Archive for category About method and progress

Beautiful mathematics vs. qualitative insights

Which is better for fundamental physics: beautiful mathematics based on pure concepts, or qualitative insights based on natural phenomena?

According to Lee Smolin in a 2015 arxiv paper [1], it’s the latter.

As I understand him, Smolin’s main point is that elegant qualitative explanations are more valuable than beautiful mathematics, that physics fails to progress when ‘mathematics [is used] as a substitute for insight into nature‘ (p13).
‘The point is not how beautiful the equations are, it is how minimal the assumptions needed and how elegant the explanations.‘ (
The symmetry methodology receives criticism for the proliferation of assumptions it requires, and the lack of explanatory power. Likewise particle supersymmetry is  identified as having the same failings. Smolin is also critical of of string theory, writing, ‘Thousands of theorists have spent decades studying these [string theory] ideas, and there is not yet a single connection with experiment‘ (p6-7).

Mathematical symmetries: More or fewer?

Smolin is especially critical of the idea that progress might be found in increasingly elaborate mathematical symmetries.
I also wonder whether the ‘symmetries’ idea is overloaded. The basic concept of symmetry is that some attribute of the system should be preserved when transformed about some dimension. Even if it is possible to represent this mathematically, we should still be prudent about which attributes, transformations, and dimensions to accept. Actual physics does not necessarily follow mathematical representation. There is generally a lack of critical evaluation of the validity of specific attributes, transformations, and dimensions for the proposed symmetries. The *time* variable is a case in point. Mathematical treatments invariably consider it to be a dimension, yet empirical evidence overwhelmingly shows this not to be the case.
Irreversibility shows that time does not evidence symmetry. The time dimension cannot be traversed in a controlled manner, neither forward and especially not backward. Also, a complex system of particles will not spontaneously revert to its former configuration.   Consequently *time* cannot be considered to be a dimension about which it is valid to apply a symmetry transformation even when one exists mathematically. Logically, we should therefore discard any mathematical symmetry that has a time dimension to it. That reduces the field considerably, since many symmetries have a temporal component.
Alternatively, if we are to continue to rely on temporal symmetries, it will be necessary to understand how the mechanics of irreversibility arises, and why those symmetries are exempt therefrom. I accept that relativity considers time to be a dimension, and has achieved significant theoretical advances with that premise. However relativity is also a theory of macroscopic interactions, and it is possible that assuming time to be a dimension is a sufficiently accurate premise at this scale, but not at others. Our own work suggests that time could be an emergent property of matter, rather than a dimension (  This makes it much easier to explain the origins of the arrow of time and of irreversibility. So it can be fruitful, in an ontological way, to be sceptical of the idea that mathematical formalisms of symmetry are necessarily valid representations of actual physics. It might be reading too much into Smolin’s meaning when he says that ‘time… properties reflect the positions … of matter in the universe’ (p12), but that seems consistent with our proposition.

How to find a better physics?

The solution, Smolin says, is to ‘begin with new physical principles‘ (p8). Thus we should expect new physics will emerge by developing qualitative explanations based on intuitive insights from natural phenomena, rather than trying to extend existing mathematics. Explanations that are valuable are those that are efficient (fewer parameters, less tuning, and not involving extremely big or small numbers) and logically consistent with physical realism (‘tell a coherent story’). It is necessary that the explanations come first, and the mathematics follows later as a subordinate activity to formalise and represent those insights.
However it is not so easy to do that in practice, and Smolin does not have suggestions for where these new physical principles should be sought. His statement that ‘no such principles have been proposed‘ (p8) is incorrect. Ourselves and others have proposed new physical principles – ours is called the Cordus theory and based on a proposed internal structure to particles. Other theories exist, see vixra and arxiv. The bigger issue is that physics journals are mostly deaf to propositions regarding new principles. Our own papers have been summarily rejected by editors many times  due to ‘lack of mathematical content’ or ‘we do not publish speculative material’, or ‘extraordinary claims require extraordinary evidence’. In an ideal world all candidate solutions would at least be admitted to scrutiny, but this does not actually happen and there are multiple existing ideas in the wilds that never make it through to the formal journal literature frequented by physicists.  Even then, those ideas that undergo peer review and are published, are not necessarily widely available. The problem is that the academic search engines, like Elsevier’s Compendex and Thompson’s Web of Science,  are selective in what journals they index, and fail to provide  reliable coverage of the more radical elements of physics. (Google Scholar appears to provide an unbiassed assay of the literature.) Most physicists would have to go out of their way to inform themselves of the protosciences and new propositions that circulate in the wild outside their bubbles of knowledge. Not all those proposals can possibly be right, but neither are they all necessarily wrong. In mitigation, the body of literature in physics has become so voluminous that it is impossible for any one physicist to be fully informed about all developments, even within a sub-field like fundamental physics. But the point remains that new principles of physics do exist, based on intuitive insights from natural phenomena, and which have high explanatory power, exactly how Smolin expected things to develop.
Smolin suspects that true solutions will have fewer rather than more symmetries. This is also consistent with our  work, which indicates that both the asymmetrical leptogenesis and baryogenesis processes can be conceptually explained as consequences of a single deeper symmetry ( That is the matter-antimatter species differentiation ( That also explains asymmetries in decay rates (
In a way, though he does not use the words, Smolin tacitly endorses the principle of physical realism: that physical observable phenomena do have deeper causal mechanics involving parameters that exist objectively. He never mentions the hidden-variable solutions. Perhaps this is indicative of the position of most theorists, that the hidden variable sector has been unproductive. Everyone has given up on it as intractable, and now ignore it. According to Google Scholar, ours looks to be the only group left in the world that is publishing non-local hidden-variable (NLHV) solutions. Time will tell whether or not these are strong enough, but these do already embody Smolin’s injunction to take a fresh look for new physical principles.

Dirk Pons

26 February 2016, Christchurch, New Zealand

This is an expansion of a post at Physics Forum


[1] 1. Smolin, L.: Lessons from Einstein’s 1915 discovery of general relativity. arxiv 1512.07551, 1-14 (2015). doi:




, , , , , , , , ,

Leave a comment

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


1 Comment

FQXi essay contest: Questioning the Foundations

The purpose of the Foundational Questions Institute is to encourage ‘innovative ideas integral to a deep understanding of reality’.  Their 2012 essay contest invites authors to identify Which of Our Basic Physical Assumptions Are Wrong?

In our submisison we use cordus to show that the 0-D point premise can be challenged, and is likely to have profound consequences for physics when it falls. There are many things for which cordus offers explanations, and for this essay we had to focus on some and not cover others. Basically we decided to focus our essay on the conventional assumption that particles are merely points. From there we explore the alternative options and show how cordus offers a viable solution.

You can see and discuss our submission here.

Why not join in and see what new ideas are surfacing? There are some really interesting essays there, and  something for everyone whether you like the mathematical approach to physics, the descriptive, or the philosophical.


Leave a comment