Probability amplitudes; The superposition principle

K. Robert Müller

David M. Bishop, Lap Ming Cheung

Tan Tian-rong

It is proved that for a double slit diffraction experiment,superposition principle of probability amplitudes means the probability amplitude of the event that an electron passes through a certain slit and falls on somewhere of the screen has nothing to do with the condition whether or not the other slit is open,from which it is concluded that the probability itself does not obey superposition principle.Consequently,the total probability formula as a relation among the measurable probabilities is invalid herein.As a result,it is unnecessary to give up the classical idea that an electron moves along an orbit,and thereby it is unnecessary to distinguish between classical physics and quantum physics.

F.J. Duarte

Twelve mathematical statements that define the quantum mechanics of interference and entanglement are listed in the chapter. The importance of superposition probability amplitudes, via the Dirac–Feynman principle, in quantum mechanics is highlighted. Particular attention is given to the proper description of experimental configurations via probability amplitudes. The refinement of spatial accuracy, only limited by Nature’s availability of shorter and shorter wavelengths, in N -slit quantum interferometers is described. The transition from superposition probability amplitudes to quantum probabilities is discussed. In all this, the essential importance of the nonlocality of the photon is emphasized. The importance of the probability amplitude of quantum entanglement at the foundations of quantum physics is discussed relative to quantum interference. The intrinsic link between these two principles is highlighted via a series of transparent mathematical statements.

Прохоров Лев Васильевич

Tan Tian-rong

It is proved that in a double slit diffraction experiment, superposition principle of probability amplitude means (the probability amplitude of the event) that an electron passes through a certain slit and arrives somewhere on the screen under the condition that two slits open simultaneously, is equal to the sum of two probability amplitudes of the same event under the condition that two slits open in turn. From this thesis it is concluded that the probabilities do not obey superposition principle, which is just the reason that classical probability theory is inapplicable for the very experiment. Kolmogorov's probability theory is based on two foundations: frequency definition of probabilities and Boolean algebra of event operations. In micro processes, the former holds true while the latter, especially its multiplicative permutation law is violated. So long as we do not deal with event operations, joint probabilities holds good in micro processes. But, the event operation formulae provided are applied and the wrong conclusions present probably. The famous Bell's inequality is a wrong conclusion. (Nature and Science. 2005;3(2):82-91).