Dear Aleks, On one hand I like very much your example and discussion, but on the other hand I do not think that your example can be used to illustrate the situation with Bell´s inequality.
Aleks:> Bell\'s formulation implies that the hidden variable is independent of> the configuration of the detectors. On the other hand, if we allow > for > the fact that the hidden variable is dependent on the mutual > configuration, then there is no need to abandon the classical> framework. Andrei:I completely agree with this viewpoint. > To some extent this does imply some sort of non-locality. But it is > the > same type of non-locality as in a perfectly classical context. Let me> describe an experiment. Andrei: I completely agree with this viewpoint. Andrei: But regarding the experiment -- see my comment after your description of the experiment. Aleks:> Imagine a bathtub. Imagine primitive measurement technology that > involves putting person A in the water so that his nose is aligned > with > the water. He is measuring the incoming waves, and outputs 1 when a > wave > splashes into his eyes, and 0 otherwise. There is another person B > measuring in the same way on the other side of the bathtub. You can > change the orientation of both people, and this will clearly affect > the > frequency of water splashing into their eyes. Now throw a stone in > the > bathtub, creating an entangled pair of wavefronts propagating in both> > directions. Measure the correlation of splashes into person A\'s eyes> and > person B\'s eyes. > There are three interpretations of the resulting correlations of > splashes:> * (QM) The waves are in a superposition of splashing and > not-splashing, > until person A experiences a splash or not-splash, and collapses the > wave function. The collapse telepathically \"informs-at-a-distance\" > the > other entangled wavefront whether person B will experience a splash> or not. > * (New Age) The two detectors are not independent - they are an > entangled pair in the aether of global consciousness, with the > incredible ability of transmitting thoughts at a distance. > > * (classical) The fact that two people are in a bathtub with their> big > measuring apparatuses (bodies, noses and eyes) will affect the joint > distribution of splashes. The position of one person will affect the > measurements experienced by the other person, because it affects the > shape of the body of water in which the wavefronts propagate. Andrei: Unfortunately, you would not be able to violate Bell\'s inequality in this way. Although you use waves, these are classical waves. The crucial difference between the classical wave mechanics and quantum wave mechanics is that the system of two classical waves is still described by the wave on the same three dimensional physical space, but in the quantum case (and this was first time emphasized by Schrodinger) the corresponding equation for the the system of two quantum waves, <<quantum particles>>, is written on the R^6 and not on the physical space R^3. Essentially this is responsible for a special quantum correlations and the violation of Bell\'s inequality. So if you like the source of nonlocality is already in Schrodinger equation. Therefore I am not much excited by the Bell inequality. However, one may say: well we have a rather strange description of quantum waves-particles, namely, by using the tensor product of Hilbert spaces to describe composite systems, but it may be, nevertheless, a purely classical and local model behind this? Of course, Bell would say you: not at all. But I say: it seems yes. And here I would like to follow precisely your argument:>if we allow > for > the fact that the hidden variable is dependent on the mutual > configuration, then there is no need to abandon the classical> framework. There is one thing that couple both detectors. This is nothing else than time. In all experiments there is such a thing as TIME WINDOW and experimenter identify two clicks as belonging to an entangled pair if these clicks are inside the time window. There is no other way to identify a pair. We do not know times of emissions from the cristal. Moreover, particles (considered as entangled and belonging to the same pair) can be emited by different atoms. This time window couple two detectors or I would like to say determine unification of two local contexts of measurements. If there are two fixed orientations A and B in lab1 and lab2, respectively, then by using the time window we identify a special series of clicks in labs, so we extract a special ensemble S_AB of particles. If we choose another orientations, say C and D, then through the time window we shall get another ensemble S_CD. If the situation is really such and ensembles are really statistically different, then this gives us purely classical explanation of the violation of Bell\'s inequality. However, it is common to say that S_AB has the same statistical properties as S_CD. This is so called FAIR SAMPLING ASSUMPTION. I thing it is not justified, see http://www.arxiv.org/abs/quant-ph/0309010 [Experimental Scheme to Test the Fair Sampling Assumption in EPR-Bell Experiments] The main problem for me: to find such a dependence of statistics on experimental settings in other domains of science. May be somebody could come with some ideas? With Best Regards, Andrei Khrennikov Director of International Center for Mathematical Modeling in Physics, Engineering, Economy and Cognitive Sc., University of Vaxjo, Sweden _______________________________________________ fis mailing list fis@listas.unizar.es http://webmail.unizar.es/mailman/listinfo/fis
