Question

So Gerard 't Hooft has a brand new paper (thanks to Mitchell Porter for making me aware of it) so this is somewhat of a expansion to the question I posed on this site a month or so ago regarding 't Hoofts work.

Now he has taken it quite a big step further: http://arxiv.org/abs/1207.3612

Does anyone here consider the ideas put forth in this paper plausible? And if not, could you explain exactly why not?

Answer 1

I only see these writings now, since usually I ignore blogs. For good reason, because here also, the commentaries are written in haste, long before their authors really took the time to think.

My claim is simple, as explained umpteen times in my papers: I construct REAL quantum mechanics out of CA like models. I DO have problems of a mathematical nature, but these are infinitely more subtle than what you people are complaining about. These mathematical problems are the reason why I try to phrase things with care, trying not to overstate my case. The claim is that the difficulties that are still there have nothing to do with Bell's inequalities, or the psychological problems people have with entangled states.

Even in any REAL QM theory, once you have a basis of states in which the evolution law is a permutator, the complex phases of the states in this basis cease to have any physical significance. If you limit your measurements to measuring which of these basis states you are in, the amplitudes are all you need, so we can choose the phases at will. Assuming that such CA models might describe the real world amounts to assume that measurements of the CA are all you need to find out what happens in the macro world. Indeed, the models I look at have so much internal structure that it is highly unlikely that you would need to measure anything more. I don't think one has to worry that the needle of some measuring device would not be big enough to affect any of the CA modes. If it does, then that's all I need.

So, in the CA, the phases don't matter. However, you CAN define operators, as many as you like. This, I found, one has to do. Think of the evolution operator. It is a permutator. A most useful thing to do mathematically, is to investigate how eigenstates behave. Indeed, in the real world we only look at states where the energy (of particles, atoms and the like) is much below the Planck energy, so indeed, in practice, we select out states that are close to the eigenstates of the evolution operator, or equivalently, the Hamiltonian.

All I suggest is, well, let's look at such states. How do they evolve? Well, because they are eigenstates, yes, they now do contain phases. Manmade ones, but that's alright. As soon as you consider SUCH states, relative phases, superposition, and everything else quantum, suddenly becomes relevant. Just like in the real world. In fact, operators are extremely useful to construct large scale solutions of cellular automata, as I demonstrated (for instance using BCH). The proper thing to do mathematically, is to arrange the solutions in the form of templates, whose superpositions form the complete set of solutions of the system you are investigating. My theory is that electrons, photons, everything we are used to in quantum theory, are nothing but templates.

Now if these automata are too chaotic at too tiny Planckian scales, then working with them becomes awkward, and this is why I began to look at systems where the small scale structure, to some extent, is integrable. That works in 1+1 dimensions because you have right movers and left movers. And now it so happens that this works fantastically well in string theory, which has 1+1 dimensional underlying math.

Maybe die-hard string theorists are not interested, amused or surprised, but I am. If you just take the world sheet of the string, you can make all of qm disappear; if you arrange the target space variables carefully, you find that it all matches if this target space takes the form of a lattice with lattice mesh length equal to 2 pi times square root of alphaprime.

Yes, you may attack me with Bell's inequalities. They are puzzling, aren't they? But please remember that, as in all no-go theorems that we have seen in physics, their weakest part is on page one, line one, the assumptions. As became clear in my CA work, there is a large redundancy in the definition of the phases of wave functions. When people describe a physical experiment they usually assume they know the phases. So, in handling an experiment concerning Bells's inequalities, it is taken for granted (sorry: assumed) that if you have measured one operator, say the z component of a spin, then an other operator, say the x component, will have some value if that had been measured instead. That's totally wrong. In terms of the underlying CA variables, there are no measurable non-commuting operators. There are only the templates, whose phases are arbitrary. If you aren't able to measure the x component (of a spin) because you did measure the z component, then there is no x component, because the phases were ill-defined.

Still, you can ask what actually happens when an Aspect like experiment is done. In arguments about this, I sometimes invoke "super determinism", which states that, if you want to change your mind about what to measure, because you have "free will", then this change of mind always has its roots in the past, all the way to time -> minus infinity, whether you like it or not. The cellular automaton states cannot be the same as in the other case where you did not change your mind. Some of the templates you use have to be chosen different, and so the arbitrary phases cannot be ignored.

But if you don't buy anything of the above, the simple straight argument is that I construct real honest-to-god quantum mechanics. Since that ignores Bell's inequalities, that should put the argument to an end. They are violated.