Two General Postulates from which Born’s Interpretation of Wave Function is Derived as a Special Case

The Born Interpretation of Ѱ(X) is that the probability density of finding a particle at point X is proportional to 〖│Ѱ(X)│ 〗^2 . As can be seen, in spite of many good and positive features, this rule lacks generality because it is related to only one special case of the relationships between the quantum system and the observer, while many evidences such as the double-slit experiment tell us that this relation is more wider than just using a detector in a point to obtain either a positive or negative result. For example, there are cases in which even the negative result obtained in one point causes the wave to collapse and a particle to appear in another point, and Born’s Interpretation has nothing to say in such cases. The absence of a general interpretation of the wave function that covers all the cases explains the inability to resolve the paradoxes of the wave-particle duality in many situations. Now, let us go straight to my proposed alternative general interpretation of the wave function which satisfies the following requirements: It covers all the cases of the relation between the quantum system and the observer. It can be used to derive Born’s Interpretation as a special case. It is testable and falsifiable. It solves the paradoxes of the wave-particle duality. It doesn’t use external concepts and doesn’t challenge fundamental hypotheses and intuitions. Let a quantum system be described by the wave function Ѱ(X), if we put a detector at the point X_1 then this may cause the wave function to collapse and a particle to exist in a point X_2.Our interpretation of the wave function is: Postulate 1 The probability density that the wave function will collapse because of interaction with the detector at the point X_1 is proportional to │Ѱ (X_1) │. Postulate 2 The Probability density that the particle produced by the wave collapse will exist at the point X_2 is proportional to │Ѱ (X_2) │. We can see that this interpretation coincides with Born’s Interpretation because if we put a detector at a point X in which the wave function is Ѱ(X) and try to find the particle at this point, then the application of our proposed postulates tell us that the probability is proportional to 〖│Ѱ(X)│ 〗^2 which is the same answer obtained from Born’s Interpretation. Satisfactions of other requirements mentioned above are clear.