This paper generalizes `classical probability' and `imprecise probability' to the notion
of `neutrosophic probability' in order to model Heisenberg's Uncertainty Principle of a
particle's behavior, Schrödinger's Cat Theory, and the state of bosons which do not obey Pauli's
Exclusion Principle (in quantum physics). Neutrosophic probability is closely related to neutrosophic
logic and neutrosophic set, and is etymologically derived from `neutrosophy'.
One postulate of the Heisenberg's Uncertainty Principle is that it is impossible to fully
predict the behavior of a particle, and the causality principle cannot be applied at the atomic level.
For example, the Schrödinger's Cat Theory says that the quantum state of a photon
can basically be in more than one place at the same time which, when translated to
the neutrosophic set, means that an element (quantum state) belongs and does not belong to
a set (a place) at the same time; or an element (quantum state) belongs to two
different sets (two different places) at the same time. It is a question of `alternative worlds'
theory very well represented by the neutrosophic set theory.
In Schrodinger's Equation which is about the behavior of electromagnetic waves
and `matter waves' in quantum theory, the wave function, which describes the superposition
of possible states may be simulated by a neutrosophic function, i.e., a function whose
values are not unique for each argument from the domain of definition (the vertical line test
fails, intersecting the graph in more points).
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