Although quantum mechanics is generally considered to be fundamentally incompatible with classical logic, it is argued here that the gap is not as great as it seems. Any classical, discrete, time reversible system can be naturally described using a quantum Hubert space, operators, and a Schrödinger equation. The quantum states generated this way resemble the ones in the real world so much that one wonders why this could not be used to interpret all of quantum mechanics this way. Indeed, such an interpretation leads to the most natural explanation as to why a wave function appears to "collapse" when a measurement is made, and why probabilities obey the Born rule. Because it is real quantum mechanics that we generate, Bell's inequalities should not be an obstacle.
Although quantum mechanics is generally considered to be fundamentally incompatible with classical logic, it is argued here that the gap is not as great as it seems. Any classical, discrete, time reversible system can be naturally described using a quantum Hubert space, operators, and a Schrödinger equation. The quantum states generated this way resemble the ones in the real world so much that one wonders why this could not be used to interpret all of quantum mechanics this way. Indeed, such an interpretation leads to the most natural explanation as to why a wave function appears to "collapse" when a measurement is made, and why probabilities obey the Born rule. Because it is real quantum mechanics that we generate, Bell's inequalities should not be an obstacle.
Some aspects of the interpretation of quantum theory are discussed.It is emphasized that quantum theory is formulated in a Cartesian coordinate system; in other coordinates the result obtained with the help of the Hamiltonian formalism and commutator relations between 'canonically conjugated' coordinate and momentum operators leads to a wrong version of quantum mechanics.In this connection the Feynman integral formalism is also discussed.In this formalism the measure is not well-defined and there is no idea how to distinguish between the true version of quantum mechanics and an incorrect one; it is rather a mnemonic rule to generate perturbation series from an undefined zero order term.The origin of time is analyzed in detail by the example of atomic collisions.It is shown that the time-dependent Schrödinger equation for the closed three-body (two nuclei + electron) system has no physical meaning since in the high impact energy limit it transforms into an equation with two independent time-like variables; the time appears in the stationary Schrödinger equation as a result of extraction of a classical subsystem (two nuclei) from a closed three-body system.Following the Einstein-Rosen-Podolsky experiment and Bell's inequality the wave function is interpreted as an actual field of information in the elementary form.The relation between physics and mathematics is also discussed.
Interpreting quantum mechanics is a hard problem basically because it means explaining why and how the mathematics exploited to formulate wave-particle duality are related to observations or reality in classical physics. Consequently, interpretation of quantum mechanics and its formalism should involve proper physical mathematics, physical logic and classical physics, which is not the case from the Copenhagen interpretation. Here, we shall revisit all the postulates of quantum mechanics with proper physics and physical logic and reconstruct them to establish the less-complex interpretation of quantum mechanics with additional new postulates from classical physics. A new quantum mechanical postulate (Postulate 9) is also introduced to understand the meaning of the forbidden gap between discrete energy levels and/or electron orbitals in atoms that is valid for molecules and condensed matter based on quantum mechanics that is technically well-defined and experimentally observable. Here, we tackle all the problems arise from the Copenhagen interpretation systematically by revising and/or extending them with proper classical and quantum physics without violating established experiments and without proposing ideas that violate physical reality.
Quantum nonlocality is shown to be an artifact of the Copenhagen interpretation, in which each observed quantity has exactly one value at any instant. In reality, all physical systems obey quantum mechanics, which obeys no such rule. Locality is restored if observed and observer are both assumed to obey quantum mechanics, as in the many-worlds interpretation (MWI). Using the MWI, I show that the quantum side of Bell's inequality, generally believed nonlocal, is really due to a series of three measurements (not two as in the standard, oversimplified analysis), all three of which have only local effects. Thus, experiments confirming "nonlocality" are actually confirming the MWI. The mistaken interpretation of nonlocality experiments depends crucially on a question-begging version of the Born interpretation, which makes sense only in "collapse" versions of quantum theory, about the meaning of the modulus of the wave function, so I use the interpretation based on the MWI, namely that the wave function is a world density amplitude, not a probability amplitude. This view allows the Born interpretation to be derived directly from the Schrödinger equation, by applying the Schrödinger equation to both the observed and the observer.
Schrodinger wave equation, Hilbert space formalism, born’s rule for probability and hermitian operator are mainly the core of quantum theory and quantum description is generally based on Hilbert space of states, observables are described by self adjoint operators on the space of states, physical symmetries are explained by unitary transformations, and time evolution is a one-parameter group of unitary transformations on the Hilbert space of states. In this paper, I have discussed why a generalized philosophy is required before the development of quantum probability to fill up the gap.
A type of mechanics will be presented that possesses some distinctive properties. On the one hand, its physical description & rules of operation are readily comprehensible & intuitively clear. On the other, it fully satisfies all observable predictions of non-relativistic quantum mechanics. Within it, particles exist at points in space, follow continuous, piecewise differentiable paths, and their linear momentum is equal to their mass times their velocity along their path. Yet the probabilities for position and momentum, conditioned on the state of the particle's environment, follow the rules of quantum theory. Indeed, all observable consequences of quantum theory are satisfied; particles can be entangled, have intrinsic spin, this spin is not local to the particle, particle identity can effect probabilities, and so forth. All the rules of quantum mechanics are obeyed, and all arise in a straightforward fashion. After this is established, connections will be drawn out between this type of mechanics and other types of quantum worlds; those that obey Bohmian mechanics, stochastic mechanics, the many worlds interpretation, and physical collapse. In the final section, a relativistic version of the mechanics will be presented.
This paper is intended to show the Schrodinger equation, within its structure, allows the manifestation of the wave function collapse within a very natural way of reasoning. In fact, as we will see, nothing new must be inserted to the classical quantum mechanics, viz., only the dialectics of the physical world must be interpreted under a correct manner. We know the nature of a physical system turns out to be quantical or classical, and, once under the validity of the Schrodinger equation to provide the evolution of this physical system, the dialectics, quantum or classical, mutually exclusive, must also be under context through the Schrodinger equation, issues within the main scope of this paper. We will show a classical measure, the obtention of a classical result, emerges from the structure of the Schrodinger equation, once one demands the possibility that, over a chronological domain, the system begins to provide a classical dialectic, showing the collapse may be understood from both: the structure of the Schrodinger equation as well as from the general solution to this equation. The general solution, even with a dialectical change of description, leads to the conservation of probability, obeying the Schrodinger equation. These issues will turn out to be a consequence of a general potential energy operator, obtained in this paper, including the possibility of the classical description of the physical system, including the possibility of interpretation of the collapse of the quantum mechanical state vector within the Schrodinger equation scope.