The Folklore of the Untestability of String Theory

I recently received an email from an undergraduate after agreeing to give a talk to their society about string cosmology and testing string theory. The undergraduate expressed amazement about being able to test string theory, given the "folklore that it is untestable". I thought this warranted some explanation, obvious to any sensible Bayesian. Here is an extended version of my reply to this student.

I apologise for overstating Bayesian, but I wanted to ram it down the student's throat: you, my discerning readers, may not need so much ramming. I also apologise to any better Bayesians than I for perhaps liberal use of terminology and butchering of concepts.

Firstly, the folklore applies to string theory "as a whole", rather than individual models. I will ignore the obvious point to be made that string theory "as a whole" is a beautiful mathematical framework and testing it is not the point. I will instead approach things as a cosmologist and a Bayesian.

The folklore is too simplistic, in the sense that one can always assume a model and verify its parameters. This is what one always does in a Bayesian philosophy of science, which is manifestly what practicing science actually is. However one is able to construct other models that may have similar consequences. This is often the case in fundamental theory: think of the plethora of models being tested at the LHC! (Although silly particle theorists aren't Bayesians and use silly concepts like the "look elsewhere effect". Tut tut...)

The selection for the models to test, outwith unexpected and contradictory results (lack of concordance, which we all hope and pray for), comes down to a selection based on priors (also Bayesian, except Bayesians choose to recognise them!). These priors are either (arbitrary) prejudice based on intuition, unification etc, or (less arbitrary) priors based on fine tuning and the ability to perform meaningful calculations. String theory and other theories fall into both camps on priors depending on your taste. In my opinion string theory falls into both at once positively and negatively. A Bayesian picks one model and tests it, then compares models to one another.

String theory comes up trumps in (practical) cosmology because it is complete enough to actually give meaningfully testable cosmological models, although many of them. More standard particle theories also give such many models, as can explicitly non-fundamental models. Currently the data cannot tell them apart, therefore a Bayesian accepts both as equally likely modulo the priors. By this I mean that I accept modified gravity is equally as likely as a cosmological constant based on the evidence, but my prior is a hard prejudice that it is not the truth.

An aside on this point: there many theories of modified gravity and field theory Lagrangians. As many as low-energy models based on string theory? More? I don't know: what is the measure on theory space? Clearly all these low-energy theories (paradigms?) fall foul of being "untestable" based on the folklore, which I now hope you are starting to agree is fallacious.

The folklore refers to "complete" theories, so the testable other models referred to above in particle and non-fundamental theory (by which I mean low-energy modifications of gravity) are manifestly not "complete". But then, "completeness" is still an arbitrary prior.

The folklore is applied in an ideal world that may not exist. In this ideal world the many additional parameters needed to turn string theory into a model make it unpalatable (although, as I've said we do measure some of them in the *context* of cosmological models. For example I can construct a stringy model of inflation and use the scalar amplitude to bound some property of the compactification.). In this ideal world one can do experiments at arbitrarily high energy and across all of space time and "test" whatever you like. But this is not the world we live in, certainly in practice, and in fact maybe not even in theory. In theory I mean we cannot do all the experiments required to gain complete knowledge of cosmology. In simple terms this is due to the special relativity fact that events outside your light cone are inaccessible to you. In more refined terms it is boiled up in complex arguments about the existence of observables in quantum gravity in de-Sitter space and eternal inflation.

Anyhoo, practically we are always limited by our finitude and fallibility to not have access to a perfect world of infinite data at the Planck scale, and so we are Bayesians. Comparing models we have and measuring their parameters. Sometimes these models come from string theory, and we may prefer these models to low-energy field theory models for their being part of a larger framework. Or we may not. Model selection with insufficient data is prior driven. But you do need a theory that gives you models to test, and string theory certainly does that in cosmology!