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) 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.
Given the classical dynamics of a non-relativistic particle in terms of a Hamiltonian or an action, it is relatively straightforward to obtain the non-relativistic quantum mechanics (NRQM) of the system. These standard procedures, based on either the Hamiltonian or the path integral, however, do not work in the case of a relativistic particle. As a result we do not have a single-particle description of relativistic quantum mechanics (RQM). Instead, the correct approach requires a transmutation of dynamical variables from the position and momentum of a single particle to a field and its canonical momentum. Particles, along with antiparticles , reappear in a very nontrivial manner as the excitations of the field. The fact that one needs to adopt completely different languages to describe a relativistic and non-relativistic free particle implies that obtaining the NRQM limit of QFT is conceptually nontrivial. I examine this limit in several approaches (like, for e.g., Hamiltonian dynamics, Lagrangian and Hamiltonian path integrals, field theoretic description etc.) and identify the precise issues which arise when one attempts to obtain the NRQM from QFT in each of these approaches. The dichotomy of NRQM and QFT does not originate just from the square root in the Hamiltonian or from the demand of Lorentz invariance, as is sometimes claimed. The real difficulty has its origin in the necessary existence of antiparticles to ensure a particular notion of relativistic causality. Because of these conceptual issues, it turns out that one cannot , in fact, obtain some of the popular descriptions of NRQM by any sensible limiting procedure applied to QFT. To obtain NRQM from QFT in a seamless manner, it is necessary to work with NRQM expressed in a language closer to that of QFT. This fact has several implications, especially for the operational notion of space coordinates in quantum theory. A close examination of these issues, which arise when quantum theory is combined with special relativity, could offer insights in the context of attempts to combine quantum theory with general relativity.
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.
An Ising-type classical statistical model is shown to describe quantum fermions. For a suitable time-evolution law for the probability distribution of the Ising-spins our model describes a quantum field theory for Dirac spinors in external electromagnetic fields, corresponding to a mean field approximation to quantum electrodynamics. All quantum features for the motion of an arbitrary number of electrons and positrons, including the characteristic interference effects for two-fermion states, are described by the classical statistical model. For one-particle states in the non-relativistic approximation we derive the Schrödinger equation for a particle in a potential from the time evolution law for the probability distribution of the Ising-spins. Thus all characteristic quantum features, as interference in a double slit experiment, tunneling or discrete energy levels for stationary states, are derived from a classical statistical ensemble. Concerning the particle-wave-duality of quantum mechanics, the discreteness of particles is traced back to the discreteness of occupation numbers or Ising-spins, while the continuity of the wave function reflects the continuity of the probability distribution for the Ising-spins.
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.
Abstract The theoretical results of quantum mechanics (QM) have been verified by experiments, but the probabilistic Copenhagen interpretation is still controversial, and many counterintuitive phenomena are still difficult to understand. To trace the origin of probability in QM, we construct the amplitudes of a space-time position in a multiparticle quantum objective system and find that the probability in QM originates from the particle number distribution rate in a unit volume near position r at time t in the multiparticle quantum objective system. Based on the origin of probability, the quantization conditions of action and the principle of least action for an elementary particle (referred to as particle) , we find that when a particle moves in space-time, it periodically and alternately exhibit particle and wave state. We have derived the formula for the fringe positions in the double-slit experiment with particles, a new certainty relation and the uncertainty relation, obtain the localized and nonlocalized spatiotemporal range of the particle, the apparent trajectory of the particle motion. Based on this, through rigorous mathematical derivation and analysis, we propose new physical interpretations of the quantum superposition state, wave-particle duality, the double-slit experiment, the Heisenberg uncertainty principle, and the quantum tunnelling effect, and these interpretations are physically logical and not counterintuitive.