Progress in science is often based on a close allegiance between theory and experiment. Generations of scientists have searched for ways to describe and explain their view of the world. The idea that all science can be derived from observations and experiments is known as empiricism.
Formally most scientists strive to find models that are both empirical and realistic. Does string theory satisfy these stipulations? At present, no.
Empiricism has become a widely accepted scientific principle. Closely related is the concept of scientific realism, which claims that the world described by science is the real world. This gives us rules for deciding whether to trust our scientific theories. Theories are thrown out if they fail to explain new observations and lauded if they make accurate predictions.
So how can we make progress? After all, strings are far too small to detect: distinctively stringy behaviour, such as higher string harmonics, should occur at energies far beyond those accessible to present colliders. Perhaps it’s a problem of practice rather than principle; we can always just wait for technology to improve.
The methodology of string theory, and other unifying theories, is completely different from that of most other science. They investigate realms that cannot be probed even by our most powerful detectors, and physicists use abstract mathematical tools. Some would say that the concepts are so deep and rich that they must describe nature. But skeptics argue that string theory is currently only a mathematical framework, not a valid theory in itself.
One of the biggest empirical problems string theory faces is underdeterminism. We encounter this issue when we don’t have enough information to pick the correct solution. Imagine trying to connect dots in a child’s drawing book without the numbers to follow, you almost certainly won’t get the correct picture.
There are five possible known string theories. These can be unified in M-theory, but this has a very large number – some estimates give 10500 - of low energy solutions! Primarily these arise from the variety of different ways we could wrap up the six extra dimensions. The web of M-theory links this vast number of solutions, but we have no idea which one describes our reality. Neither the theory nor current technology provide enough information to whittle down the options to the few that represent physics correctly.
One way to deal with underdeterminism is to apply the anthropic principle. This says that some properties of our universe have no deep fundamental origin, but take the values they do purely because if they didn’t, we wouldn’t be here!
This makes it easier to sift through the string theory solutions: we only need to look for ones that model the world we see. But the anthropic principle is a contentious issue in physics. Many complain that a theory shouldn’t predict huge numbers of different solutions for us to pick from, but rather have just one solution that explains why the world is the way it is.
Another issue in string theory that troubles philosophers is duality. Ontological realism makes the intuitive claim that many different objects exist. The properties of these objects do not depend on us and so they would be exactly the same whether we were there or not. But the dualities in string theory directly contradict this by claiming that two completely different physical situations are the same. The properties of the strings depend on the theory we use.
Unifying theories are rife with philosophical problems. We need to decide to what extent the worries of philosophers will help or hinder progress. Will we need to answer more philosophical questions than scientific ones to lead us down the path to unification?