Reconstruction of quantum theory on the basis of the formula of total probability
نویسنده
چکیده
The notion of context (complex of physical conditions) is basic in this paper. We show that the main structures of quantum theory (interference of probabilities, Born’s rule, complex probabilistic amplitudes, Hilbert state space, representation of observables by operators) are present in a latent form in the classical Kolmogorov probability model. However, this model should be considered as a calculus of contextual probabilities. In our approach it is forbidden to consider abstract context independent probabilities: “first context and then probability.” We start with the conventional formula of total probability for contextual (conditional) probabilities and then we rewrite it by eliminating combinations of incompatible contexts from consideration. In this way we obtain interference of probabilities without to appeal to the Hilbert space formalism or wave mechanics. However, we did not just reconstruct the probabilistic formalism of conventional quantum mechanics. Our contextual probabilistic model is essentially more general and, besides the projection to the complex Hilbert space, it has other projections. The most important new prediction is the possibility (at least theoretical) of appearance of hyperbolic interference. A projection of the classical contextual probabilistic model to the hyperbolic Hilbert space (a module over the commutative two dimensional Clifford algebra) has some similarities with the projection to the complex Hilbert space. However, in the hyperbolic quantum mechanics the principle of superposition is violated. Our realistic (but contextual!) approach to quantum mechanics does not contradict to various “no-go theorems”, e.g., von Neumann, Bell, Kochen-Specker. We emphasize that our projection of the classical probabilistic model to the complex Hilbert space is based on two incompatible observables (“reference observables”), e.g., the position and the momentum, or the position and the energy. Only these two observables can be considered as objective properties of quantum systems.
منابع مشابه
Quantum Chemistry Study & Evaluation of Basis Set Effects on Prediction of Amino Acids Properties:
The potential energy surface of gaseous glycine determined years ago in the ab initio B3LYP/6-311++G** calculations is composed of thirteen stable conformers. We performed the ab initiomolecular orbital calculations as the starting point to carry out a force field and normal coordinatecalculation on the most stable conformer of non-zwitterionic glycine [conformer (I)]. Thecalculations were carr...
متن کاملElectronic Structure Investigation of Octahedral Complex and Nano ring by NBO Analysis: An EPR Study
To calculation non-bonded interaction of the [CoCl6]3- complex embedded in nano ring, we focus on the single wall boron-nitride B18N18 nano ring. Thus, the geometry of B18N18 nano ring has been optimized by B3LYP method with EPR-II (Electron paramagnetic resonance) basis set and geometry of the [CoCl6]3- complex has been optimized at B3LYP method with Aldrich’s VTZ basis set and Stuttgart RSC 1...
متن کاملElectronic Structure Investigation of Octahedral Complex and Nano ring by NBO Analysis: An EPR Study
To calculation non-bonded interaction of the [CoCl6]3- complex embedded in nano ring, we focus on the single wall boron-nitride B18N18 nano ring. Thus, the geometry of B18N18 nano ring has been optimized by B3LYP method with EPR-II (Electron paramagnetic resonance) basis set and geometry of the [CoCl6]3- complex has been optimized at B3LYP method with Aldrich’s VTZ basis set and Stuttgart RSC 1...
متن کاملQuantum mechanical investigation of 4-hydroxy phenyl azobenzene adsorption on the boron nitride nanotubes
In this study, the adsorption of 4-hydroxy phenyl-azobenzene on the surface of (4, 0) zigzag open-end boron nitride nanotube (BNNT) has been investigated by quantum calculations. In order to find the preferred adsorption site, different positions and orientations were considered. The impacts of donor-acceptor electron delocalization on the structural and electronic properties and reactivity of ...
متن کاملQuantum mechanical investigation of 4-hydroxy phenyl azobenzene adsorption on the boron nitride nanotubes
In this study, the adsorption of 4-hydroxy phenyl-azobenzene on the surface of (4, 0) zigzag open-end boron nitride nanotube (BNNT) has been investigated by quantum calculations. In order to find the preferred adsorption site, different positions and orientations were considered. The impacts of donor-acceptor electron delocalization on the structural and electronic properties and reactivity of ...
متن کاملیک نظریه جایگزین برای مکانیک بوهمی
In this article, a causal model on the basis of trajectory is introduced for description of quantum systems. This theory is structurally very similar to Bohme mechanics, and like Bohme theory reproduces all statistical consequences of standard quantum mechanics. Particle trajectories in this model are different from anticipated ones by Bohme model. Quantum potential (force) form, which is give...
متن کامل