A simple two-page proof of local realism
Posted: Wed Feb 12, 2014 2:37 pm
As some of you may know, I have written up a very simple two-page proof of Einstein's local realism: http://libertesphilosophica.info/blog/w ... 1/EPRB.pdf.
Bell's theorem supposed to have proved that it is impossible to produce the EPR-Bohm correlation purely locally, with or without determinism. But the above model proves otherwise (I thank Michel Fodje and John Reed for producing the cited simulations of the model). Further details of the proof, an extensive discussion on the origins of *ALL* quantum correlations, and the specifics of an experimental test of my hypothesis, can be found on my blog: http://libertesphilosophica.info/blog/.
It is very important to realize that the above simple proof of local realism is the end of the road for Bell's theorem. There is no way out for the supporters of Bell's theorem. Let me explain this for the benefit of those unfamiliar with the subject and those who are declining to see the logical power of elementary mathematics:
Bell's argument is exceedingly simple to understand. He argued that no functions of the form A(a, L) = +1 or -1 and B(b, L) = +1 or -1 can reproduce the EPR-Bohm correlation. Here a and b are local experimental parameters, chosen freely by Alice and Bob, who are space-like separated from each other, and L is a common cause shared by both of them. Thus L is a hidden variable, or initial state, or complete state, that deterministically determines the outcomes A and B of the measurements made by Alice and Bob. It is not difficult to see that the functions A(a, L) = +1 or -1 and B(b, L) = +1 or -1 are manifestly local. A(a, L) does not depend on either b or B, and likewise B(b, L) does not depend on either a or A. Moreover, L can be anything one wants. It can be a single variable, or a set of variables, or even a mixed set of discrete or continuous functions. It simply does not matter what L is, as long as it remains confined to the overlap in the backward light-cones of Alice and Bob (cf. the figure in my two-page proof linked above). So, as you can see, nothing can be more clear and transparent than the locality of the functions A(a, L) and B(b, L).
Now, as I noted, Bell's claim is that no such functions can reproduce the EPR-Bohm correlation predicted by quantum mechanics. More precisely, Bell claimed that the product moment E(a, b) = 1/n Sum_i^n { A(a, L^i) B(b, L^i) } cannot be equal to -cosine(a, b) for any such functions A(a, L) and B(b, L), no matter how large the n is.
But it is not difficult to see from the two-page document linked above that this claim is simply false. You might better appreciate what I am saying if you take a look at this supporting document: http://libertesphilosophica.info/blog/w ... mplete.pdf. But even without the backing of this document it is quite easy to see from my two-page proof that Bell's claim is simply wrong. You may now wonder why, then, is there still so much determined resistance to accept this elementary mathematical demonstration? Well, to understand that you may have to consult some sociologists of science. Or better still, read "The Golem" by Harry Collins and Trevor Pinch.
Joy Christian
Bell's theorem supposed to have proved that it is impossible to produce the EPR-Bohm correlation purely locally, with or without determinism. But the above model proves otherwise (I thank Michel Fodje and John Reed for producing the cited simulations of the model). Further details of the proof, an extensive discussion on the origins of *ALL* quantum correlations, and the specifics of an experimental test of my hypothesis, can be found on my blog: http://libertesphilosophica.info/blog/.
It is very important to realize that the above simple proof of local realism is the end of the road for Bell's theorem. There is no way out for the supporters of Bell's theorem. Let me explain this for the benefit of those unfamiliar with the subject and those who are declining to see the logical power of elementary mathematics:
Bell's argument is exceedingly simple to understand. He argued that no functions of the form A(a, L) = +1 or -1 and B(b, L) = +1 or -1 can reproduce the EPR-Bohm correlation. Here a and b are local experimental parameters, chosen freely by Alice and Bob, who are space-like separated from each other, and L is a common cause shared by both of them. Thus L is a hidden variable, or initial state, or complete state, that deterministically determines the outcomes A and B of the measurements made by Alice and Bob. It is not difficult to see that the functions A(a, L) = +1 or -1 and B(b, L) = +1 or -1 are manifestly local. A(a, L) does not depend on either b or B, and likewise B(b, L) does not depend on either a or A. Moreover, L can be anything one wants. It can be a single variable, or a set of variables, or even a mixed set of discrete or continuous functions. It simply does not matter what L is, as long as it remains confined to the overlap in the backward light-cones of Alice and Bob (cf. the figure in my two-page proof linked above). So, as you can see, nothing can be more clear and transparent than the locality of the functions A(a, L) and B(b, L).
Now, as I noted, Bell's claim is that no such functions can reproduce the EPR-Bohm correlation predicted by quantum mechanics. More precisely, Bell claimed that the product moment E(a, b) = 1/n Sum_i^n { A(a, L^i) B(b, L^i) } cannot be equal to -cosine(a, b) for any such functions A(a, L) and B(b, L), no matter how large the n is.
But it is not difficult to see from the two-page document linked above that this claim is simply false. You might better appreciate what I am saying if you take a look at this supporting document: http://libertesphilosophica.info/blog/w ... mplete.pdf. But even without the backing of this document it is quite easy to see from my two-page proof that Bell's claim is simply wrong. You may now wonder why, then, is there still so much determined resistance to accept this elementary mathematical demonstration? Well, to understand that you may have to consult some sociologists of science. Or better still, read "The Golem" by Harry Collins and Trevor Pinch.
Joy Christian