expect to see logical inconsistencies creep in as the theory was extended to other areas. So far there are none of those problems, but more work is necessary and until then we admit that this is still an open question. Nonetheless that it has been possible to achieve this, when no other theory has been able to come close to answering these questions, is promising.

The implications for fundamental physics are potentially far-reaching. Serious consideration must now be given to the likelihood that at the deeper level, particules have internal structure after all. This theory does not conflict with quantum mechanics but rather subsumes it: QM becomes a stochastic approximation to a deeper determinism, and the Standard Model of particle physics is re-interpreted as a set of zero-dimensional point-approximations to a finer-scaled covert structure. Now that would be something to be excited about.


Answers, according to the Cordus theory

Q: What is the atomic nucleus made of?

A: The nucleus consists of protons and neutrons that are rod-like structures (as opposed to 0-D points) that link into chains. These chains form a Nuclear polymer that is generally a closed loop (exceptions for the lightest nuclides) and there can be bridges across the loop. The polymer is required to take a specific shape, which is to wrap around the edges of a set of interconnected cubes.

Q: How are the protons held together in the nucleus?

A: An interlocking (synchronous) interaction. Forget the strong force – it turns out that’s not a helpful way to conceptualise the situation. What seems to be really happening is that the synchronous interaction holds both protons and neutrons together. It works by the synchronisation between discrete force emissions from neighbouring particules. One reactive end from each particule is thus locked together. The other reactive ends are free to make bonds with other particules. This explains why the effect is so ‘strong’ – it is an interlock. It also explains why the nucleus does not collapse in on itself (equivalent to ‘repulsive’ strong force). Furthermore these discrete forces continue out into the external environment (equivalent to ‘constant’ strong force at long-range). Furthermore, the Cordus theory predicts that the electrostatic force does not operate in the nucleus as it only applies to discoherent matter. Likewise the synchronous interaction only applies to coherent matter.

The theory gives an explanation of the nucleus, based in physical realism. This is a radical and highly novel outcome. If true, a conceptual revolution will be required at the fundamental level. Maybe its time … Physics is overdue for an earthquake.

Dirk Pons


12 Sept 2014
Read more…

D J Pons, A D Pons, A M Pons, and A J Pons, Wave-particle duality: A conceptual solution from the cordus conjecture. Physics Essays. 25(1): p. 132-140. DOI: http://physicsessays.org/doi/abs/10.4006/0836-1398-25.1.132, (2012).

D J Pons, A D Pons, and A J Pons, Synchronous interlocking of discrete forces: Strong force reconceptualised in a NLHV solution Applied Physics Research. 5(5): p. 107-126. DOI: http://dx.doi.org/10.5539/apr.v5n5107 (2013).

D J Pons, A D Pons, and A J Pons, Differentiation of Matter and Antimatter by Hand: Internal and External Structures of the Electron and Antielectron. Physics Essays. 27: p. 26-35. DOI: http://vixra.org/abs/1305.0157, (2014).

D J Pons, A D Pons, and A J Pons, Explanation of the Table of Nuclides: Qualitative nuclear mechanics from a NLHV design. Applied Physics Research 5(6): p. 145-174. DOI: http://dx.doi.org/10.5539/apr.v5n6p145 (2013).

D J Pons, A D Pons, and A J Pons, Annihilation mechanisms. Applied Physics Research 6(2): p. 28-46. DOI: http://dx.doi.org/10.5539/apr.v6n2p28 (2014).

D J Pons, A Pons, D., and A Pons, J., Beta decays and the inner structures of the neutrino in a NLHV design. Applied Physics Research. 6(3): p. 50-63. DOI: http://dx.doi.org/10.5539/apr.v6n3p50 (2014).


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Time dilation is like yacht racing

An explanation of time dilation by analogy with yacht racing

In yacht racing, unlike say motor racing, it is difficult to know which boat is in front when they have taken different paths. Consider the case of two-yachts, e.g. an America’s Cup type event. One boat might look closer to the finish line, but if it is substantially down-wind of the mark  then it will be moving slower than another boat upwind but further away. In addition, the boats might move into regions of the water space where the wind is faster (or slower), or coming from a different direction, and this will affect the outcome.

For a spectator, it is very difficult to see which boat is winning, or how the boats are doing against each other when they are on different parts of the water, unless that spectator has a lot of sailing knowledge him/herself. Plus the spectators are invariably far away and low to the water, so have very little ability to perceive the depth of the visual field. All this makes watching yachting a boring spectacle.

To improve the situation Virtual Eye, based in New Zealand, has developed a data acquisition, software, and rendering system to visually show spectators how the race is progressing. This is a  neat system as it shows the advantage between the boats, and avoids the need for the spectator to have specialised sailing knowledge…which of course is important in getting the wider public interested in the sport. Here for example is an image showing a red boat ahead of a black one. It would otherwise not be clear which one was leading.


Yacht racing: Visualising advantage (http://live.virtualeye.tv/slidorion/img/volvo2011-12.jpg)

Yacht racing: Visualising advantage (http://live.virtualeye.tv/slidorion/img/volvo2011-12.jpg)

Things start to get more complex when there are multiple boats, all taking very different paths across the water. In this next image, the white boat with the blue line is ahead of the black boat (Oracle). This would have been hard for a land-lubber to determine, as black looks ahead. The larger the physical space between the boats, the harder it is to see which boat is ahead. This also applies to the yachties on board their boats.


White leads black in this visualisation of a yacht race. Image from Visual Eye (http://virtualeye.tv/images/stories/sailing/large05.jpg)

White leads black in this visualisation of a yacht race. Image from Visual Eye (http://virtualeye.tv/images/stories/sailing/large05.jpg)


By now you will probably be seeing where this discussion is heading. Yachting is done on a 2D course where there are an infinite many loci possible. The boat’s velocity depends on which part of that 2D space it travels through, how fast the wind flows in those spaces, and the relative orientation of boat and wind.

Now replace the flow of the wind with the flow of time, and the time dilation situation emerges. If two space craft were to take different paths through space, going through different regions of gravitational strength  and accelerating differently, then it would be difficult to determine from afar which was ahead in time. Hence the Andromeda Paradox.

Time dilation is often illustrated with the idea that ‘you’ stay on Earth and ‘your twin’ goes off in a spacecraft. In which case we are protagonists embedded within the time dilation, and like the yachties on their boats, find it difficult to comprehend our relative progress. Visual Eye’s software looks down on the yacht race from an independent third-party perspective, and worldlines do this for cosmology though not nearly so engagingly.

Time dilation only applies when two (or more) protagonists take different routes through space. One can never be totally sure which protagonist is ahead in time, because you don’t know what future choices they will make regarding the gravitational and acceleration regimes they will be exposed to. It is only when the protagonists are brought back together in the same location that you can see the time difference. In the case of time dilation this will show up as one clock indicating a later time or date, or a biological organism showing greater age. (This part may sound weird, and indeed it is still something of an open question as to how time occurs at the level of fundamental physics. You can just accept that the clocks will show a difference. There are many explanations of time-dilation on the internet. They invariably address the question of  what is is and how to formulate it mathematically. The much harder question is how it occurs. If you want the additional mental gymnastics, start by thinking about atomic clocks (i.e. like atomic vibrations), as this feels less weird.  Then you can ponder how atomic time scales up to the level of clockwork timepieces.  Then explain to yourself how this determines biological time at the cellular level.  Finally, work out the implication for yourself as a biological being. It is a interesting and rewarding personal gedanken experiment. The initial weirdness, which arises from the psychological incongruence between what physics and our own senses tell us of the *now*, becomes resolved and one gains an appreciation of time and the nature of the gift. Our own explanation of time is referenced below).

In the case of yachting, this time dilation shows up as one boat ahead of the other, i,e, one boat enters a region of 2D space before the second boat enters the same space. So whatever has happened before on the water, when the boats come together, heading in the same direction, then it is apparent who is in front, as the image shows. The finish line is one such 2D space, and the most important one. But there are also others where the precedence becomes visible, e.g. going around marker buoys.


White leads Black. Differences in time are definitively evident only when the boats are in the same space. Image source Virtual Eye. http://virtualeye.tv/images/stories/sailing/thumb06.jpg

So the outcomes of time dilation only become clearly evident when the protagonists are brought back to a common location in space. At this point the ambiguity of which one is ahead collapses. The Andromeda-type paradoxes exploit this ambiguity, but the ambiguity only exists when the protagonists are far away in space – bring them together again and the paradox collapses. Just like in yachting, all the ambiguity during the race collapses at the finish line: both boats have to cross the same region of 2D space, and the first one there is the winner.


PS: If you don’t like wet, then alternatively, time dilation is like hiking up a mountain where there are no paths and each hiker takes his/her own route. Some paths might look like a more direct route to the summit, but if they are steeper then progress may be slower. This is actually what I was thinking of first since I was hiking at the time and realised that hiking was just like yachting, and then realised both were like time dilation.

Dirk Pons 23 April 2014

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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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New non-local hidden-variable solutions

‘Hidden variable solutions’ are theories of fundamental physics that propose that particles (e.g. the electron) have inner structure. By comparison quantum mechanics (QM) and the Standard Model are based on the premise that a particle is a zero-dimensional (0D) point.

However it is known from experiment that particles have many properties, that make them different to other particles. For example the electron has negative charge, a certain mass, and a spin.

How does QM explain these? It doesn’t. Instead it proposes that these are ‘intrinsic’ properties. i.e. disembodied attributes. How might these properties arise then? According to QM, that is not a meaningful question to ask. The mathematics simply requires these attributes, and QM pointedly rejects the notion that there might be natural explanations at a deeper level of physics. Consequently the more extremist interpretations of QM would have us believe that reality is fundamentally mathematical, and that the probabilistic nature of superposition is simply all there is, that there is nothing deeper (Copenhagen interpretation). Hence an assumption that indeterminism is fundamental (Born & Heisenberg).

The hidden variable theories propose that there is a deeper inner structure to a particle. This physical structure then causes the properties of charge, mass, spin (etc). These internal structures are ‘hidden’ to external inspection, hence the name. According to this perspective, the probabilistic equations of QM are approximations to a deeper mechanics. Einstein believed that QM was fundamentally incomplete (EPR, 1935) and suspected the existence of hidden variables. However the hidden sector has historically failed to live up to expectations, the main difficulty being the sheer lack of specific solutions. It is all very well to say that in principle a particle might have inner structure, but to do anything useful one has to propose a specific internal design. That’s where things have failed to progress. There is no obvious hidden variable solution, and very few candidate designs.

To make things harder, one whole category of possibilities, the local hidden-variable designs, have been eliminated by the Bell type inequalities (Bell, 1964). The other category, the non-local hidden variable (NLHV) designs, is also under theoretical siege (Leggett, 2013)(Groblacher 2007) such that the remaining solution space is limited. As those authors have commented, if a NLHV solution exists at all, it must be counter-intuitive.

The candidate hidden-variable designs are as follow:

  1. The de-Broglie-Bohm theory (Bohm, 1966), also called the ‘pilot-wave’ theory. (See wikipedia). This has not done well, though there are still scientists who are progressing the idea and seeking to extend it. However in its present state it is not able to explain a diverse range of other fundamental phenomena, and hence is not yet as extensive as QM. There are many things it cannot explain.  Some have even suggested it is merely another interpretation of QM, but I think that’s taking it a bit too far.
  2. Others?At the present time, if you search for NLHV solutions there is not much more than de-Broglie-Bohm. This goes to show how hard it has been to come up with candidates that can evade the Bell-type inequalities. Here are a few more ideas. These are mostly mathematical treatments rather than specific proposals for natural structures, so are difficult to interpret or apply, and their ontological explanatory power is weak, but they show that people are still chipping away at the problem in creative ways.
    1. Lokajícek’s hidden variable theory.
    2. Bach’s theory, here or here, with a critique here.
    3. Others?
  3. The Cordus theory (covered elsewhere on this site) can be considered a NLHV design. Unusually, it has been developed using a systems engineering design methodology, as opposed to the mathematical theory building that every other attempt has used. Consequently it is descriptive theory, rather than a mathematical formalism. Nonetheless it has good ontological explanatory power, arguably better than QM. All that weirdness of quantum mechanics gets washed away in natural explanations involving the deeper sub-components of the particle. We think it can explain, in an ontological sense, anything that quantum mechanics purports to explain (which is not always a lot). But it doesn’t do the quantitative formalism as well as QM, so is limited in that regard.

Most physicists believe that quantum mechanics is a complete description of reality, and only needs extending. They are generally dismissive of hidden variable designs. However NLHV designs are not dead, just incredibly hard to find. It’s not impossible that a new physics could be found in the hidden sector.

Dirk Pons, 29 March 2014


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Why three colour charges?

Why are there exactly three colour charges for quarks?

The Cordus theory, which is a type of non-local hidden-variable design, gives a straight-forward answer: because three is the number of geometric directions for emission of discrete forces. Thus the number of fractional charges (colours) is dependent on the nature of spacetime.

The Cordus theory also explains why colour is only seen in fractional charge situations: because there are none of the three emission directions may be unfilled in unit-charge particules.

The pattern of discrete forces is represented in HED notation, which simply indicates the number of discrete forces in each of three orthogonal spatial directions [r, a, t].

Cordus particule structure. The top part shows a generic physical structure, and below that is the short-hand notation. Many problems and paradoxes in fundamental physics could be resolved if fundamental particles had this type of structure.

Cordus particule structure. The top part shows a generic physical structure, and below that is the short-hand notation. Many problems and paradoxes in fundamental physics could be resolved if fundamental particles had this type of structure.

For more, see the following paper [1] on the annihilation process.


1. Pons, D.J., Pons, A.D., Pons, A.J.: Annihilation mechanisms. Applied Physics Research 6(2), 28-46 (2014). http://dx.doi.org/10.5539/apr.v6n2p28

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Free-will compromised on a grand scale: Can the universe be controlled from outside?

Most of the developments of the Cordus theory have focussed on fundamental physics, e.g. the proposed inner structure of the fundamental particles and that of the nuclides (isotopes). However the theory also has cosmological implications. We have explored some of these in the theory for time, and that of the cosmological frontier (the outer edge of the universe).

These start to raise some interesting philosophical questions. In particular, the implications for free-will. In this post I explore some of these, starting at the cosmological level.

The explicit implication of the conventional idea of the cosmological horizon is that the inner universe of 3D matter could be controlled from outside, by an intelligent Agent that could access the outer 2D horizon. This philosophically thought-provoking idea has significant existential implications for reality.  The Cordus theory rejects this as a fanciful notion, for the following reasons.

First, the Agent would need to control the whole entire horizon simultaneously (as opposed to only one patch). This task is physically infeasible, given the size of the universe, and the necessary coordinated control would need to be instantaneous to have any useful control purpose. This excludes any physical Agent.

Second, a physical Agent is further excluded because such an Agent, positioned around the cosmological boundary, would therefore become part of the process whereby the vacuum of the universe colonises the wider void. (The Cordus theory proposes that time is created by the existence of matter, and therefore time does not exist outside the cosmological horizon). Thus a matter-based Agent would create time and therefore become part of the universe being measured and controlled, and the unidirectional causality could not be maintained. It is therefore not possible, according to the Cordus theory, to have an independent physical Agent, observer, or even inanimate instrumentation, at the boundary. The Cordus theory shows that the act of observation changes the system, i.e. observation is necessarily contextual. This applies to photons in double-slit and interferometer apparatus. In the case of the cosmological boundary there is a similar principle, except here the addition of the Agent adds to the system under observation.

The third objection is that there is, according to the Cordus theory, no bidirectional causality between the 2D surface and the inner 3D volume anyway. Even if there was a non-physical (metaphysical) Agent at the boundary, one nonetheless able to meddle with the discrete forces protruding from the expanding universe, such a frontier interaction would do nothing to change the emitting particule way back in the depths of the universe. This interpretation arises because the Cordus theory suggests that discrete fields are unilateral interactions with mono-directional causality: they are not conduits for bi-directional force transfer.[1] Consequently, the discrete field pulses that are received at any inspection point remote from the emitting body are a force on any matter at that inspection point, and have no reciprocal effect back on the emitting body.

The only way for an Agent on the boundary to change the particules inside the universe is for the Agent to emit its own discrete fields back into the universe to target those particules. However this would require a physical agent (which we already exclude) to generate the discrete fields. This is because discrete fields are a feature of matter, and do not have an independent pre-existence. There is a further obstacle too: even if it were somehow possible to generate discrete fields without matter, these would take time to arrive at their target within the universe, thereby adding a practical limitation to the efficacy of the control.

So there are three objections to the holographic control idea, the most fundamental of which is that simply intercepting the discrete fields of the original emitting particule is insufficient for controlling that particule. The universe can therefore not be controlled from its boundary, under this theory.  The Cordus theory excludes the possibility of placing a physical Agent at the boundary of the universe, and of such an Agent having any practical  way to control the universe from the outside. The control aspects of the holographic principle are therefore rejected.

We have not excluded the possibility that a metaphysical Being or Deity may be able to achieve this level of control, but even this seems unlikely for two reasons. One, it is unclear how a metaphysical Being could create or interfere with the discrete forces protruding from the frontier. More importantly, such manipulation would take ages to propagate back to their target in the physical universe, so the control effect would lack immediacy.

So the conclusion we reach, is that the Cordus theory rejects the idea that free-will may be compromised on a grand scale by an Agent controlling the whole universe from its outer surface. We have not proved that free-will exists, but simply shown that the cosmological frontier is not relevant to consideration of free-will under this theory.

[This post has looked at the cosmological scale at its widest, just for the fun of it. I would like to come back to this in future work, by starting at the opposite end of the scale, by examining the implications of this theory  for determinism at the fundamental level. ]

Read the full paper (open access) here:

Pons DJ, Pons A, D. (2013) Outer boundary of the expanding cosmos: Discrete fields and implications for the holographic principle The Open Astronomy Journal 6:77-89. doi: http://dx.doi.org/10.2174/1874381101306010077

[1] The idea that forces like gravitation are bidirectional is a tacit assumption in classical mechanics. The relation for gravitation, F = G ma mb /r2 specifically identifies that the force depends on both masses, not one. The Cordus theory accepts this at the macroscopic level, but suggests that the effect is not a bidirectional force conduit between the two masses, but rather two independent effects that are aggregated.  More specifically, that discrete fields emitted from source A cause their recipient target  B to experience prescribed constraints on the re-energisation location of its reactive ends, and this is what we perceive as force. The recipient body B also sends out its own discrete fields, some of which are intercepted by A, and the mutual attraction/repulsion of the EMG forces arises by a combination of the individual unilateral effects. Simple passive access of field information does not necessitate control of the emitting source, according to the Cordus theory.

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