Sunday, June 7, 2015

It's only a crisis if there's no foundation

Cosmic ray shower. Image credit: NASA.
Mark Thoma points us to a NYTimes article where the authors claim a crisis in fundamental particle physics. Mark points out that he thinks there's a connection to economics and I'd agree. Actually I think the NYTimes article is more appropriate for economics than physics.

The authors complain that after the Higgs was found, there's no way to empirically validate theory anymore. They take exception to a couple of physicists who say that isn't exactly a problem.

I'm going to suspend my disbelief in later paragraphs; however, the fact is that they're wrong -- just because they can't think of a way to test string theory doesn't mean there isn't one. Sure, brute force approaches (i.e. accelerator experiments) are probably coming to an end in their usefulness. Super-symmetric partners (sparticles) might be beyond a feasible accelerator. But what about data-mining high energy cosmic rays? The universe itself is a 10^10 GeV accelerator with a very low luminosity. Lack of imagination of how to empirically test string theory is not a proof of impossibility.

So now let's say they're right and we won't be able to empirically validate high energy particle theory. We still have a foundation of all of the successful theory we've empirically validated. Call that F. If you propose new theory T that is far simpler than F that reduces to F in the proper limits I'd call that a major success ... even if T has no additional predictions or only predicts things that can't be empirically tested.

And you know what? We have an example of this! Classical Yang Mills theory [1] is based on a beautiful symmetry principle and can give us all of electromagnetism and not much else. I'd rather have U(1) Yang Mills than Biot-Savart + Faraday + Gauss + no magnetic monopoles + topological effects + permittivity + permeability + Lorentz symmetry (those are the various assumptions and equations of electrodynamics). There's a reason physicists refer to electromagnetism as simply U(1).

Even if string theory gives us no testable predictions, the simple Nambu-Goto action [2] is better than U(1) × SU(2) × SU(3) + 20 masses and couplings + general relativity. Plus string theory lets you calculate the proper entropy for a black hole!

That is to say fundamental research that gives us a new unified theory (T) while remaining consistent with the empirically tested standard model (F) to as many decimal places we can measure it is a perfectly good aim when we've run out of things to test empirically. Which we haven't [3]. 

That brings us back to macroeconomics: macroeconomics doesn't have an F!

Therefore all of the philosophical objections in the NYTimes article do apply to macro ... and there may indeed be a crisis not at its edge, but at its heart if it isn't supported by empirical data.


[1] Classical Yang-Mills is basically defined by the Lagrangian:

L = tr F ∧ ★F

... which should be on the t-shirts instead of Maxwell's equations. Some nice notes on it can be found here.

[2] Ok; that is just the simplest string theory, but you get the point.

[3] A couple of friends of mine put some limits on string theory with a table-top experiment.

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