After the review by Hauge and Stovneng the old question of How long does it take to tunnel through the barrier? has not still lost its relevance. As before, there is no clear answer to this question even for the one-dimensional completed scattering (OCS). In this paper we show that this seemingly simple question stands alongside with such fundamental problems of quantum mechanics (QM) as the Schrodinger's-cat and and EPR-Bohm paradoxes. Their common feature is that the states of a scattered particle, a radioactive atom and electron EPR-pair represent pure {\it micro-cat} states. It is widely accepted that the EPR-Bohm paradox implies the non-existence of local hidden variables (LHVs), the cat paradox represents a macro-objectification problem and the tunneling time is an observer-dependent quantity whose definitions must be 'operational'. At the same time, according to the probabilistic approach (Accardi, Khrennikov, Philipp, Hess {\it et al.}) to Bell's inequality that underlies the EPR-Bohm experiments, its experimental violation means simply that it contains probability distributions associated with mutually incompatible statistical data. We argue that this approach must be extended onto micro-cat states because they describe, too, mutually incompatible statistical data. The current practice to interpret the squared modulus of a micro-cat state as the probability density should be recognized as erroneous. It is this practice that makes QM incompatible with classical physical theories and, thereby, makes the micro-world 'unspeakable'. The known 'operational' tunneling-time concepts, elaborated in line with this practice, are logically inconsistent. We argue that the TTP and the cat paradox must be solved at the level of single electrons and atoms, without resorting to environment and measurement contexts. We present a new model of the OCS and solve the TTP on its basis.
After the review by Hauge and Stovneng the old question of How long does it take to tunnel through the barrier? has not still lost its relevance. As before, there is no clear answer to this question even for the one-dimensional completed scattering (OCS). In this paper we show that this seemingly simple question stands alongside with such fundamental problems of quantum mechanics (QM) as the Schrodinger's-cat and and EPR-Bohm paradoxes. Their common feature is that the states of a scattered particle, a radioactive atom and electron EPR-pair represent pure {\it micro-cat} states. It is widely accepted that the EPR-Bohm paradox implies the non-existence of local hidden variables (LHVs), the cat paradox represents a macro-objectification problem and the tunneling time is an observer-dependent quantity whose definitions must be 'operational'. At the same time, according to the probabilistic approach (Accardi, Khrennikov, Philipp, Hess {\it et al.}) to Bell's inequality that underlies the EPR-Bohm experiments, its experimental violation means simply that it contains probability distributions associated with mutually incompatible statistical data. We argue that this approach must be extended onto micro-cat states because they describe, too, mutually incompatible statistical data. The current practice to interpret the squared modulus of a micro-cat state as the probability density should be recognized as erroneous. It is this practice that makes QM incompatible with classical physical theories and, thereby, makes the micro-world 'unspeakable'. The known 'operational' tunneling-time concepts, elaborated in line with this practice, are logically inconsistent. We argue that the TTP and the cat paradox must be solved at the level of single electrons and atoms, without resorting to environment and measurement contexts. We present a new model of the OCS and solve the TTP on its basis.
After the review by Hauge and Stovneng the old question of "How long does it take to tunnel through the barrier?" has not still lost its relevance. As before, there is no clear answer to this question even for the one-dimensional completed scattering (OCS). In this paper we show that this seemingly simple question stands alongside with such fundamental problems of quantum mechanics (QM) as the Schrodinger's-cat and and EPR-Bohm paradoxes. Their common feature is that the states of a scattered particle, a radioactive atom and electron EPR-pair represent pure {\it micro-cat} states. It is widely accepted that the EPR-Bohm paradox implies the non-existence of local hidden variables (LHVs), the cat paradox represents a macro-objectification problem and the tunneling time is an observer-dependent quantity whose definitions must be 'operational'. At the same time, according to the probabilistic approach (Accardi, Khrennikov, Philipp, Hess {\it et al.}) to Bell's inequality that underlies the EPR-Bohm experiments, its experimental violation means simply that it contains probability distributions associated with mutually incompatible statistical data. We argue that this approach must be extended onto micro-cat states because they describe, too, mutually incompatible statistical data. The current practice to interpret the squared modulus of a micro-cat state as the probability density should be recognized as erroneous. It is this practice that makes QM incompatible with classical physical theories and, thereby, makes the micro-world 'unspeakable'. The known 'operational' tunneling-time concepts, elaborated in line with this practice, are logically inconsistent. We argue that the TTP and the cat paradox must be solved at the level of single electrons and atoms, without resorting to environment and measurement contexts. We present a new model of the OCS and solve the TTP on its basis.
The quantum theory (QT) and new stochastic approaches have no deterministic prediction for a single measurement or for a single time‐series of events observed for a trapped ion, electron or any other individual physical system. The predictions of QT being of probabilistic character apply to the statistical distribution of the results obtained in various experiments. The Copenhagen interpretation (CI) of QT acknowledged the abstract and statistical character of the predictions of QT but at the same time claimed that a state vector Ψ provided complete description of each individual physical system. The assigning the state vector to an individual physical system together with a postulate of its instantaneous reduction in the measurements was shown by Einstein Podolski and Rosen to lead to so called EPR paradox for the experiments with the entangled pairs of the particles. EPR concluded that a state vector could not provide a complete description of the individual systems and the question arose whether the probabilistic predictions of QT could be derived from some more fundamental spatio‐temporal deterministic description of the invisible sub‐phenomena by introduction of supplementary parameters. The experimental violation of the Bell inequalities in the spin polarization correlation experiments (SPCE) which were the implementations of Bohm and EPR gedanken experiments eliminated so called local and realistic models of the sub‐phenomena. Quite often the violation of these inequalities has been incorrectly interpreted as a proof of the completeness of QT or as the violation of the locality and causality in the micro‐world. The local and realistic models overlooked the fact that an experimental outcome is only the information about a particular system‐system or system‐instrument interaction. Namely the quantum phenomena are described in terms of the probabilities. It is well known that the probability distribution is not an attribute of a dice but it is a characteristic of a whole random experiment: “rolling a dice”. In this paper we will underline: that the quantum probabilities do not describe the lack of knowledge about the physical systems but the lack of knowledge about the experiments and therefore they are “contextual” and that the statistical long range correlations between two random variables X and Y are not a proof of any causal relation between these variables. Moreover any probabilistic model used to described a random experiment is consistent only with a specific protocol telling how the random experiment has to be performed. The probabilistic model used to prove Bell inequalities implied a protocol completely inappropriate and impossible to implement for SPCE . We conclude that the meaningful question about the predictable completeness of QT is still open and it should be answered by a careful and unconventional analysis of the experimental data. The correct understanding of statistical and contextual character of QT is essential for the research in the domain of quantum information and quantum computing.
The origin of nonlocality in quantum mechanics (QM) is analyzed from the viewpoint of our new model of a one-dimensional (1D) completed scattering. Our study of quantum nonlocality complements those carried out by Volovich and Khrennikov. They pointed to an unphysical character of nonlocality in Bell's theorem whose context does not contain the very structure of the space-time. However, there is another reason leading to nonlocality in QM. The existing model of a 1D completed scattering evidences that QM, as it stands, even with a proper space-time context, contradicts special relativity. By our model this scattering process represents an entanglement of two coherently evolved alternative sub-processes, transmission and reflection; whose characteristics are measured well after the scattering event. Quantum nonlocality appears in this problem due to the inconsistency of the superposition principle with the corpuscular properties of a particle. It can take part only in one of the sub-processes. However the superposition principle allows introducing observables common for them. In the fresh wording, this principle must forbid introducing observables for entangled states.
As contrasted with physicists to idolize Bell's theorem and quantum nonlocality, we argue that quantum mechanics (QM), in reality, respects the principles of a macroscopic realism (PMRs). The current QM to tell us that "... the state of a system can be instantaneously changed by a distant measurement >..." cannot be treated as a physical theory. Its key statements - that the EPR-Bell experiments to violate Bell's inequality verify nonlocality, and nonlocal correlations respect special relativity - are false. Both the EPR-Bell experiments and theorems to support the "non-signalling principle" are based on the implicit assumption that all quantum postulates and, in particular, Born's averaging rule are fully applicable to Cat states. However, this is not the case. Introducing observables (e.g., correlations) for Cat states violates the correspondence principle. Pure (macro- and micro-)Cat states must be governed both by the PMRs and superposition principle. Our (macrorealistic) model of a one-dimensional completed scattering shows how these principles coexist with each other, in the case of a one-electron micro-Cat state.
In recent decades there has been a resurge of interest in the foundations of quantum theory, partly motivated by new experimental techniques, partly by the emerging field of quantum information science. Old questions, asked since the seminal article by Einstein, Podolsky and Rosen (EPR), are being revisited. The work of John Bell has changed the direction of investigation by recognising that those fundamental philosophical questions can have, after all, input from experiment. Abner Shimony has aptly termed this new field of enquiry experimental metaphysics. The objective of this Thesis is to contribute to that body of research, by formalising old concepts, proposing new ones, and finding new results in well-studied areas. Without losing from sight that the appeal of experimental metaphysics comes from the adjective, every major result is followed by clear experimental proposals with detailed analysis of feasibility for quantum-atom optical setups. After setting the appropriate terminology and the basic concepts, we will start by analysing the original argument of Einstein, Podolsky and Rosen. We propose a general mathematical form for the assumptions behind the EPR argument, namely those of local causality and completeness. That formalisation entails what was termed a Local Hidden State model by Wiseman et al., which was proposed as a formalisation of the concept of steering first introduced by Schrodinger in a reply to the EPR paper. Violation of any consequences that can be derived from the assumption of that model therefore implies a demonstration of the EPR paradox. We will show how one can then re-derive the well-known EPR-Reid criterion for continuous-variables correlations, and derive new ones applicable to the spin setting considered by Bohm. The spin set-up of the EPR-Bohm was used by Bell to derive his now famous theorem demonstrating the incompatibility of the assumption of local causality and the predictions of quantum mechanics. The inequalities which bear his name can be derived for any number of discrete outcomes, but so far there has been no derivation which can be directly applied to the continuous-variables case of the original EPR paradox. We close the circle by deriving a class of inequalities which make no explicit mention about the number of outcomes of the experiments involved, and can therefore be used in continuous-variables measurements with no need for binning the continuous results into discrete ones. Apart from that intrinsic interest, these inequalities could prove important as a means to perform an unambiguous test of Bell inequalities since optical homodyne detection can be performed with high detection efficiency. The technique, which is based on a simple variance inequality, can alsobe used tore-derive alarge class of well-known Bell-type inequalities and at the same time find their quantum bound, making explicit from a formal point of view that the non-commutativity of the local operators is at the heart of the quantum violations. Finally, we address the issue of macroscopic superpositions originally sparked by the infamous cat paradox of Schrodinger. We consider macroscopic, mesoscopic and ‘S -scopic’ quantum superpositions of eigenstates of an observable, and develop some signatures for their existence. We define the extent, or size S of a (pure-state) su-perposition, with respect to an observable X, as being the maximum difference in the outcomes of X predicted by that superposition. Such superpositions are referred to as generalised S -scopic superpositions to distinguish them from the extreme superpo-sitions that superpose only the two states that have a difference S in their prediction for the observable. We also consider generalised S -scopic superpositions of coherent states. We explore the constraints that are placed on the statistics if we suppose a system to be described by mixtures of superpositions that are restricted in size. In this way we arrive at experimental criteria that are sufficient to deduce the existence of a generalised S -scopic superposition. The signatures developed are useful where one is able to demonstrate a degree of squeezing.
We show that scattering a quantum particle on a one-dimensional potential barrier as well as scattering the electromagnetic wave on a quasi-one-dimensional layered structure (both represent scattering problems with one 'source' and two 'sinks') violate the superposition principle; the role of nonlinear elements is played here by the potential barrier and the layered structure, splitting the incident (probability and electromagnetic) wave into two parts (transmitted and reflected). This explains why all attempts to solve the tunneling time problem within the framework of the standard (linear) models of these processes, both in quantum mechanics and in classical electrodynamics, have been unsuccessful. We revise the traditional formulation of the superposition principle, present a new (nonlinear) wave model, by the example of the quantum-mechanical scattering process, and show that concepts of the tunneling time developed on its basis are free from the Hartman paradox.