A local interpretation of quantum mechanics is presented. Its main ingredients are: first, a label attached to one of the virtual paths in the path integral formalism, determining the output for measurement of position or momentum; second, a mathematical model for spin states, equivalent to the path integral formalism for point particles in space time, with the corresponding label. The mathematical machinery of orthodox quantum mechanics is maintained, in particular amplitudes of probability and Born's rule; therefore, Bell's type inequalities theorems do not apply. It is shown that statistical correlations for pairs of particles with entangled spins have a description completely equivalent to the two slit experiment, that is, interference (wave like behaviour) instead of non locality gives account of the process. The interpretation is grounded in the experimental evidence of a point like character of electrons, and in the hypothetical existence of a wave like, the de Broglie, companion system. A correspondence between the extended Hilbert spaces of hidden physical states and the orthodox quantum mechanical Hilbert space shows the mathematical equivalence of both theories. Paradoxical behaviour with respect to the action reaction principle is analysed, and an experimental set up, modified two slit experiment, proposed to look for the companion system.
A local interpretation of quantum mechanics is presented. Its main ingredients are: first, a label attached to one of the virtual paths in the path integral formalism, determining the output for measurement of position or momentum; second, a mathematical model for spin states, equivalent to the path integral formalism for point particles in space time, with the corresponding label. The mathematical machinery of orthodox quantum mechanics is maintained, in particular amplitudes of probability and Born's rule; therefore, Bell's type inequalities theorems do not apply. It is shown that statistical correlations for pairs of particles with entangled spins have a description completely equivalent to the two slit experiment, that is, interference (wave like behaviour) instead of non locality gives account of the process. The interpretation is grounded in the experimental evidence of a point like character of electrons, and in the hypothetical existence of a wave like, the de Broglie, companion system. A correspondence between the extended Hilbert spaces of hidden physical states and the orthodox quantum mechanical Hilbert space shows the mathematical equivalence of both theories. Paradoxical behaviour with respect to the action reaction principle is analysed, and an experimental set up, modified two slit experiment, proposed to look for the companion system.
AbstractAn alternative interpretation of QM is presented. Hidden vari-ables prescribe the output of measurements for individual states ofthe ensemble, but a distribution of amplitudes of probability, insteadof a distribution of probabilities, is associated to them, as in orthodoxQM. Consequently, Bell’s type inequalities do not apply. In this in-terpretation, locality is restored in EPR experiments with entangledsubsystems, as the observable relative frequencies are obtained by theusual interference for sum of amplitudes, in complete parallelism withthe two slit experiment. The action reaction principle seems to be vio-lated in some QM measurements, and the existence of hidden variablescould solve this paradox too. In indirect measurements it remains ob-scure the way it could be restored. A version of the two slit experimentis proposed to search for the hidden reaction. Keywords: Alternative interpretations of QM, measurement problem, nonlocality, path integral formalism.PACS numbers: 03.65.Ca, 03.65.Ta, 03.65.Ud
In this paper, we try to give a new approach to the quantum mechanics(QM) on the framework of quantum field theory(QFT). Firstly, we make a detail study on the (non-relativistic) Schrodinger field theory, obtaining the Schrodinger equation as a field equation, after field quantization, the Heisenberg equations for the momentum and position operators of the particles excited from the (Schrodinger) field and the Feynman path integral formula of QM are also obtained. We then give the probability concepts of quantum mechanics in terms of a statistical ensemble, realizing the ensemble(or statistical) interpretation. With these, we make a series of conceptual modifications to the standard quantum mechanics, especially propose a new assumption about the quantum measurement theory which can solve the EPR paradox from the view of the QFT. Besides, a field theoretical description to the double-slit interference experiment is developed, obtaining the required particle number distribution. In the end, we extend all the above concepts to the relativistic case so that the ensemble interpretation is still proper. Two extra topics are added, in the first one, an operable experiment is proposed to distinguish the Copenhagen interpretation from the ensemble one via very different experimental results. While the second topic concerns with the extensions of the concept of coherent state to both the Bosonic and Fermionic field cases, to obtain the corresponding classical fields. And in the concluding section, we make some general comparisons between the standard QM and the one derived from the QFT, from which we claim that the QFT is the fundamental theory.
In this paper, we try to give a new approach to the quantum mechanics(QM) on the framework of quantum field theory(QFT). Firstly, we make a detail study on the (non-relativistic) Schrödinger field theory, obtaining the Schrödinger equation as a field equation, after field quantization, the Heisenberg equations for the momentum and position operators of the particles excited from the (Schrödinger) field and the Feynman path integral formula of QM are also obtained. We then give the probability concepts of quantum mechanics in terms of a statistical ensemble, realizing the ensemble(or statistical) interpretation. With these, we make a series of conceptual modifications to the standard quantum mechanics, especially propose a new assumption about the quantum measurement theory which can solve the EPR paradox from the view of the QFT. Besides, a field theoretical description to the double-slit interference experiment is developed, obtaining the required particle number distribution. In the end, we extend all the above concepts to the relativistic case so that the ensemble interpretation is still proper. Two extra topics are added, in the first one, an operable experiment is proposed to distinguish the Copenhagen interpretation from the ensemble one via very different experimental results. While the second topic concerns with the extensions of the concept of coherent state to both the Bosonic and Fermionic field cases, to obtain the corresponding classical fields. And in the concluding section, we make some general comparisons between the standard QM and the one derived from the QFT, from which we claim that the QFT is the fundamental theory.
In the Einstein-Bohr debate, Einstein considered quantum mechanics incomplete and disagreed with Born's probabilistic interpretation of wave-functions, which collapse abruptly once measurements are performed on the corresponding microscopic objects. Inspired by Einstein, Bell and his followers intended to complete quantum mechanics within the framework of local realism. Regrettably, the deterministic correlation between distant components of a separable system in Einstein's local-realist description of the world is mistaken for the so-called non-locality or "nonlocal-interaction" in the world described by Bell's theorem, which leads to the questionable interpretation of the experimental results obtained by testing Bell inequalities. This article introduces a new principle, the general principle of measurements, which is proved as a mathematical theorem and allows quantum mechanics to be completed within the framework of local realism while keeping the formal axiomatic definition of a general Hilbert space essentially unchanged. Using disjunction ("or") as the logical relation between orthonormal vectors spanning a given Hilbert space, the completed quantum theory precludes inexplicable collapses of wave-functions and is intuitively comprehensible, thus alleviating much difficulty in understanding quantum mechanics. Among various world views, Einstein's local-realist world view is correct.
The action reaction principle is violated in the standard formulation of Quantum Mechanics, so that its phase space is incomplete. Moreover, projection of state of a quantum system under indirect measurement, when there are alternative virtual paths and one of them is discarded by negative detection implies, according to the action reaction principle, a reaction on the detector, although its macroscopic state does not change. If all interactions are local, mediated by fields with relativistically causal evolution, some system, different from the particle which follows another path, must locally interact with the detector. Relativistic locality and the action reaction principle predict the existence of de Broglie fields. A formulation of Quantum Mechanics in extended Hilbert spaces is presented, in which kinematic and dynamical representations of physical magnitudes are distinguished.
The standard Copenhagen interpretation of quantum mechanics relies on a set of historically established, ad hoc postulates to describe particle-wave duality, measurement, and non-locality. In this paper, we propose a single foundational axiom that fully reproduces the standard mathematical formalism of quantum mechanics while eliminating the need for supplementary assumptions. From this singular postulate, we rigorously derive the fundamental origin of the wave function and the mathematical generator of the Schrödinger equation. Furthermore, we demonstrate via isomorfism that all seemingly inexplicable quantum phenomena—including wave-function collapse and quantum entanglement—are mathematically and conceptually reducible to the underlying dynamics of the double-slit experiment. By establishing a direct fundamental correlation between the double-slit interference mechanism and the Monty Hall phenomenon, we prove that these effects are distinct manifestations of the exact same principle. We framed the double-slit experiment as an interference of the space of possibilities affected by information and simetrys. Ultimately, by anchoring the existing quantum mathematical framework to this unique axiom, this work provides a coherent, paradox-free ontological foundation that resolves the interpretational crisis of quantum mechanics without altering its empirical predictive power.