Re: Mirowski and critiques

[Johan Hauknes <johan@xxxxxxxxxxx>]

Herb Gintis wrote

   .....only in classical physics BTW  .....

On the contrary, the field where this is most extensively used is in qunatum field theory, most systematically in terms of local gauge symmetry. Well knomwn examples are are  quantum electrodynamics (the quantized form of electromagnetism) in quantum chromodynamics and electroweak interaction (the Weinberg-Salaam model, the unification of QED and teh socalled weak interaction betweens elementary particles ).

Sthe symmetry corresponds to charge conservation as in QED. But in addition there's a fact that the actual world does not conserve all the electroweak charges. The interpretation is that the symmetry is dynamically broken, i.e. through the dynamics of the theory there arises (energydependent) interactions which below a certain energy breaks the       symmetry. The way the symmetry is broken in theory is through an ad hoc mechanism called the Higgs mechanism. The broken symmetry shows up as detectable particles, this is the reason for the hunt for the Higgs boson. (This is an oversimplified description, I admit, but illustrates the point) Well known examples are phase transitions where there appears long range ordering 'below' the transition point, as in superconductors, spontaneouslyagnetized  systems(and a circular dinner table with plates and napkinsconsecutively around the table,the first to pick a napkin breaks the left-right napkin- plate symmetry giving rise to a wave of napkin picking around, the syst
em falling into the new unsymmetric ground state).

It is easy to see that a symmetry of the dynamics, i.e. of the Hamiltonian operator is realted to a conservation in the solution to the initial value problem. If H is the symmetric Hamiltonian  and F is a symmetry operator, and (fi) a solution of a particular IVP, then

	H = FHF'

(F' is F-inverse, compliment to emacs) implies

	FH(fi) = HF(fi) = H(fi')

which means that (fi) and (fi') are solutions to the same IVP (disregarding intial values breaking the symmetry). Because of the possibility of dynamical symmetry breaking, the realtion is not exact; solutions  might not conserve quantities ralted to symmetries of the Hamiltonian. (The Hamiltonian is not necessarily given the interpretation it has in physics as the 'energy')

I liked Mirowskis book, but I think that the parallell between the two fields has more of historical than real interest. Economics is not social physics in any interpreation of the term. But htat does not exclude the possibility that something can be learned both ways. (Is it something I hate, then that is disciplinary arrogance, both from physicists, economists.....  and other.)

Waht seems to me part of the problem is that both in physics and economics you have several different time concepts. This is still an unsolved problem in physics. Between a parametric time as in calssical conservative mechanics, time in relation to 'open' systems, exogeneous time, realtivistic time and entropy time.

BTW my background is from theoretical physics and mathematics.

Now working for a research institution in economics, innovations studies and technical change.

johan.hauknes@xxxxxxxxxxx
STEP Group
Studies in technology, innovation and economic policy