Hidden VariablesDavid Bohm in 1951 and 1952 proposed "hidden variables" as a way to explain the apparent "nonlocality" of simultaneous measurements of the entangled spins of electrons that are separated at a great distance. The hidden variables provide the information needed at the distant “entangled” particle, so it can coordinate its properties perfectly with the “local” particle. The hidden variables are thought to be "local," traveling with the particles to exert an "influence" on the particles that can explain their perfect correlations. Bohm wrote in 1952,
The usual interpretation of the quantum theory is based on an assumption having very far-reaching implications, ~i.e., that the physical state of an individual system is completely specified by a wave function that determines only the probabilities of actual results that can be obtained in a statistical ensemble of similar experiments. This assumption has been the object of severe criticisms, notably on the part of Einstein, who has always believed that, even at the quantum level, there must exist precisely definable elements or dynamical variables determining (as in classical physics) the actual behavior of each individual system, and not merely its probable behavior. Since these elements or variables are not now included in the quantum theory and have not yet been detected experimentally, Einstein has always regarded the present form of the quantum theory as incomplete, although he admits its internal consistency.Because 1) the measurements are simultaneous, because 2) the particles are in a "space-like" separation, because 3) the spins are randomly up or down according to the uncertainty principle of quantum mechanics, and because 4) measurement of each particle changes the electron spin direction to be aligned with the Stern-Gerlach measuring device, it is mistakenly thought that measurements would result in outcomes that are randomly + -, - +, + +, and - -. Some mechanism is thought to be needed to ensure that only perfectly opposite spins of + - and - + are observed. Since the particles are in a space-like separation, any "action-at-a-distance" to ensure their spins are opposite would have to be faster than the speed of light, so impossible. John Bell in 1964 developed a theorem and proposed an experiment that he said could distinguish between the predictions of "local hidden variables" and standard quantum mechanics. In the years since, hundreds of such experiments have proved that no such "local hidden variables" exist. We propose that just before their simultaneous measurements, the two-particle wave function describing the particles has no preferred direction of spins and total spin angular momentum zero, conserving total spin from the spherically symmetric wave function at initial entanglement. We call this constant spin zero a "hidden constant of the motion." It is not a "hidden variable" that must act at a distance, but a "hidden constant," the jointly shared property of the two particles, true from their initial state preparation, that provides the conditions needed to measure their spins as + - and - +, provided the two measuring devices are perfectly aligned (by prior agreement).
ReferencesBelinfante, F. J. (1973) A Survey of Hidden-Variable Theories, Pergamon Press. Bohm, D. (1951) Quantum Theory. Prentice-Hall. Bohm, D. (1952) A Suggested Interpretation of the Quantum Theory in Terms of "Hidden" Variables. I ______, A Suggested Interpretation of the Quantum Theory in Terms of "Hidden" Variables. II Bohm, D. and Y. Aharononov (1957) Discussion of Experimental Proof for the Paradox of Einstein, Rosen, and Podolsky Einstein A., B.Podolsky, and N. Rosen (1935) "Can Quantum-mechanical Description of Physical Reality Be Considered Complete?," Quantum Theory and Measurement, Ed. Wheeler and Zurek, p.138, Physical Review, 47, 777-80 (PDF)