Archive for March, 2014

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).

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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:

[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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