We do not yet fully understand string theory. In particular physicists lack the defining mathematics for much of M-theory. Without this machinery the puzzle is far from complete and our limited comprehension restricts the predictive power of the theory.
It may be decades before we have a reliable map of the string theory landscape. Perhaps in hindsight we‚Äôll see a much simpler mathematical approach. On the other hand, M-theory may forever be shrouded by complex computations. Some would argue that there‚Äôs no place for messy calculations in a perfect theory.
At present string theory has produced no testable experimental predictions. In the eyes of many scientists this renders string research unscientific: without experimental proof string theory becomes a mere intellectual exercise. We can only hope that future work will provide some progress on this front.
There remain many basic questions to which we have no answers.
Has string theory some deep underlying principle? Such an idea is certainly appealing: it would better organise the diverse elements of the theory. And it might clarify why strings are the fundamental objects of nature, rather than just a convenient concept.
What are the fundamental equations of space and time? String theory is normally formulated with a fixed background spacetime, a background-dependent approach. It would be preferable to have a form of the equations which makes no reference to the background. The associated theory would be genuinely¬†non-perturbative¬†and could provide further insight into M-theory. In a non-quantum setting, Einstein’s theory of¬†gravity¬†generates the geometry of spacetime. Can this be replicated in the quantum regime?
Will we need a new theory of quantum mechanics? String theory assumes the standard rules of quantum mechanics. But some think that this modus operandi may be lacking. Just as Newtonian mechanics was overthrown by new quantum laws, quantum mechanics may itself be¬†superseded. If so, we would have to think differently about string theory.
Finally there are some things that strings struggle to master. Like dark energy. This is a hypothetical form of energy, smeared across the cosmos. In principle present in Einstein’s equations but long believed to vanish, cosmologists found they required it to account for the accelerating expansion of the universe. If string theory is the ultimate theory, it should surely shed some light on this mysterious quantity. But so far nobody has come up with a satisfying stringy interpretation.
Sometimes problems hint at real trouble ahead; other times they merely highlight insufficient scientific thinking.¬†It may be that string theory emerges victorious from these travails. But perhaps we need a different interpretation altogether.