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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:



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Time: There Already Are Answers If You Look A Little Wider. . .

Space vs time: One has to go – but which? This is the question asked by Anil Ananthaswamy at New Scientist asks. As he says, ‘If we want to progress towards a theory of everything, we need to understand how space and time fit together – if they do at all.’ He goes on to review the usual candidates: quantum mechanics and general relativity, and finds them wanting. Then he checks out string theory (and AdS/CFT) and then takes in loop quantum gravity. Ultimately there are no definitive answers. As he concludes, ‘Many potential ways around lead to different worlds of space and time – and we have as yet little clue which route to follow.’

Here’s our take on this subject, being a copy of our post at the NS article:

We have a theory that time is an emergent property of matter, as opposed to being a dimension of its own or a property of space. The idea being that particles of matter emit discrete forces at their de Broglie frequency, and these are meshed together over space to create a fabric of discrete fields. The particles then interact with each other via the discrete field forces that they send to and receive from this fabric, and since those interactions are not instantaneous (for reasons given in the theory), so the arrow of time emerges.

This is an unorthodox perspective, especially since it starts from a non-local hidden-variable (NLHV) solution, but it has the benefit of being able to explain everything that quantum mechanics, general relativity, LQG, and string/M theory can explain about time, and quite a lot more. We call this the Cordus theory. It becomes quite simple to explain why time as measured by atomic clocks is consistent with time as we perceive it as humans, how time dilation occurs, where the arrow (irreversibility) arises, how time began, whether time exists outside an expanding universe, and many other such niggly little questions at fundamental and cosmological levels.

I can’t explain the whole thing in one post – instead I just want to point out that there already are answers for pretty much all the questions raised in the article, providing one is prepared to be open-minded and look beyond the fixed mental models provided by the orthodox theories. According to this Cordus theory there is nothing wrong with QM and GR per se, it is just that they are situationally-accurate but merely special-case approximations of a deeper mechanics. The only reason time is such a quandary to QM and GR is because those theories have premises that limit what kind of solutions can be admitted. But at the deeper level it is easy to unify the forces, resolve wave-particle duality, and explain entanglement and locality. So there is a lot of progress being made in the unorthodox areas of physics, even if the mainstream has stagnated.

Of course we could also be wrong! Make up your own mind: See the full time paper here or a simpler series of explanations here

Thank you

Dirk Pons

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