Well, summer has come and I’ve gotten a bit lazy. Actually, I’ve been trying – and ‘trying’ is the key word here – to relax since the semester ended. Hence I haven’t posted in awhile. At any rate, I have been reading, however. In particular I’ve been working through Chris Isham’s recent paper on topos methods in formulating physical theories. It’s pretty interesting reading and we’ve had some interesting discussions about related things over at the nForum.
But it got me thinking about something. Now, Isham’s approach may indeed lead somewhere eventually. In fact I think his approach is almost precisely what I had envisioned for this idea of relational empiricism that I was trying to cook up. But the question is, what will it really serve to accomplish in the end?
Personally I think it may accomplish quite a bit, but here’s the thing. Both GR and QM are excellent working theories. That is, the formalism for each is used on a daily basis by scientists (and even some engineers, e.g. GPS) to accomplish a wide variety of tasks. Thus a full theory of quantum gravity would naturally be expected to recover the essence of these formalisms (since they are different formalisms, a unified theory would not likely be able to capture all of each – the important thing, of course, is that a unified theory match experiment).
But some approaches to quantum gravity seem to be motivated solely by an effort to find a unified description of these two phenomena. That is certainly a laudable – and possibly even an unachievable – one. But ideally a full theory of quantum gravity ought to also offer new physical insights, perhaps explaining the unexplained.
And this is where I worry a bit about Isham’s approach. As much as I am a major proponent of category theory, I am more in favor of a ‘radically de-abstracted’ category theory. In other words, I love the essence of category theory but it can get so abstract at times to be almost unapproachable. I worry that any new insights this approach will lead to could leave too much room for interpretation. These insights will naturally be couched in the language of category theory and topos. Being as abstract as it is, it is possible that there could be multiple routes from this language to the physical phenomena themselves making any theoretical results gleaned from this method murky at best.
Isham’s method, of course, is just an example. And as I said I am generally in favor of it – the essence of category theory is fantastic. But clear lines must be drawn between the objects, symbols, definitions, etc. in category and topos theory to physical phenomena so that new theoretical discoveries are not ambiguous. Otherwise, all we’re doing is translating from one language to another. Quantum gravity needs to have the spirit of a universal language in the manner conceived by John Wilkins – not just to facilitate communication between disparate ideas, but also to offer new insight.