If you knew SUSY

Now, I don't really know SUSY (supersymmetry) very well at all. Actually, I don't know SUSY at all. But I have just come across a new word in the realm of particle physics: adinkra. Now if you think that word is strange, remember that quark was once just as strange, though it has had a charmed existence since. And the choice of the word adrinka is just as arbitrary (from the physics point of view) as was the choice of the word quark.

My source for this new addition to my vocabulary is an article in the June 2010 issue of Physics World by James Gates entitled "Symbols of Power" and featured under the generic heading of "Physics and geometry". James Gates is a theoretical physicist (ie his physics is theoretical, not James himself) at the University of Maryland in the United States.

This is the rough idea.

Physicists like equations - indeed, the article suggests that physicist belong to a company called "Equations-R-Us". Key points in the progress of physics are marked by the adoption or discovery of key equations that describe a phenomenon of physics - Maxwell's equations for electromagnetism, Einstein's equations for General Relativity, Schrodinger's equations for quantum mechanics, etc - and then it becomes a question of solving the equations for every imaginable situation.

Then it so happens that the equations can sometimes be represented geometrically. This helps make sense of the equations, but calculations using the geometry can also suggest new predictions from or solutions to the equations. The best known example of this sort of thing is probably the use of Feynman diagrams to solve problems in quantum electrodynamics. In the Standard Model, the different symmetries of particles such as photons, protons and neutrons can be represented geometrically. It was the observation of patterns in these geometric representations that led to the suggestion that the particles concerned must be made up of smaller, more fundamental particles, what we now happily call quarks.

What SUSY does is suggest that each particle in the Standard Model, which already has its own symmetry properties, also has a "super partner" particle that obeys the equations of supersymmetry. This has the effect of achieving a unification among different types of particles. These super partner particles have yet to be observed (looking out for experimental evidence of their existence is reported by the article as one of the main tasks of the Large Hadron Collider). But meanwhile, how about trying to develop a geometric representation of these super partner particles and their physics equations, in the hope that the geometry will reveal more about the equations and about SUSY? After all, this is a strategy that has been very successful before. These geometrical shapes are what the researchers have called adinkras. Of course, it turns out that three dimensions won't do if you want to represent equations that have any physical meaning; four dimensions is the least number.

All of this is just the preamble for the really interesting bit - so stay with me.

Adinkras made up of four or more dimensions can be separated to give two adinkras representing fewer particles, these two adinkras also obeying the relevant equations. It's a bit like splitting a set into two sub-sets that can be added together again to give the original set. The technical term for it is "folding", the merging together of different points on the geometric shape following careful rules for doing so. Understanding why some "foldings" work and others don't ... well, this has been achieved by representing each point on the geometric shape by a binary number ... and realising that foldings that preserve the properties of SUSY all obey one of the simplest error correction codes familiar to the digital transmission of data. The required sum of the binary numbers of folded points is 1111..

The punchline: the mathematical relations between these super partner particles seems to be intimately bound up with information theory.

For the most part [information theory] is a science that has largely developed in ways that are unrelated to the fields used in theoretical physics. However, with the observation that structures from information theory - codes - control the structure of equations with the SUSY property, we may be crossing a barrier. I know of no other example of this particular intermingling occurring at such a deep level. Could it be that codes, in some deep and fundamental way, control the structure of our reality?... As for my own collaboration on adrinkas, the path my colleagues and I have trod since the early 2000s has led me to conclude that codes play a previously unsuspected role in equations that possess the property of supersymmetry. This unsuspected connection suggests that these codes may be ubiquitous in nature, and could even be embedded in the essence of reality.

I am not a proponent of immediately drawing theological conclusions from the physical sciences - there is a mediating role for metaphysics, in particular, the idea of analogy of being, between the raw physics and theological understanding. But the suggestion that information is in some way embedded in the heart of reality is thought provoking  to say the least, and seems amenable to an analogical theological expression. However, some care needs to be taken to make sure that that analogical expression does not say something that isn't what the physics itself says - the pioneer to whom James Gates makes reference towards the end of his article , John Archibald Wheeler, for example, links the information-theoretic aspect to the problem of measurement, the measurement (subjectively) determining the reality that has been measured. James Gates own work, being theoretical, seems to me to present an information-theoretic basis that is independent of this question of measurement.

PS. The Large Hadron Collider might, of course, show that SUSY's super partner particles don't exist any way ....