Interpreting Quantum Logic as a Pragmatic Structure

Many scholars maintain that the language of quantum mechanics introduces a quantum notion of truth which is formalized by (standard, sharp) quantum logic and is incompatible with the classical (Tarskian) notion of truth. We show that quantum logic can be identified (up to an equivalence relation) with a fragment of a pragmatic language \(\mathcal {L}_{G}^{P}\) of assertive formulas, that are justified or unjustified rather than trueor false. Quantum logic can then be interpreted as an algebraic structure that formalizes properties of the notion of empirical justification according to quantum mechanics rather than properties of a quantum notion of truth. This conclusion agrees with a general integrationist perspective that interprets nonstandard logics as theories of metalinguistic notions different from truth, thus avoiding incompatibility with classical notions and preserving the globality of logic.     

Interpreting Quantum Parallelism by Sequents

We introduce an interpretation of quantum superposition in predicative sequent calculus, in the framework of basic logic. Then we introduce a new predicative connective for the entanglement. Our aim is to represent quantum parallelism in terms of logical proofs.     

Failure of Standard Quantum Mechanics for the Description of Compound Quantum Entities

We reformulate the separated quantum entities theorem, i.e., the theorem that proves that two separated quantum entities cannot be described by means of standard quantum mechanics, within the fully elaborated operational Geneva–Brussels approach to quantum axiomatics, where the basic mathematical structure is that of a State Property System. We give arguments that show that the core of this result indicates a failure of standard quantum mechanics, and not just some peculiar shortcoming due to the axiomatic approach to quantum mechanics itself.     

Quantum Statistics of Identical Particles

Foundations of Physics - This paper is concerned with the causally symmetric version of the familiar de Broglie–Bohm interpretation, this version allowing the spacelike nonlocality and the...     

A Representation for Compound Quantum Systems as Individual Entities: Hard Acts of Creation and Hidden Correlations

We introduce an explicit definition for hidden correlations on individual entities in a compound system: when one individual entity is measured, this induces a well-defined transition of the proper state of the other individual entities. We prove that every compound quantum system described in the tensor product of a finite number of Hilbert spaces can be uniquely represented as a collection of individual entities between which there exist such hidden correlations. We investigate the significance of these hidden correlation representations within Aerts' creation-discovery approach and in particular their compatibility with the hidden measurement formalism. This leads us to the introduction of the notions of soft and hard acts of creation and to the observation that our approach can be seen as a theory of individuals when it is compared to the standard quantum theory.     

Identical Quantum Particles and Weak Discernibility

Saunders has recently claimed that “identical quantum particles” with an anti-symmetric state (fermions) are weakly discernible objects, just like irreflexively related ordinary objects in situations with perfect symmetry (Black’s spheres, for example). Weakly discernible objects have all their qualitative properties in common but nevertheless differ from each other by virtue of (a generalized version of) Leibniz’s principle, since they stand in relations an entity cannot have to itself. This notion of weak discernibility has been criticized as question begging, but we defend and accept it for classical cases likes Black’s spheres. We argue, however, that the quantum mechanical case is different. Here the application of the notion of weak discernibility indeed is question begging and in conflict with standard interpretational ideas. We conclude that the introduction of the conceptual resource of weak discernibility does not change the interpretational status quo in quantum mechanics.     

Physics of Interference of Quantum Particles

Physics of the Solid State - The bra + ket quantum language, introduced earlier by the authors to explain quantum correlation at macroscopic distances, makes it possible to understand the physical...     

The Elementary Particles of Quantum Fields

The elementary particles of relativistic quantum field theory are not simple field quanta, as has long been assumed. Rather, they supplement quantum fields, on which they depend on but to which they are not reducible, as shown here with particles defined instead as a unified collection of properties that appear in both physical symmetry group representations and field propagators. This notion of particle provides consistency between the practice of particle physics and its basis in quantum field theory.     

Quantum Transport of Particles and Entropy

A unified view on macroscopic thermodynamics and quantum transport is presented. Thermodynamic processes with an exchange of energy between two systems necessarily involve the flow of other balancable quantities. These flows are first analyzed using a simple drift-diffusion model, which includes the thermoelectric effects, and connects the various transport coefficients to certain thermodynamic susceptibilities and a diffusion coefficient. In the second part of the paper, the connection between macroscopic thermodynamics and quantum statistics is discussed. It is proposed to employ not particles, but elementary Fermi- or Bose-systems as the elementary building blocks of ideal quantum gases. In this way, the transport not only of particles but also of entropy can be derived in a concise way, and is illustrated both for ballistic quantum wires, and for diffusive conductors. In particular, the quantum interference of entropy flow is in close correspondence to that of electric current.     

Propagation of Relativistic Quantum Particles in Spacetime in Quantum Field Theory

The paper deals with a recent systematic study of the propagation of relativistic quantum particles in spacetime. This study was a reaction to the overwhelming number of experiments dealing with the localization of not only massive but also of photons by detectors. The method of study is based on a configuration unitarity expansion of the vacuum-to-vacuum transition amplitudes as, massive and massless, particles propagate between emitters and detectors. Topics treated are the amplitudes of propagation from one time-space coordinate to another, limiting velocities of particles and their reconciliations with relativity, emergence of particles into cones in detection regions versus the direction of their moments, stimulated emissions by external sources in spacetime, scattering theory in quantum field theory in configuration space, and finally a spacetime for mulation of closed-time path for multi-particle states.     

No Labeling Quantum Mechanics of Indiscernible Particles

Our aim in this paper is to show an example of the formalism we have developed to avoid the label-tensor-product-vector-space-formalism of quantum mechanics when dealing with indistinguishable quanta. States in this new vector space, that we call the Q-space, refer only to occupation numbers and permutation operators act as the identity operator on them, reflecting in the formalism the unobservability of permutations, a goal of quasi-set theory.     

Quantum Correlations in Systems of Indistinguishable Particles

We discuss quantum correlations in systems of indistinguishable particles in relation to entanglement in composite quantum systems consisting of well separated subsystems. Our studies are motivated by recent experiments and theoretical investigations on quantum dots and neutral atoms in microtraps as tools for quantum information processing. We present analogies between distinguishable particles, bosons, and fermions in low-dimensional Hilbert spaces. We introduce the notion of Slater rank for pure states of pairs of fermions and bosons in analogy to the Schmidt rank for pairs of distinguishable particles. This concept is generalized to mixed states and provides a correlation measure for indistinguishable particles. Then we generalize these notions to pure fermionic and bosonic states in higher-dimensional Hilbert spaces and also to the multi-particle case. We review the results on quantum correlations in mixed fermionic states and discuss the concept of fermionic Slater witnesses. Then the theory of quantum correlations in mixed bosonic states and of bosonic Slater witnesses is formulated. In both cases we provide methods of constructing optimal Slater witnesses that detect the degree of quantum correlations in mixed fermionic and bosonic states.     

Stochastically and Intrinsically Extended Non-relativistic Quantum Particles

Stochastically and intrinsically extended non relativistic quantum particles are described by combining the ideas of a stochastic quantum theory and a quantum functional theory. The former relates the extension to imperfect real measurements while the latter considers it as intrinsic. Physical states, Positive-Operator-Valued measures connected to measurement, and propagators are given and discussed. The stochastic theory is sufficient when the bilocal field describing the particle has a product form.     

Interpreting Observables in a Quantum World from the Categorial Standpoint

We develop a relativistic perspective on structures of quantum observables, in terms of localization systems of Boolean coordinatizing charts. This perspective implies that the quantum world is comprehended via Boolean reference frames for measurement of observables, pasted together along their overlaps. The scheme is formalized categorically, as an instance of the adjunction concept. The latter is used as a framework for the specification of a categorical equivalence signifying an invariance in the translational code of communication between Boolean localizing contexts and quantum systems. Aspects of the scheme semantics are discussed in relation to logic. The interpretation of coordinatizing localization systems, as structure sheaves, provides the basis for the development of an algebraic differential geometric machinery suited to the quantum regime.     

Interpreting Quantum Mechanics according to a Pragmatist Approach

The aim of this paper is to show that quantum mechanics can be interpreted according to a pragmatist approach. The latter consists, first, in giving a pragmatic definition to each term used in microphysics, second, in making explicit the functions any theory must fulfil so as to ensure the success of the research activity in microphysics, and third, in showing that quantum mechanics is the only theory which fulfils exactly these functions. This work received financial support from the European Union (Marie Curie Actions).     

Excitation of a Quantum Oscillator by Charged Particles

Journal of Experimental and Theoretical Physics - The excitation of a linear quantum oscillator (LQO) upon a collision with a charged particle moving in a rectilinear trajectory is analyzed. The...