Applications of

Quantum Mechanics

Quantum Mechanics

Implications of

Quantum Mechanics

Quantum Mechanics

36. Bell-Aspect Experiments. Non-Locality.

Summary

Bell showed theoretically and Aspect demonstrated experimentally that there can be no local hidden variable theory underlying quantum mechanics.

In 1964, Bell (Ref. 5) proved that if all the ‘information’ regarding a particle-like state was contained locally, say within a millimeter of the localized wave function, then there would be a conflict with quantum mechanics. In particular, he showed that if two particles, electrons or photons, were initially in a bound spin 0 state which split into two single-particle states that moved away from each other, there would be correlations between the two measured spin or polarization states that would be different from what quantum mechanics predicted. This experiment has been done by Aspect (Ref. 5) and others, and it was found that the results agreed with the results predicted by quantum mechanics but violated the inequalities in Bell’s ‘locality’ theorem. Thus we have a proof that there can be no

*local*hidden variable theories (in which the hidden variables carry the ‘information’ about the state of the system).

In interpreting the results of this experiment, it is often assumed there are (localized) particles. Under that assumption, one needs instantaneous long-range signaling between the particles to account for the non-local correlations in the Aspect experiment. But if there are no particles, which is our conclusion in No Evidence for Particles, there is no need for signaling; it is just quantum mechanics as usual, with its

*inherent*non-locality.

Non-locality via the wave function. With all due respect to Bell—he started a major line of inquiry in quantum mechanics—it seems to me that one could reasonably expect hidden variable theories to be non-local, in contrast to Bell’s assumption. First, one knows that the wave functions of quantum mechanics contain non-local information; the Aspect experiment and theory tell us that. Second, we see from the Bohm Hidden Variable model that the hidden variables can depend locally on the wave function (velocities in that model are derivatives of the local phase angle of the wave function). So one could imagine a hidden variable theory in which there is indirect non-locality; each of the hidden variable sets for the two particle-like states takes its informationCorrelations vs. ‘influence.’ On the surface, it looks like the measurement on one ‘particle’ influences the state of the distant ‘particle.’ But if there are no particles, and if there is no collapse, then detection of the state of one particle-like wave function does not in any way affect or influence the quantum state of the second, distant particle-like wave function. All we can say is there is alocallyfrom thewave function. But because the wave function contains non-local information, the conditions for Bell’s theorem no longer apply. Thus there are reasonable objections to Bell’s locality assumption for hidden variable theories.

*correlation*between the measurements on the two distant particle-like wave functions.