Thursday, December 22, 2011

The Higgs Boson -- and the value of money

What does the (tentatively discovered) Higgs Boson have to do with finance? Nothing. At least nothing obvious. Still, it's a fascinating topic with grand sweeping themes. I've written an essay on it for Bloomberg Views, which will appear later tonight or tomorrow. I'll add the link when it does.

The interesting thing to me about the Higgs Boson, and the associated Higgs field (the boson is an elementary excitation of this field), is the intellectual or conceptual history of the idea. It seems crazy to think that as the universe cooled (very shortly after the big bang) a new field, the Higgs field, suddenly appeared, filling all space, and giving particles mass in proportion to how strongly they interact with that field. It would be a crazy idea if it were just a proposal pulled out of thin air. But the history is that Higgs' work (and the work of many others at the same time, the early 1960s) had very strong stimulation from the BCS theory of superconductivity of ordinary metals, which appeared in 1957.

That theory explained how superconductivity originates through the emergence below a critical temperature of a condensate of paired electrons (hence, bosons) which acts as an extremely sensitive electromagnetic medium. Try to impose a magnetic field inside a superconductor (by bringing a magnet close, for example) and this condensate or field will respond by stirring up currents which act precisely to cancel the field inside the superconductor. This is the essence of superconductivity -- its appearance changes physics inside the superconductor in such a way that electromagnetic fields cannot propagate. In quantum terms (from quantum electrodynamics), this is equivalent to saying that the photon -- the carrier of the electromagnetic fields -- comes to have a mass. It does so because it interacts very strongly with the condensate.

This idea from superconductivity is pretty much identical to the Higgs mechanism for giving the W and Z particles (the carriers of the weak force) mass. This is what I think is fascinating. The Higgs prediction arose not so much from complex mathematics, but from the use of analogy and metaphor -- I wonder if the universe is in some ways like a superconductor? If we're living in a superconductor (not for ordinary electrical charge, but for a different kind of charge of the electroweak field), then it's easy to understand why the W and Z particles have big masses (more than 100 times the mass of the proton). They're just like photons traveling inside an ordinary superconductor -- inside an ordinary metal, lead or tin or aluminum, cooled down to low temperatures.

I think it's fitting that physics theory so celebrated for bewildering mathematics and abstraction beyond ordinary imagination actually has its roots in the understanding of grubby things like magnets and metals. That's where the essential ideas were born and found their initial value.

Having said that none of this has anything to do with finance, however, I should mention a fascinating proposal from 2000 by Per Bak, Simon Nørrelykke and Martin Shubik, which draws a very close analogy between the process which determines the value of money and any Higgs-like mechanism. They made the observation that the absolute value of money is essentially undetermined:
The value of money represents a “continuous symmetry”. If, at some point, the value of money was globally redefined by a certain factor, this would have no consequences whatsoever. Thus, in order to arrive at a specific value of money, the continuous symmetry must be broken.
In other words, a loaf of bread could be worth $1, $10, or $100 -- it doesn't matter. But here and now in the real world it does have one specific value. The symmetry is broken.

This idea of continuous symmetry is something that arises frequently in physics. And it is indeed the breaking of a continuous symmetry that underlies the onset of superconductivity. The mathematics of field theory shows that, anytime a continuous symmetry is broken (so that some variables comes to take on one specific value), there appears in the theory a new dynamical mode -- a so-called Goldstone Mode -- corresponding to fluctuations along the direction of the continuous symmetry. This isn't quite the appearance of mass -- that takes another step in the mathematics, but this Goldstone business is a part of the Higgs mechanism.

I'll try to return to this paper again. It offers a seemingly plausible dynamical model for how a value of money can emerge in an economy, and also why it should be subject to strong inherent fluctuations (because of the Goldstone mode). None of this comes out of equilibrium theory, nor should one expect it to as money is an inherently dynamical thing -- we use it as a tool to manage activities through time, selling our services today to buy food next week, for example.


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  2. I always understand "Higgs bosom".

  3. A loaf of bread couldn't be worth any amount of money through some symmetrical math theory. It must have a value related to the physical world from which it derives.

    Consider: it always takes 4.2 Joules to raise a gram of water 1 degree Celcius. The "individual quanta of natural resource" (think chemical bond) needed to create the heat that raises the temperature of the water can only ever do so once, because of the 2nd law of thermodynamics.

    The heat is generated when a chemical bond breaks (or in some cases when a nuclear bond breaks). It will always require an input of energy from a source external to the system under consideration (usually the sun) to rejoin that individual bond. So the price of creating the heat is asymmetrical.

    i.e. we can only ever evaporate the water from a finite amount of unleavened dough. (a.k.a. bake bread)

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