QUANTUM THEORY: Reconsideration of Foundations—4

On Wave‐Particle Duality
View Description Hide DescriptionBy means of a thought‐experiment, consisting of an interference experiment with two interfering beams, it is shown that it can be demonstrated experimentally that with one single particle a wave can be associated that propagates in space and time as a physical reality, i.e. that it should not merely be considered as a distribution of probabilities. The notion “physical reality” should be understood such that, when this physical reality is considered in a particular space at a particular time, it should be experimentally possible to influence this reality in such a way that future results of experiments show unambiguously that this reality has been causally influenced by the experimental act in this space and at that time.

Interaction‐free Measurements
View Description Hide DescriptionBy means of thought‐experiments it is shown that, contrary to common opinion, there exist measurement processes that do not affect at all the measured system. These “negative” measurements consist in the ascertainment of the absence of measurement outcomes that are predicted to occur with a specific probability, and that allow—in analogy with “genuine” measurements—to make new statements about the measured system, and lead, hence, to “reduction of the wave function” in the same way as this is the case with normal, “positive”, observations that do disturb the measured system. The compelling consequence is, that the usual justification for the uncertainty relation as an unavoidable retroaction of any measurement process on the measured system breaks down, and that the real justification consists in the permanent influence on the particle of all matter in its immediate or more distant neighbourhood, independent of whether this matter is part of a measurement apparatus or not.

Universality of the EPR‐chameleon model
View Description Hide DescriptionIn terms of EPR‐chameleon models and local and causal measures, the Bell's argument is reanalyzed. Contrary to Bell, it is shown that the nontriviality of the joint probability measure does not always imply the nonlocality. It is analyzed that under what conditions correlations of distant particles are obtained which are different from the standard correlations. The protocol for the correlations of distant particles admits nontrivial probability measures respecting the locality.

Objective and Subjective Probabilities in Quantum Mechanics
View Description Hide DescriptionThe concept of probability was prominent in the original foundations of quantum mechanics and continues to be so today. Indeed, the controversies regarding objective and subjective interpretations of probability have again become active. I argue that, although both objective and subjective probabilities have domains of relevance in QM, their roles are quite distinct. Even where both are legitimate, the objective and subjective probabilities differ, both conceptually and numerically. There are quantum probabilities that have no useful subjective interpretations, and there are subjective probabilities that cannot be realized as quantum probabilities.

A Curious Geometrical Fact about Entanglement
View Description Hide DescriptionI sketch how the set of pure quantum states forms a phase space, and then point out a curiousity concerning maximally entangled pure states: they form a minimal Lagrangian submanifold of the set of all pure states. I suggest that this curiousity should have an interesting physical interpretation.

Unresolved Classical Electromagnetic Aspects of the Aharonov‐Bohm Phase Shift
View Description Hide DescriptionThe long‐standing controversy regarding the Aharonov‐Bohm phase shift is reviewed. The shifts of both optical and particle interference patterns are summarized. It is pointed out that a line of electric dipoles and a line of magnetic dipoles (a long solenoid) both produce experimentally observed phase shifts similar to that produced by introducing a rectangular block of glass behind one slit of a double‐slit interference pattern; the double‐slit pattern is shifted while the single‐slit envelope remains undisplaced. The quantum explanation for the magnetic interference pattern shift introduced by Aharonov and Bohm in 1959 involves completely different ideas from those suggested by a semiclassical analysis. Experiments planned by Caprez, Barwick, and Batelaan should clarify the connections between classical and quantum theories in connection with the Aharonov‐Bohm phase shift.

Operational Axioms for ‐algebra Representation of Transformations
View Description Hide DescriptionIt is shown how a ‐algebra representation of the transformations of a physical system can be derived from two operational postulates: 1) the existence of dynamically independent systems; 2) the existence of symmetric faithful states. Both notions are crucial for the possibility of performing experiments on the system, in preventing remote instantaneous influences and in allowing calibration of apparatuses. The case of Quantum Mechanics is thoroughly analyzed. The possibility that other no‐signaling theories admit a ‐algebra formulation is discussed.

Reality and Locality in Quantum Mechanics
View Description Hide DescriptionIt is argued in this work that in order to explain the conflict between Bell's inequality (BI) and quantum mechanics (QM), it is neither necessary to give up the notion of Einstein locality (LOC), nor that of reality, as is done in some recent work. The definite existence of EPR's “elements of reality” is shown by using a result in a former thought experiment by M. Renninger. Einstein locality is saved by sticking to the failure of counterfactual definiteness (CFD) at the level of individual quantum processes.

Simulating Quantum Computation on a Macroscopic Model
View Description Hide DescriptionWe present examples of macroscopic systems entailing a quantum mechanical structure. One of our examples has a structure which is isomorphic to the spin structure for a spin 1/2 and another system entails a structure isomorphic to the structure of two spin 1/2 in the entangled singlet state. We elaborate this system by showing that an arbitrary tensor product state representing two entangled qubits can be described in a complete way by a specific internal constraint between the ray or density states of the two qubits, which describes the behavior of the state of one of the spins if measurements are executed on the other spin. Since any n‐qubit unitary operation can be decomposed into 2‐qubit gates and unary operations, we argue that our representation of 2‐qubit entanglement contributes to a better understanding of the role of n‐qubit entanglement in quantum computation. We illustrate our approach on two 2‐qubit algorithms proposed by Deutsch, respectively Arvind et al.

From Copenhagen to Neo‐Copenhagen Interpretation
View Description Hide DescriptionPositive and negative features of the Copenhagen interpretation are discussed. As positive features can be mentioned its pragmatism and its awareness of the crucial role of measurement. However, the main part of the contribution is devoted to the negative features, to wit, its pragmatism (once again), its confounding of preparation and measurement, its classical account of measurement, its completeness claims, the ambiguity of its notion of correspondence, its confused notion of complementarity. It is demonstrated how confusions and paradoxes stemming from the negative features of the Copenhagen interpretation can be dealt with in an amended interpretation, to be referred to as ‘neo‐Copenhagen interpretation’, in which the role of the measuring instrument is taken seriously by recognizing the quantum mechanical character of its interaction with the microscopic object. The ensuing necessity of extending the notion of a quantum mechanical observable from the Hermitian operator of the standard formalism to the positive operator‐valued measure of a generalized formalism yields a sound mathematical basis for a transition from the Copenhagen contextualistic‐realist interpretation to the neo‐Copenhagen empiricist one. Applications to the uncertainty relations and to the Bell inequalities are briefly discussed.

On a Mathematical Model of Brain Activities
View Description Hide DescriptionThe procedure of recognition can be described as follows: There is a set of complex signals stored in the memory. Choosing one of these signals may be interpreted as generating a hypothesis concerning an “expexted view of the world”. Then the brain compares a signal arising from our senses with the signal chosen from the memory leading to a change of the state of both signals. Furthermore, measurements of that procedure like EEG or MEG are based on the fact that recognition of signals causes a certain loss of excited neurons, i.e. the neurons change their state from “excited” to “nonexcited”. For that reason a statistical model of the recognition process should reflect both—the change of the signals and the loss of excited neurons. A first attempt to explain the process of recognition in terms of quantum statistics was given in [1]. In the present note it is not possible to present this approach in detail. In lieu we will sketch roughly a few of the basic ideas and structures of the proposed model of the recognition process (Section). Further, we introduce the basic spaces and justify the choice of spaces used in this approach. A more elaborate presentation including all proofs will be given in a series of some forthcoming papers [2, 3]. In this series also the procedures of creation of signals from the memory, amplification, accumulation and transformation of input signals, and measurements like EEG and MEG will be treated in detail.

Quantum Logic and Macroscopic Quantum Games
View Description Hide DescriptionExamples of macroscopic situations when stochasticity is described by the quantum probability amplitude instead of the Kolmogorovian probability are given. They are based on the nondistributive quantum logical lattices obtained from some Boolean distributive ones by putting away some of its elements as unobservable. The possibility of the macroscopic quantum game based on these examples is discussed.

The Born Rule
View Description Hide DescriptionI review the Born probabilistic interpretation of quantum mechanics from its inception to the present, including my recent sharpenings. The paper looks closely at a few issues, and does not even mention many others.

Decoherence, Disentanglement and Foundations of Quantum Mechanics
View Description Hide DescriptionDecoherence and disentanglement are phenomena central to quantum mechanics. Here, we consider the relative rates of decoherence and disentanglement in two‐qubit, three‐qubit, and two‐qutrit systems when subject to pure dephasing noise alone, and a very recent result for systems. Of particular interest is the specific counterintuitive effect related to the nonadditivity of such weak noises, known as Entanglement Sudden Death (ESD), in which the entanglement of a composite quantum system goes abruptly to zero in finite time, coherence only exponentially decaying. We discuss these results in the context of the foundations of quantum mechanics.

Prequantum Classical Statistical Field Theory—PCSFT
View Description Hide DescriptionIn this short note we present (without to go into mathematical details) the main notions of Prequantum Classical Statistical Field Theory (PCSFT): theory of classical fields which fluctuations produce averages approximatively coinciding with averages given by the quantum formalism. Thus the conventional quantum mechanics can be considered as a probabilistic approximation of a more detailed classical field model. Experimental predictions of PCSFT are discussed

Bell's Inequality: Nonlocalty, “Death of Reality”, or Incompatibility of Random Variables?
View Description Hide DescriptionWe remind the viewpoint that violation of Bell's inequality might be interpreted not only as an evidence of the alternative—either nonlocality or “death of reality” (under the assumption the quantum mechanics is incomplete). Violation of Bell's type inequalities is a well known sufficient condition of incompatibility of random variables—impossibility to realize them on a single probability space. Thus, in fact, we should take into account an additional interpretation of violation of Bell's inequality—a few pairs of random variables (two dimensional vector variables) involved in the EPR‐Bohm experiment are incompatible. They could not be realized on a single Kolmogorov probability space. Thus one can choose between: a) completeness of quantum mechanics; b) nonlocality; c) “death of reality”; d) non‐Kolmogorovness. In any event, violation of Bell's inequality has a variety of possible interpretations. Hence, it could not be used to derive the unique conclusion on the relation between quantum and classical models.

Tomographic Entropy and New Entropic Uncertainty Relations
View Description Hide DescriptionSuch entropies as Shannon entropy, Renyi entropy, and von Neumann entropy are discussed for quantum states. New inequalities for quantum tomographic‐probability densities are considered.

Probability Instead of Wave Function and Bell Inequalities as Entanglement Criterion
View Description Hide DescriptionReview of the probability representation of quantum mechanics, in which a fair probability distribution is used instead of the density matrix or wave function to describe quantum states is presented. Bell inequalities are formulated as properties of joint probability distributions describing the states of multipartite spin systems in the probability representation. Probability distributions depending on extra parameters are discussed in the connection with problems of classical and quantum statistical mechanics, where these distributions can be considered in the context of non‐Kolmogorov probability theory.

The Pullback Mechanism in Stochastic Electrodynamics
View Description Hide DescriptionAn argument is given why the classical theory called Stochastic Electrodynamics may reproduce scattering and ionization experiments of electrons on atomic hydrogen.