In previous posts, I’ve speculated that quantum Shannon Information Theory might help string theory. String theorists themselves have already made some attempts to apply quantum entanglement and information transmission concepts to the study of Hawking radiation and black holes.
But what about quantum complexity theory and its more applied sibling, quantum computing, can those help string theory too?
Some might say that string theory needs the help. It’s now 43 years old. In that time, thousands of papers have been written about the subject. But no one has yet managed to use string theory to make any precise quantitative predictions that could be used to test its validity. 43 years is a huge amount of time for a physics theory. All preceding, successful, physics theories have demonstrated their validity and worth in much less time than 43 years. String theory, you better hurry. Your biological clock is ticking away. 43 is almost too late to have babies.
String theory claims to be a theory of everything (TOE). I wonder, shouldn’t a TOE overlap significantly with computational complexity theory (CCT)? After all, they both try to determine the limitations and behavior of extremely large and complex things. Furthermore, any physics theory can be viewed as a computation theory and vice versa.
I see smart people like Scott Aaronson studying the rich links between CCT and quantum mechanics. The natural and logical next step would be to study the links between CCT and those elaborations of quantum mechanics that we call quantum field theory and string theory. String theorists are not currently doing this. Currently, top string theorists like Ed Witten use extensively the mathematical tools of differential geometry and group theory, but not those of CCT. Am I a loony for believing that they should be using CCT too?
Maybe CCT motivated constraints can help us formulate string theory in the same way that, for example, requiring general covariance helps us formulate general relativity. For instance, it’s very likely that P!=NP. This is a highly non-trivial observation about our universe, as nontrivial as is the observation that we live in 4-dimensions (at low energies, at least). Can’t CCT observations like P!=NP be used to constrain a TOE? Who knows, perhaps CCT ideas could yield a vacuum selection criterion for string theory.
String Theory Joe, your mission, if you decide to accept it, is to use CCT tools to elucidate string theory. As usual, this blog post will self-destruct in five seconds… Fizz.
P.S. I know very little about either string theory or quantum complexity theory. Therefore, as in that Far Side cartoon where a deer in the crosshairs is pointing at a nearby deer, I defer any questions about this topic to Scott Aaronson and professional string theorists.