Principle of locality means that any local change (perturbation) of the stationary state wave function field propagates with finite speed, and therefore reaches distant regions of the field with time delay. If a one-particle or multi-particle non-relativistic quantum system is initially in a stationary state, and its wave function field is locally perturbed, then perturbed and non-perturbed sub-regions appear in the region. According to Schrodinger equation, borders of the perturbed sub-region propagate with infinite speed, and the perturbation instantaneously affects all infinite region. It means that Schrodinger equation predicts infinite speed of the wave function perturbations propagation. This feature of classical Schrodinger equation is traditionally interpreted as non-locality of quantum mechanics. From physical point of view, such mathematical behavior of Schrodinger equation solutions is questionable because it is difficult to accept that in real world infinite physical objects can instantaneously appear. We introduce a hypothesis that in reality speed of propagation of the perturbed sub-region borders is equal speed of light. On this basis we develop and analyze a finite propagation speed concept for non-relativistic quantum equations. It leads to local interpretation of non-relativistic quantum mechanics consistent with principle of locality and free of local hidden variables. The theory is applied to analysis of Einstein-Podolsky-Rosen (EPR) paradox, entanglement and properties of perturbed matter waves. We proved that formulated theory agrees with results of classical experiments on electron matter waves diffraction.
Principle of locality means that any local change (perturbation) of the stationary state wave function field propagates with finite speed, and therefore reaches distant regions of the field with time delay. If a one-particle or multi-particle non-relativistic quantum system is initially in a stationary state, and its wave function field is locally perturbed, then perturbed and non-perturbed sub-regions appear in the region. According to Schrödinger equation, borders of the perturbed sub-region propagate with infinite speed, and the perturbation instantaneously affects all infinite region. It means that Schrödinger equation predicts infinite speed of the wave function perturbations propagation. This feature of classical Schrödinger equation is traditionally interpreted as non-locality of quantum mechanics. From physical point of view, such mathematical behavior of Schrödinger equation solutions is questionable because it is difficult to accept that in real world infinite physical objects can instantaneously appear. We introduce a hypothesis that in reality speed of propagation of the perturbed sub-region borders is equal speed of light. On this basis we develop and analyze a finite propagation speed concept for non-relativistic quantum equations. It leads to local interpretation of non-relativistic quantum mechanics consistent with principle of locality and free of local hidden variables. The theory is applied to analysis of Einstein-Podolsky-Rosen (EPR) paradox, entanglement and properties of perturbed matter waves. We proved that formulated theory agrees with results of classical experiments on electron matter waves diffraction.
We consider the propagation of a classical electromagnetic wave through a transmission line, formed by identical superconducting charge qubits inside a superconducting resonator. Since the qubits can be in a coherent superposition of quantum states, we show that such a system demonstrates interesting effects, such as a ``breathing'' photonic crystal with an oscillating band gap and a ``quantum Archimedean screw'' that transports, at an arbitrary controlled velocity, Josephson plasma waves through a transmission line. The key ingredient of these effects is that the optical properties of the Josephson transmission line are controlled by the quantum coherent state of the qubits.
The Einstein-Podolsky-Rosen (EPR) paradox challenges the completeness of quantum mechanics under the assumptions of separability and locality, while Bell's theorem and its loophole-free experimental confirmations rule out local hidden variables and establish that entangled correlations are nonlocal yet no-signaling. This paper formulates, within the spacetime-quantum unified-field theory, a self-contained resolution of the paradox. Starting from the six axioms of the theory, we model the entangled pair as two local excitations of the single global spacetime-quantum field, a coherent superposition of discrete spacetime quanta (Axiom 1). We show that the EPR elements of reality are not attributes of the separated subsystems but properties of the global coherent configuration established within the common past light cone, so that EPR's tacit separability premise fails in this ontology (Axioms 1 and 5). Measurement is identified as a strictly local energy exchange (Axioms 2 and 5) whose influence propagates at most at the speed of light by the local hyperbolic master equation (Axiom 3), and we prove, by the invariance of the reduced density matrix, that no signaling is possible. The Bell correlations are reproduced as a consistency condition inherited from the standard-model sector (Axiom 4), with the Tsirelson bound 2√2 following from the no-signaling structure. Complete derivations of the correlation function, the Clauser-Horne-Shimony-Holt inequality and its violation, the no-signaling theorem, the local measurement model, and the coherence-entanglement relation are provided in the appendices.
Abstract We consider the propagation of a classical electromagnetic wave through a transmission line, formed by identical superconducting charge qubits inside a superconducting resonator. Since the qubits can be in a coherent superposition of quantum states, we show that such a system demonstrates interesting new effects, such as a “breathing” photonic crystal with an oscillating bandgap. Similar behaviour is expected from a transmission line formed by flux qubits. The key ingredient of these effects is that the optical properties of the Josephson transmission line are controlled by the quantum coherent state of the qubits (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
The Einstein-Podolsky-Rosen (EPR) paradox gives an argument for the incompleteness of quantum mechanics based on a plausible criterion for reality, as well as the assumption of locality. A general view is that the argument is compromised, because EPR's premises are falsified by Greenberger-Horne-Zeilinger (GHZ) and Bell experiments. In this paper, we present an EPR argument based on premises not falsified by these experiments. First, we consider macroscopic EPR-Bohm, Bell, and GHZ experiments using spins ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{S}}_{\ensuremath{\theta}}$ defined by two macroscopically distinct states. The analyzers that realize the unitary operations ${U}_{\ensuremath{\theta}}$ determining the measurement settings $\ensuremath{\theta}$ are nonlinear devices creating macroscopic superposition states. We note two definitions of macroscopic realism (MR). For a system with two macroscopically distinct states available to it, MR posits a predetermined outcome for the measurement ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{S}}_{\ensuremath{\theta}}$ distinguishing between the states. Deterministic macroscopic realism assumes MR for the system defined prior to the interaction ${U}_{\ensuremath{\theta}}$ being carried out but is falsifiable by the macroscopic Bell and GHZ proposals. Motivated by arguments to uphold MR (without resorting to decoherence), as well as no-signaling and the properties of a meter, we define a set of premises referred to as weak macroscopic realism (wMR). Weak macroscopic realism (wMR) posits MR for the system after ${U}_{\ensuremath{\theta}}$, at the time
tf---when the system is prepared with respect to the measurement basis, ready for a ``pointer'' measurement and readout. For this system, wMR posits that the outcome of ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{S}}_{\ensuremath{\theta}}$ is determined and not changed by interactions that might subsequently occur at a remote system
B. The premise wMR also posits a weaker version of EPR's criterion for reality. Importantly, we show that the GHZ and Bell predictions are consistent with wMR. Yet, an EPR paradox arises for a macroscopic EPR-Bohm state, based on wMR. As considered by Schr\"odinger, it is possible to measure two complementary spins of system
A simultaneously, ``one by direct, the other by indirect measurement'': If we assume wMR, then once both settings are fixed, the outcomes of the two spins are both determined. We revisit the original EPR paradox and find a similar result: An EPR argument can be based on a set of premises, weak local realism, which we show are not falsifiable by GHZ or Bell experiments.