Does God Play Dice? is not a treatise on religion and gambling, but is instead Gerard ‘t Hooft’s submission to
Physics Today Physics World concerning the reconcilliation of quantum theory with general relativity. The most interesting part of this short note is not that ‘t Hooft comes out squarely on the side of hidden variable theories, but instead in his description of an idea for how general relativity might arise in such a theory:
An even more daring proposition is that perhaps also general relativity does not appear in the formalism of the ultimate equations of nature. This journal does not allow me the space to explain in full detail what I have in mind. At the risk of not being understood at all, I’ll summarize my explanation. In making the transition from a deterministic theory to a statistical treatment — read: a quantum mechanical one —, one may find that the quantum description develops much more symmetries than the, deeper lying, deterministic one. If, classically, two different states evolve into the same final state, then quantum mechanically they will be indistinguishable. This induces symmetries not present in the initial laws. General coordinate covariance could be just such a symmetry.
That general coordinate covariance may not be fundamental but is instead a product of our inability to access the beables of a theory seems like quite an interesting idea. It would be interesting to think if this type of hidden variable theory, which is not totally general because it needs to recover the general coordinate covariance, is indeed large enough to be consistent with quantum theory. I.e. in the same way the Bell’s theorem rules out local hidden variable theories, is there a similar theorem ruling out ‘t Hooft’s property? I certainly have no inclination about the answer to this question in either direction.
Of further interest, ‘t Hooft claims as motivation for his perspective the following
Nature provides us with one indication perhaps pointing in this direction: the unnatural, tiny value of the cosmological constant. It indicates that the universe has the propensity of staying flat. Why? No generally invariant theory can explain it. Yet, if an underlying, deterministic description naturally features some preferred flat coordinate frame, the puzzle will cease to perplex us.
Finally, for no reason but to turn some portion of the readers of this blog happy and the other portion of this blog angry, here is ‘t Hooft on string theory:
I am definitely unhappy with the answers that string theory seems to suggest to us. String theory seems to be telling us to believe in “magic”: duality theorems, not properly understood, should allow us to predict amplitudes without proper local or causal structures. In physics, “magic” is synonymous to “deceit”; you rely on magic if you don’t understand what it is that is really going on. This should not be accepted.
I wish I understood what ‘t Hooft means in this critique by “proper local or causal structures.”