Classical Probabilities and Bell' s Theorem
Tan Tian-rong
It is proved that: What the two-slit experiments have refuted is the preconceived idea that of the event that a micro particle passing through one slit arrives somewhere on the screen is irrelative to the condition that whether or not the other slit is open. Consideringaddition theorem of probabilities, the above idea can be expressed as follows:
(a)Assum that a beam passes through a partition with two slit and arrives a screen. The of the event that an indivedual particle falls on somewhere of the screen under the condition that two slit open simultaneously, is equal to the sum of two of the same event under that two slit open in turn.
Defining the experimental condition such as two slit open simultaneously or in turn as passage the proposition (a)is manifested as probabilities is independent of passage conditions.
On the other hand, in terms of the above, superposition principle of in quantum mechanics ought to be indicated as probability amplitudes is independent of passage conditions. Correspondingly, (a)is named hereof as superposition presumption of probability.
For lack of the conception of passage conditions, (a)is confused with theorem of probabilities. As a result, classical physics tacitly approve (a), and thereby it fails to comprehend the two-slit experiments. In reverse, to explain two-slit experiments, quantum mechanics spurns addition theorem of so that it meets with various difficults about explanation.
Any alternative of quantum mechanics must be able to explain two-slit experiments, therefore it must contain passage conditions or amplitudes. But hidden variable theory Bell used dissatisfies such a prerequisite. It comes thus into conflict with experiment facts inevitably. As a result, Lochak's argument that Bell's inequality is irrelative to locality is rediscovered.
Journal of Changzhou Institute of Technology•Jan 1, 2002•0 citations