A colleague of mine in the Faculty of Education here at Waikato has drawn my attention to an elegantly titled paper by Andreas Quale: "On the Role of Mathematics in Physics" Science and Education (2011), 20:359-372, for those of you who like references.
The paper is about the way mathematics relates to physics, highlighting the problem of teachers presenting the view (either explicitly or implicitly) that mathematics leads to physics. In other words, if you find a solution to an equation used in physics, that solution HAS to mean something. The one example quoted is Dirac's 'discovery', by theoretical means alone, of the positron, or anti-electron - here DIrac's equation, which he developed to obey certain conditions, had some unexpected solutions.
[1 Feb 12 - wrote this last night and got interrupted halfway through by a phone call - I now see I didn't finish this paragraph! Dirac's equation, which described in mathematical terms a quantum theory consistent with special relativity, also had solutions that didn't seem to make sense. Dirac then thought through what the solutions would mean in term of physics, and came up with the interpretation of them being negative energy solutions - this in turn led to the idea of an anti-particle. Now, as it turned out, the anti-particles were later shown to exist, but did Dirac just get lucky here? Was there any reason per se that the strange solutions to the equation HAD to represent something physical? Probably not - for example, the average physicist is quite adept at picking the 'right' root from a quadratic equation and dismissing the other as 'unphysical'. Above all, physics is based on EXPERIMENT - i.e. the real world, not a theoretically constructed world (and remember, you're reading a theoretical physicist in this blog!]
Specifically, the author talks about the problem of presenting a realist ontology to students learning physics, whereas a better strategy would be to present a relativist ontology, as adopted by radical constructivism.
I have a couple of problems with this article. First of all, I'm not sure that the average physics teacher would recognize 'radical constructivism' if he got hit on the head with it or be able to tell at a glance a realist from a relativist. I certainly struggle with this education-speak. But, most significantly, the author presents no evidence that the problem he describes is actually occuring. In other words, do physics teachers REALLY present the view that maths leads to physics - solve the equations and physics emerges no matter what. Maybe some do, but has anyone actually established this? If they have, could we have a reference or two for it. In fact, there isn't a single reference for the first five pages of the article!- something that I have never, ever, seen in a physics paper.
You see, my recent interviews of physicists gives no evidence that this problem is happening - not in the tertiary sector at any rate. So, if there's a difference between what my data suggests and what the article suggests, I'd like to know some more details. And it's not there. Frustrating.
It will inspire me to do a bit of searching around, though.