Gerard 't Hooft is searching for a deterministic and local theory to underlie quantum mechanics. By Bell's theorem this should not be possible, but the theorem does have some small print. 't Hooft knows this and says: "one does not have the freedom to do arbitrary measurements at the Planck scale". However, this is no escape, because we still appear to have the freedom to do Bell-type experiments at the macroscopic level, and 't Hooft's theory has to accommodate those experiments too. I am not happy with the solution that the photons know in advance how they are going to be measured since the experimenter's choices were predetermined at the time of the big bang!
I propose another reconcilation of 't Hooft's theory-in-spe with the success of quantum mechanics at explaining the real world: a Bell-inequality violating loophole-free Bell-type experiment can never be carried out because quantum mechanics itself prohibits the required initial conditions - the feasibility to create "to order" a bipartite system of two well separated and well localized components, in close to a Bell entangled state. One could think of this as a kind of uncertainty relation.
I call this point of view "Bell's fifth position" since John Bell listed four possible positions to hold in the light of the theoretical violation of his inequality by quantum mechanics. It turns out that several others hold the same or a similar view : Emilio Santos and Iain Perceval, to mention but two. Bell admitted in a letter to Santos that this fifth position is a logical possibility, though Bell said that he did not expect it to be the answer.
To summarize: it could be that quantum mechanics itself prevents us from carrying out a definitive experiment to prove that there cannot be a local and deterministic theory from which QM emerges. So we will never know; 't Hooft's quest is not doomed from the start; a quantum computer may never succeed in factoring large integers, ... .
To physicists who think this is all stupid I would like to say: well, go ahead then, and perform a loophole free and succesful Bell experiment.
Time, Finite Statistics, and Bell's Fifth Position
http://arxiv.org/pdf/quant-ph/0301059
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“I am not happy with the solution that the photons know in advance how they are going to be measured since the experimenter's choices were predetermined at the time of the big bang!”
I think you are rejecting the most interesting class of hidden variable theories (the deterministic ones) by trying to keep the free-choice assumption.
In my opinion, the experimental violation of Bell’s inequalities forces one to make a choice between determinism+locality+realism and indeterminism+non-locality or indeterminism+non-realism. Of course, the “fifth position” could be valid as well.
It seems natural to me to go with determinism+locality+realism (at least until this path is proven false) as it is in agreement with the classical view and intuitive as well. One must, of course, accept that free-choice is an illusion but this seems to be a very small price to pay in comparison with accepting non-local mechanisms or the impossibility of a mechanism at all (non-realism).
While it is true that any deterministic theory would make everything dependant on the conditions at the time of big-bang one does not need to formulate a deterministic hidden variable theory that way. I would further propose a toy mechanism that could bypass Bell’s theorem without invoking strange conspiracies at big-bang. Three assumptions are needed:
1. a pair of entangled particles is only emitted if two suitable absorbers (detectors) exist. That is, the source will only emit after a signal from the two detectors (containg information about the position/momenta of each quark/electron in them) arrives at the speed of light.
2. the source can extrapolate the state of the two detectors at the time of detection given the available information (this is not something unheard of in physics, we see such extrapolations in electromagnetism – for uniform motion – and general relativity – for both uniform and uniform accelerated motion)
3. the source emits a pair of entangled particles, according to Malus’s law, towards the extrapolated position of the two absorbers.
Whether these assumptions can be used to build a credible interpretation of QM I do not know, it is possible that the math does not allow such an idea to go too far. But as an example of non-conspirational mechanism that it is both local and realistic and gives the required results it should be good enough.
I should add that this mechanism should answer your objections regarding to how it is possible for the source to “guess” the experimenter’s “choice”. The experimenter is a part of a deterministic quark/electron system. Knowledge of the past state of the system allows the source to “extrapolate” the future state.
Regards,
Andrei Bocan
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