String theory and mathematical fertility

“String theory dominates the research landscape of quantum gravity physics (despite any direct experimental evidence) due to its mathematical fertility. String theory has generated many surprising, useful, and well-confirmed mathematical ‘predictions’ made on the basis of general physical principles entering into string theory. The success of the mathematical predictions are then seen as evidence for the framework that generated them. Smolin argues that if mathematical fertility could be an indicator of truth, then we ought to take the success of knot theory as evidence for the idea that atoms are indeed knotted bits of ether. Hence, we have an apparent reductio ad absurdum of the idea that I am arguing for in this paper, that mathematical fertility might lead us to believe more strongly in a theory. But the fact that Kelvin’s theory was eventually disconfirmed does not mean that it was a bad theory—after all, it was discussed and studied as a serious theory for some 20 years. It was precisely the fact that it was taken seriously as a physical theory that led to the development of knot theory. The physics of knots forms an integral part of modern physics, especially in condensed matter physics, quantum field theory, and quantum gravity.” Dean Rickles, “Mirror Symmetry and Other Miracles in Superstring Theory,” Found. Phys. 2011.

“String theory has not yet been able to make contact with experiments that would give us strong reasons to accept it as the ‘sure winner’ in the race to construct a theory of quantum gravity. However, though experiment can often function as a decisive arbiter in situations where there are several competing theories, there are many more theoretical virtues that play a role in our evaluation of theories. Taking these extraexperimental factors into account, string theory is very virtuous indeed, it is arguably the most mathematically fertile theory of the past century or so. I would go further and say that no direct experiment is likely to ever come about (other than ones that could be explained by multiple approaches), so we can assume that non-experimental factors will have to be relied upon more strongly in our assessments of future research in fundamental physics.”

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