According to particle physics, the fundamental building blocks of the universe are point-like particles, essentially small dots of energy with no dimension. String theory posits that these dots are actually minuscule vibrating loops of energy. A violin string vibrating at different frequencies produces different musical notes; similarly these filaments are said to be able to vibrate at different frequencies, each one creating a different particle of our universe. One note is an electron, another is a photon, and so on.
String theory hasn’t been proven — it hasn’t made any testable predictions so far, in fact. Yet it exists because scientists are looking for a ‘theory of everything’: a single theory that can explain both gravity and quantum physics. At present these two theories together explain their particular domains very well but scientists don’t know how they fit together. String theory is one of a few theory programmes trying to reconcile them; others include loop quantum gravity and twistor theory.
On January 7, scientists from Hungary, Israel, and the US published a curious paper in Nature. Stumped by the complex shapes of neurons, they reportedly found a solution in some arcane equations in string theory and, according to them, the equations also describe how blood vessels and neurons branch.
If you were an engineer designing the wiring for a brain or a vascular system, you’d probably try to save money by using the least amount of wire possible. For a long time, biologists assumed nature ‘thought’ the same way. According to this paper, however, it doesn’t, at least not necessarily. The researchers analysed high-resolution 3D scans of neurons, blood vessels, and fungi and showed that biological networks don’t care about minimising length but about minimising surface area. And to figure out the complex geometry of how these tubelike structures connect, the researchers borrowed the maths of interacting strings.
The scientific method says that if you can’t prove something with an experiment, it isn’t science. The problem for string theory is that it describes a part of space so small and so fleeting that no machine we can currently build could ever study it. Yet many physicists have stuck with it because, even though it remains entirely mathematical, they’ve glimpsed deep connections between its equations and structures and other branches of mathematics and physics. According to the physicists these connections are signs that string theory contains ‘truths’ worth exploring more and due to which it can’t simply be dismissed out of hand.
On the other hand we also have scientists like Peter Woit who have lamented, repeatedly, that string theory is a dead-end, that despite all of its mathematical elegance and structure the fact that it hasn’t made a testable prediction, and doesn’t seem like it will for the foreseeable future, it’s been a drain on physicists’ time and intelligence. Over the years however, neither side has been able to persuade or dissuade the other, and today many criticisms have hardened into denial and vitriol.
Stockholm University philosopher Richard Dawid published a provocative book in 2013 that, despite its seemingly reconciliatory premise, entrenched these divisions. In the text, titled String Theory and the Scientific Method, based on a small conference he’d conducted a short while earlier, Dawid argued that the history of science is witness to a revolution in how scientific truth can be redefined. (American philosopher and biologist Massimo Pigliucci’s essay in Aeon on the conference and how philosophy can help with science’s demarcation problem is also worth a read.) He proposed that in the absence of empirical data, experts must rely on non-empirical evidence, like the sheer mathematical elegance of a theory or the fact that no one can find a better alternative. That is, he seemed to say, a theory could be true because it’s too ‘good’ to be wrong.
I’m partial to criticisms of the book, especially those advanced by George Ellis, Joe Silk, Sabine Hossenfelder, and Carlo Rovelli, rather than the book itself.
Ellis and Silk, both cosmologists, argued that Dawid’s push for “non-empirical theory assessment” (which he prefers to “post-empirical science”) is dangerous for suggesting that a theory can be validated by its ‘elegance’ or its power to explain something post facto. The danger here is that if you move these goalposts you also let in pseudoscience. Hossenfelder, a physicist, took aim at Dawid’s argument that string theory must be true because scientists haven’t found another option that’s equally good. According to her, claiming there are no alternatives is a sociological observation rather than scientific proof, i.e. that scientists can’t imagine an alternative today doesn’t mean one doesn’t exist. It may simply be a lack of imagination, of funding for rival approaches or even of groupthink within the academic community.
Third, Rovelli, also a physicist and a cofounder of loop quantum gravity, argued that the history of science is littered with beautiful, mathematically coherent theories that turned out to be wrong. He also posited that Dawid’s “unexpected explanatory coherence”, i.e. when a theory solves problems it wasn’t built to solve, is often a result of confirmation bias and that once a community is deeply invested in a mathematical framework, it will inevitably find internal connections that look ‘miraculous’ but have no bearing on physical reality.
Hossenfelder’s and Rovelli’s criticisms also help to see the problems with using the new Nature paper to claim it verifies or legitimises the pursuit of string theory in any meaningful way. Its authors show that the mathematics of string theory handles problems in which you need to minimise the surface area very well, but this shouldn’t be surprising, as Rovelli has argued. Complex maths is often useful in disparate fields but just because calculus describes both the orbit of planets and the marginal cost of gizmos doesn’t mean gravity holds the economy together.
Similarly, that string theory describes the branching of neurons doesn’t mean the universe is fundamentally made of vibrating strings. The only way to know the latter is if the theory unifies the principles of quantum mechanics with gravity and makes a testable prediction.
The paper’s authors themselves, while taking care to temper their claims regarding the physical reality of string theory, have also expressed optimism about its mathematical necessity. They’ve called their finding a “formal mapping between surface minimisation and high-dimensional Feynman diagrams” and say they’re taking “advantage of a well-developed string-theoretical toolset”. They also clarify that they’re removing the fundamental physical properties usually associated with string theory as a ‘theory of everything’ and instead treating the matter at hand as a very difficult geometry problem. Then, however, they strongly imply that the mathematics of string theory is essential to solving this problem.
Now, is it possible to reconcile the (demonstrated) usefulness of the string theory toolkit with Rovelli’s and Hossenfelder’s criticisms? Specifically, setting aside for a moment the fact that the new study treats the maths of string theory as a toolkit: while solving the problem doesn’t ‘prove’ string theory in any meaningful way, how does one reconcile the notion that string theorists indeed developed this mathematical toolkit with Rovelli’s criticism? Is it possible to argue that only string theory could have discovered this toolkit despite Hossenfelder’s criticisms or is it possible to conclude in a reasonable way that we simply use the complex mathematics and discard the rest?
I think this entails distinguishing between the mathematical machinery and the physical claims. Rovelli’s position isn’t that string theory mathematics are ‘wrong’ or ‘useless’ but rather that internal consistency and mathematical elegance alone don’t constitute empirical proof of quantum gravity. So the fact that string theorists developed a toolkit that can solve problems in biology doesn’t contradict Rovelli, in fact it arguably supports his view that string theory has become a rich mathematical framework. The act of reconciliation lies here in accepting that string theorists spent decades exploring the geometry of interacting surfaces (which they call “worldsheets”).
Second, vis-à-vis Hossenfelder’s pushback to Dawid’s argument that there are no equally good alternatives to string theory, it also seems physically as well as historically risky to argue that only string theory could have discovered these tools. A mathematician focusing purely on topology or differential geometry could likely have arrived at similar tools without positing 10 dimensions or supersymmetry. In this sense string theory has simply been a historical catalyst, an ‘engine’ that seems to have accelerated humans’ approach to the toolkit that they subsequently used to solve a particular problem in brain biology.
I’m generally wary of non-empirical assertions, so perhaps a scientifically robust position for me to take is the instrumentalist rather than the realist view: i.e. to conclude we can use the mathematics and discard the physical dogma. This way I retain the formalism, which is the calculus of optimising 3D surfaces, because it works for the data, while rejecting the ontology, i.e. the idea that the universe is fundamentally composed of strings.