was Wolfram right after all?

Recently, Gerard 't Hooft published his own version of superstring theory.

"Ideas presented in two earlier papers are applied to string theory. ... We now also show that a cellular automaton in 1+1 dimensions that processes only ones and zeros, can be mapped onto a fermionic quantum field theory in a similar way. The natural system to apply all of this to is superstring theory ..." (*)

The earlier papers he refers to describe a duality between a deterministic cellular automaton and a bosonic quantum field theory in 1+1 dimensions and argue that Born's rule strongly points towards determinism underlying quantum mechanics (x).

All this is far from the mainstream, but 't Hooft is a physicist not a crackpot and so he points out problems of his proposal(s) in his papers, e.g. he notes that some of his models have an unbounded Hamiltonian and he does discuss the apparent contradiction with Bell's inequality.

(*) It is known for a long time that the Ising model is equivalent to a fermionic field in 2 dimensions (see e.g. this paper for references).

(x) Quantum theory without the Copenhagen 'collapse' is a deterministic theory, so it is not too surprising if one finds such a duality. But it is unusual that Born's rule 'strongly points towards' determinism.


Anonymous said...

Every theory that can be simulated on a computer can be mapped to a deterministic system that processes only ones and zeros.

wolfgang said...

Yes, but the (pseudo)random number generator is the weak part of this equivalence. But of course we could be living in The Matrix (see previous post).

If the equivalence/duality proposed by 't Hooft is interesting, then only because it is based on a direct mapping, which can be described with a handful of equations.