Ex-string theorist turned philosopher Richard Dawid has become known over the years for his arguments that string theory is a theory to be evaluated not by the conventional scientific method, in which experiment plays a role, but by “post-empirical theory assessment” methods. He has a book about this, and I’ve written about his arguments here, here and here.

Today he has a new paper out, entitled Chronic Incompleteness, Final Theory Claims, and the Lack of Free Parameters in String theory, which tries to address the “chronic incompleteness” problem of string theory’s claim to be a complete unified theory. This problem is starting to look very serious:

Rather than bringing the time horizon for the completion of fundamental physics from virtual infinity to somewhere within our lifetime, string theory’s final theory claim seems to be associated with an extension of the time horizon for the completion of this particular theory that may, once again, virtually reach towards infinity.

In other words, there’s a chronic problem of string theorists not being able to tell us what the theory actually is, and now it’s looking like they’ll never be able to do so. Dawid is right that this is the root of the problem, not usual excuses like “it predicts stuff, but you’d need an accelerator as big as the galaxy to test these predictions” or “the equations are just too hard to solve”.

One question here is that of defining what “string theory” even means anymore. Dawid does the best he can with this in a footnote:

Here as throughout the entire paper, the term ‘string theory’, if not specified otherwise, denotes the overall theory that aims at describing the observed world and is identified by the present knowledge on perturbative superstring theory, duality relations, etc.

This isn’t exactly a precise definition, it’s basically just “string theory is a conjectural theory with a certain list of properties which I’m not going to even try and describe, since that would get really complicated and different people likely have different lists”.

In the main text, Dawid explains that “string theory has no fundamental dimensionless free parameters”, a claim often made that I’ve always found kind of baffling. If you don’t know what the theory is, how do you know that it doesn’t have free parameters??? He makes a great deal of this assumption, adding in the argument that this lack of parameters means no classical limit, and I guess thus no formulation of the theory as “quantization” of something describable in classical terms.

I don’t really see what the big deal is about having a quantum system that is not defined as the quantization of some classical system. A simple example of such a system is the qubit that we often start teaching quantum mechanics with. Somehow Dawid wants to get from “not quantization of a classical system” to “we can’t ever hope to write down the theory”, but I don’t see how this follows.

He examines various possibilities for how the problem of no fundamental theory can be resolved. His alternative C is the obvious one: we just haven’t found it yet. He would like to argue that this might not be right, that string theory is a new and different kind of science:

…string theory and the conceptual context within which it is developed is in a number of ways substantially different from anything physicists have

witnessed up to this point. Therefore, it is far from clear whether prevalent physical intuitions as to which kinds of questions can be expected to have a fully calculable theoretical answer are applicable in this case. It seems

difficult to rule out that what seems to be a question that finds a fully calculable theoretical answer in fact rather resembles the case of the leaf carried by autumn winds and just defies calculation.

Dawid seems to argue that string theory may be an example of what he calls alternative A:

Even in principle, there exists no mathematical scheme that is empirically equivalent to string theory and generates quantitative results that specify the fundamental dynamics of the theory. In that case, the fundamental theory is conceptually incomplete by its very nature. It has no fundamental dynamics and no set of solutions that can be deduced from its first principles. The fundamental theory merely serves as a conceptual shell that embeds low energy descriptions (ground states of the theory) consistent with the principles encoded in the fundamental theory. Those low energy descriptions contain specified parameter values and do generate quantitative results. But there is no way to establish from first principles how probable specific ground states of the system are.

His summary of his vision of string theory is as follows:

Full access to a theory without free parameters thus might be expected to require representations that don’t have their own classical limit. The fact that they cannot be developed by generalizing away from a classical limit seems to impede the full formulation of a final theory even once one has found it. The resulting idea of a fundamental theory whose full formulation is hidden from the physicists’ grasp because its most adequate representation lacks intuitive roots has even more radical rivals, which amount to questioning the possibility of calculating the dynamics of the fundamental theory either within the bounds of human calculational power or as a matter of principle.

At one point Dawid acknowledges that some people have drawn the obvious conclusion about the current situation, the one consistent with our usual understanding of science:

It has been suggested by various exponents and observers of contemporary fundamental physics (see e.g. Smolin 2003, Woit 2003, Hossenfelder 2018) that the chronic incompleteness of string theory represents a substantial failure of the research program that is indicative of a strategical problem that has afflicted fundamental physics in recent decades.

He doesn’t like this conclusion, so argues that this time it’s different:

Considering the range and character of the very substantial differences that set the current state of fundamental physics apart from any previous stage in the history of physics, there is little reason to expect that theory building at the present stage can be judged according to criteria that seemed adequate in the past.

While he doesn’t say so, this argument takes him back to the problem of how one is to judge “string theory”, but taking a position even more radical than his earlier one. The argument now seems to be that we’re supposed to consider accepting as the final, fundamental theory of physics, a “theory” that is not just untestable, but is a “chronically incomplete” framework based on something we can never hope to define or understand. I’m having trouble understanding why this is supposed to be science rather than another human endeavor that it looks a lot more like, theology.