This study interprets four major mysteries related to observation in quantum mechanics. These are based on a new interpretation of the energy–time uncertainty relation, which yields time retrogression and suggests that a quantum state’s time evolution may fluctuate if measurement fixes its energy. The resulting time-reversed state is represented by a bra vector. The time reversed bra vector and the time-evolving ket vector interact along the time axis to generate a time-invariant bra–ket state, indicating state determination. The first topic is why observation selects one state from a superposition. Among all time-reversed states, the state with the least energy dispersion reaches farthest into the past, establishing that state while the others disappear. The existence of a single state in the farthest past explains quantum state contraction induced by observation. The second topic is the spatial contraction of the wave packet upon observation. In QFT, the wave functions forming the wave packet arise from vacuum energy fluctuations which disappear through the inner product in the bra–ket state. Consequently, external vacuum energy exerts a compressive force that contracts the wave packet. This mechanism explains both state selection and spatial contraction upon observation. The third topic is long-range correlation without transmission time in quantum entanglement. This study explains that photon states go back into the past and are determined there, accounting for the simultaneous correlation between distant photons. The fourth topic is the origin of randomness in measurement outcomes. This study interprets randomness in energy dispersion as arising from phase differences between measuring-device states. Thus, the state is determined probabilistically yet deterministically through measurement. These interpretations reinforce local-reality and restore determinism in quantum mechanics.
This study interprets four major mysteries related to observation in quantum mechanics. These are based on a new interpretation of the energy–time uncertainty relation, which yields time retrogression and suggests that a quantum state’s time evolution may fluctuate if measurement fixes its energy. The resulting time-reversed state is represented by a bra vector. The time reversed bra vector and the time-evolving ket vector interact along the time axis to generate a time-invariant bra–ket state, indicating state determination. The first topic is why observation selects one state from a superposition. Among all time-reversed states, the state with the least energy dispersion reaches farthest into the past, establishing that state while the others disappear. The existence of a single state in the farthest past explains quantum state contraction induced by observation. The second topic is the spatial contraction of the wave packet upon observation. In QFT, the wave functions forming the wave packet arise from vacuum energy fluctuations which disappear through the inner product in the bra–ket state. Consequently, external vacuum energy exerts a compressive force that contracts the wave packet. This mechanism explains both state selection and spatial contraction upon observation. The third topic is long-range correlation without transmission time in quantum entanglement. This study explains that photon states go back into the past and are determined there, accounting for the simultaneous correlation between distant photons. The fourth topic is the origin of randomness in measurement outcomes. This study interprets randomness in energy dispersion as arising from phase differences between measuring-device states. Thus, the state is determined probabilistically yet deterministically through measurement. These interpretations reinforce local-reality and restore determinism in quantum mechanics.
The Quantum Mechanics is interpreted, in this article, in a simple and direct way. By combining the unitary evolution with the quantum condition that observations require the state vector to be an eigenstate of the observable, a discontinuity in evolution (the state vector reduction) seems to be mandatory. Thus, for each such discontinuity, new initial conditions for the time evolution state vector are needed, and they are obtained by measurements. Delayed-choice experiments suggest that these new initial conditions are specified after the discontinuity takes place. Consequently, because it needs initial conditions that can be specified with a delay, the time evolving state vector is semi-realistic (in the sense that it is not completely specified until the measurement is performed), and not entirely realistic. The collapse of the wave function, especially when it is combined with the entanglement, seems to be a non-local phenomenon. In fact, the non-locality is present only as a consistency requirement for the initial conditions needed to select a solution of the evolution equation. The Direct Interpretation is intended to provide to our intuition a physical background, for helping us thinking about quantum phenomena. It identifies the main counterintuitive parts of the Quantum Mechanics in the discontinuity and the delayed initial conditions. Because it makes minimal assumptions, it is compatible with the main interpretations of Quantum Mechanics. Two principal unclear points of Quantum Mechanics are identified in the discontinuities, and the measurement problem. Both problems will be approached in subsequent articles.
We present a new interpretation of the terms superposition, entanglement, and measurement that appear in quantum mechanics. We hypothesize that the structure of the wave function for a quantum system at the sub-Planck scale has a deterministic cyclic structure. Each cycle comprises a sequential succession of the eigenstates that comprise a given wave function. Between unitary operations or measurements on the wave function, the sequential arrangement of the current eigenstates chosen by the system is immaterial, but once chosen it remains fixed until another unitary operation or measurement changes the wave function. The probabilistic aspect of quantum mechanics is interpreted by hypothesizing a measurement mechanism which acts instantaneously but the instant of measurement is chosen randomly by the classical measuring apparatus over a small but finite interval from the time the measurement apparatus is activated. At the instant the measurement is made, the wave function irrevocably collapses to a new state (erasing some of the past quantum information) and continues from thereon in that state till changed by a unitary operation or a new measurement.
This study discusses the quantum behavior of a particle, which is controlled by fluctuations in the physical space-time (ST) variables, rather than provides a novel interpretation of quantum theory. The fluctuations, i.e., inhomogeneities in a homogeneous phase ST, are prescribed by their probability. They determine the reciprocal space and correlate with the correlation entropy different from zero. Alongside with the minimum entropy, action, and the presence of the Winn-Ehrenfest adiabatic invariant (AI), the fluctuations require the Gilbert information (probabilistic) space linking the physical and the reciprocal ST. Physical quantities in the information space are represented by linear Hermitian operators, which is due to the entropy production in the presence of an AI. Evolution of a quantum system is described by the wave functions having the meaning of information concerning all virtually possible states of a quantum particle. The wave functions are the solutions to the Schrodinger equation and represent a navigation 'roadmap' for the particle to follow. A quantum system is in fact a classical Hamiltonian system in the space of coefficients of the wave function decomposition with respect to the operator eigenfunctions. It is the linearity and the Hermitian nature of the operators which determine the trajectory and the superposition principle in case of the wave behavior of fluctuations. The uncertainty principle, reflects correlation of the fluctuations and, hence, their nonlocality. This study discusses the wave function phase, the Berry phase and its relationship to quantization, discriminability of states and macroscopic quantum effects caused by localization of the particle, followed by a possible entropy change during its transition into a new thermodynamic state.
This year we celebrate 100 years of quantum mechanics (QM). Incorrect interpretations of QM and incorrect mental models of the invisible details of quantum phenomena lead to paradoxes. To explain these, we advocate the statistical contextual interpretation (SCI) of quantum mechanics. State vectors (wave functions) and various operators are purely mathematical entities that permit quantitative probabilistic predictions. “State vector” describes an ensemble of identically prepared physical systems, and a specific “operator” represents a class of equivalent measurements of a physical observable. A collapse of wavefunction is not a mysterious and instantaneous physical process; a collapsed quantum state describes a new ensemble of physical systems prepared in a particular way. A value of a physical observable, such as a spin projection, associated with a pure quantum ensemble is a characteristic of this ensemble created by its interaction with measuring instruments. Probabilities are objective properties of random experiments in which empirical frequencies stabilize. Following Einstein, SCI rejects the claim that QM provides a complete description of individual physical systems, but it remains agnostic about whether a more detailed subquantum description can be found or is necessary. In conformity with Bohr contextuality, SCI rejects Bell-local and Bell-causal hidden variable models. Nevertheless, by incorporating into a probabilistic model contextual hidden variable measuring instruments, long distance quantum correlations studied in Bell tests can be explained without evoking quantum nonlocality or retro-causality. SCI allows the explanation of several quantum phenomena without evoking quantum magic. SCI does not claim to provide a complete description of quantum phenomena; in fact, it is unknown whether quantum probabilities even provide a complete description of existing experimental data. Time series of experimental data may contain much more information than is obtained using empirical frequencies and histograms. Therefore, predictable completeness of QM must be tested and not taken for granted.
The stochastic nature of quantum mechanics is more naturally reflected in a bilinear two-process representation of density matrices rather than in squared wave functions. This proposition comes with a remarkable change of the entanglement mechanism: entanglement effects do not originate from superpositions of wave functions, but result from the bilinear structure of density matrices. Quantum interference appears as a multiplicative phenomenon rather than an additive superposition mechanism. We propose two general requirements such that the bilinear representation of density matrices is given in terms of two uniquely defined, identically distributed, Markovian stochastic jump processes. These general ideas are illustrated for the Einstein-Podolsky-Rosen and double-slit experiments. The expression of the stochastic nature of quantum mechanics in terms of random variables rather than their probability distributions facilitates an ontological viewpoint and leads us to a bra-ket interpretation of quantum mechanics.
We review the postulates of quantum mechanics with respect to the representation of physical states and measurable quantities, their time evolution, and the interpretation of measurements. We first formulate the postulates in terms of wave functions and differential operators, and then reformulate them in the abstract Hilbert space of state vectors, using Dirac’s notations. Improper states subject to Dirac’s delta normalization are introduced, and the space of physical states is extended to include them. The postulates are rationalized by associating each Hermitian linear operator with a complete orthonormal system of its eigenvectors, where measurement probabilities depend on the projections of these eigenvectors on the system’s state vector. Particularly, wave functions are identified as projections of state vectors on the position operator eigenstates. State vectors representing multidimensional systems are formulated as tensor products of vectors in their subspaces. Finally, we address the general uncertainty relations in simultaneous measurements of different observables.