Claudio Garola

INFN - Istituto Nazionale di Fisica Nucleare | INFN · Lecce

Most scholars maintain that quantum mechanics (QM) is a contextual theory and that quantum probability does not allow for an epistemic (ignorance) interpretation. By inquiring possible connections between contextuality and non-classical probabilities we show that a class TμMP of theories can be selected in which probabilities are introduced as clas...

This article aims to show that the incompatibility between the application of logic to norms and values and the expressive conception of these notions – basically summed up by the Frege–Geach problem – can be overcome. To this end, a logic is constructed for the expressive conception of norms and values which provides a solution to the Frege–Geach...

According to a standard view, quantum mechanics (QM) is a contextual theory and quantum probability does not satisfy Kolmogorov’s axioms. We show, by considering the macroscopic contexts associated with measurement procedures and the microscopic contexts (μ-contexts) underlying them, that one can interpret quantum probability as epistemic, despite...

The standard interpretation of quantum mechanics (QM) implies that QM is a contextual theory and that the probability measures associated with quantum states do not satisfy the assumptions of Kolmogorov's probability theory. These features of QM are shared nowadays by other scientific theories, as some quantum-like models of cognitive phenomena. We...

We have proposed in several recent papers a critical view of some parts of quantum mechanics (QM) that is methodologically unusual because it rests on analysing the language of QM by using some elementary but fundamental tools of mathematical logic. Our approach proves that some widespread beliefs about QM can be questioned and establishes new link...

According to a standard view, quantum mechanics (QM) is a contextual theory and quantum probability does not satisfy Kolmogorov's axioms. We show, by considering the macroscopic contexts associated with measurement procedures and the microscopic contexts (mu-contexts) underlying them, that one can interpret quantum probability as epistemic, despite...

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 {...

The ESR model has been recently proposed in several papers to offer a possible solution of the problems raising from the nonobjectivity of physical properties in quantum mechanics (QM) (mainly the objectification problem of the quantum theory of measurement). This solution is obtained by embodying the mathematical formalism of QM into a broader mat...

Most scholars concerned with the foundations of quantum mechanics (QM) think that contextuality and nonlocality (hence nonobjectivity of physical properties) are unavoidable features of QM which follow from the mathematical apparatus of QM. Moreover these features are usually considered as basic in quantum information processing. Nevertheless they...

Scholars have wondered for a long time whether the language of quantum mechanics introduces a quantum notion of truth which is formalized by quantum logic (QL) and is incompatible with the classical (Tarskian) notion. We show that QL can be interpreted as a pragmatic language of assertive formulas which formalize statements about physical systems t...

Scholars concerned with the foundations of quantum mechanics (QM) usually think that contextuality (hence nonobjectivity of physical properties, which implies numerous problems and paradoxes) is an unavoidable feature of QM which directly follows from the mathematical apparatus of QM. Based on some previous papers on this issue, we criticize this v...

Some years ago Szab\'o and Fine proposed a {\it local} hidden variable theory for the GHZ experiment based on the assumption that "the detection efficiency is not (only) the effect of random errors in the detector equipment, but it is a more fundamental phenomenon, the manifestation of a predetermined hidden property of the particles". Szab\'o and...

Secondo l'interpretazione standard della meccanica quantistica le proprieta di un sistema fisico microscopico non possono essere considerate possedute o non possedute dal sistema prima di una misura (non-oggettivita). L'esito di una misura dipende infatti dall'intero insieme di misure compatibili che sono effettuate simultaneamente (contestualita,...

The extended semantic realism (ESR) model proposes a theoretical perspective which reinterprets quantum probabilities as conditional on detection rather than absolute and embodies the mathematical formalism of standard (Hilbert space) quantum mechanics (QM) in a noncontextual, hence local, framework. The assumptions needed to prove the Bell inequal...

A crucial and problematical feature of quantum mechanics (QM) is nonobjectivity of properties. The ESR model restores objectivity reinterpreting quantum probabilities as conditional on detection and embodying the mathematical formalism of QM into a broader noncontextual (hence local) framework. We propose here an improved presentation of the ESR mo...

The interpretation of mixtures is problematic in quantum mechanics (QM) because physical properties are nonobjective in this theory. An extended semantic realism model was recently developed, restoring objectivity by reinterpreting quantum probabilities as conditional on detection and embodying the QM mathematical formalism in a broader noncontextu...

The extended semantic realism (ESR) model proposes a new theoretical perspective which embodies the mathematical formalism of standard (Hilbert space) quantum mechanics (QM) into a noncontextual framework, reinterpreting quantum probabilities as conditional instead of absolute. We provide in this review an overall view on the present status of our...

We present a procedure which allows us to recover classical and nonclassical logical structures as \emph{concrete logics} associated with physical theories expressed by means of classical languages. This procedure consists in choosing, for a given theory $\mathcal T$ and classical language $\mathcal L$ expressing $\mathcal T$, an observative sublan...

Based on known theoretical results (mainly the Bell and the Bell-Kochen-Speckertheorems) most quantumphysicistsmaintain that contextuality and nonlocality are unavoidableconsequences of the mathematical apparatus of quantum mechanics (QM).Yet contextuality and nonlocality entail known paradoxes and unsolved problems inquantum theory measurement. A...

This notes clarity authors positions on a possibility to go beyond quantum mechanics.

The extended semantic realism ( ESR ) model proposes a new theoretical perspective which embodies the mathematical formalism of Hilbert space quantum mechanics (QM) into a broader noncontextual, hence local, framework, reinterpreting quantum probabilities as conditional (in a nonstandard sense). We have proven in a previous paper that each general...

The extended semantic realism (ESR) model proposes a new theoretical perspective that embodies the mathematical formalism of standard (Hilbert space) quantum mechanics (QM) in a noncontextual framework, reinterpreting quantum probabilities as conditional instead of absolute. We provide here a Hilbert space representation of the generalized observab...

The Bell–Kochen–Specker theorem is criticized from an epistemological point of view, showing that its proofs rest on an implicit epistemological assumption which does not fit in with the operational and antimetaphysical attitude of orthodox quantum mechanics.

The extended semantic realism (ESR) model, recently worked out by the author, embodies the mathematical formalism of standard (Hilbert space) quantum mechanics (QM) in a noncontextual framework and reinterprets quantum probabilities as conditional instead of absolute. The predictions of the ESR model do not coincide with the predictions of QM, whi...

The extended semantic realism (ESR) model recently worked out by one of the authors embodies the mathematical formalism of standard (Hilbert space) quantum mechanics in a noncontextual framework, reinterpreting quantum probabilities as conditional instead of absolute. We provide here a Hilbert space representation of the generalized observables int...

The extended semantic realism (ESR) model embodies the mathematical formalism of standard (Hilbert space) quantum mechanics in a noncontextual framework, reinterpreting quantum probabilities as conditional instead of absolute. We provide here an improved version of this model and show that it predicts that, whenever idealized measurements are perfo...

Most physicists uphold that the tests of the Bell inequalities (BI) performed up to now confirm the predictions of standard quantum mechanics (SQM) and refute local realism. But some scholars criticize this conviction, defending local realism in various ways. We present here a new viewpoint based on an improved version of the extended semantic real...

Basing on known theoretical results (Bell's theorem, Bell-Kochen-Specker's theorem, etc.) most physicists believe that standard quantum mechanics (SQM) and local realism cannot hold together. Moreover, they also uphold that the experimental tests performed up to now confirm SQM and refute local realism. Some scholars, however, criticize this conclu...

The word proposition is used in physics with different meanings, which must be distinguished to avoid interpretational problems. We construct two languages ℒ * (x) and ℒ(x) with classical set-theoretical semantics which allow us to illustrate those meanings and to show that the non-Boolean lattice of propositions of quantum logic (QL) can be obtain...

Mixed states are introduced in physics in order to express our ignorance about the actual state of a physical system and are represented in standard quantum mechanics (QM) by density operators. Such operators also appear if one considers a (pure) entangled state of a compound system $\Omega$ and performs partial traces on the projection operator re...

The Geneva–Brussels approach to quantum mechanics (QM) and the semantic realism (SR) nonstandard interpretation of QM exhibit some common features and some deep conceptual differences. We discuss in this paper two elementary models provided in the two approaches as intuitive supports to general reasonings and as a proof of consistency of general as...

Introduction / C. Garola, A. Rossi and S. Sozzo -- If Bertlmann had three feet / A. Afriat -- Macroscopic interpretability of quantum component systems / R. Ascoli -- Premeasurement versus measurement: a basic form of complementarity / G. Auletta and G. Tarozzi -- Remarks on conditioning / E. G. Beltrametti -- Entangled state preparation in experim...

The term proposition usually denotes in quantum mechanics (QM) an element of (standard) quantum logic (QL). Within the orthodox interpretation of QM the propositions of QL cannot be associated with sentences of a language stating properties of individual samples of a physical system, since properties are nonobjective in QM. This makes the interpret...

This volume provides a unique overview of recent Italian studies on the foundations of quantum mechanics and related historical, philosophical and epistemological topics. A gathering of scholars from diverse cultural backgrounds, the conference provided a forum for a fascinating exchange of ideas and perspectives on a range of open questions in qua...

The Einstein, Podolski and Rosen (EPR) argument aiming to prove the incompleteness of quantum mechanics (QM) was opposed by most EPR's contemporary physicists and is not accepted within the standard interpretation of QM, which maintains that QM is a complete theory. An analysis of the semantic implications of the opponent positions shows that they...

An elementary model is given which shows how an objective (hence local and noncontextual) picture of the microworld can be constructed without conflicting with quantum mechanics (QM). This contradicts known no-go theorems, which however do not hold in the model, and supplies some suggestions for a broader theory in which QM can be embedded.

The old Bohr-Einstein debate about the completeness of quantum mechanics (QM) was held on an ontological ground. The completeness problem becomes more tractable, however, if it is preliminarily discussed from a semantic viewpoint. Indeed every physical theory adopts, explicitly or not, a truth theory for its observative language, in terms of which...

An elementary model is given which shows how an objective (hence local and noncontextual) picture of the microworld can be constructed without conflicting with quantum mechanics (QM). This contradicts known no-go theorems, which however do not hold in the model, and supplies some suggestions for a broader theory in which QM can be embedded.

One of the authors has recently propounded an SR (semantic realism) model which shows, circumventing known no-go theorems, that an objective (noncontextual, hence local) interpretation of quantum mechanics (QM) is possible. We consider here compound physical systems and show why the proofs of nonlocality of QM do not hold within the SR model. We al...

Hidden variables theories for quantum mechanics are usually assumed to satisfy the KS condition. The Bell-Kochen-Specker theorem then shows that these theories are necessarily contextual. But the KS condition can be criticized from an operational viewpoint, which suggests that a weaker condition (MGP) should be adopted in place of it. This leads on...

An SR model is presented that shows how an objective (noncontextual and local) interpretation of quantum mechanics can be constructed, which contradicts some well-established beliefs following from the standard interpretation of the theory and from known no-go theorems. The SR model is not a hidden variables theory in the standard sense, but it can...

Nonobjectivity of physical properties enters physics with the standard interpretation of quantum mechanics (QM), and a number of paradoxes of this theory follow from it. It seems, however, based on sound physical arguments (double slit experiment, Heisenberg's principle, Bell–Kochen–Specker theorem, etc.), so that most physicists think that avoidin...

The epistemological position underlying thestandard interpretation of quantum physics (QP) can beclassified as a form of verificationism: to be precise,empirical verificationism (nontestable physical statements have no meaning). This position canbe criticized and maintained to be the deep root of manyquantum paradoxes. Semantic Realism proposes ana...

It is well known that the fathers of Quantum Physics (QP) maintained that a new epistemological attitude, not only a new physical theory, was needed in order to get over the crisis of Classical Physics (CP). But it is also well known that a universal agreement on the epistemological conception that must support QP has not yet been attained: this ha...

It is a commonplace that XXth century physics has produced powerful new theories, such as Relativity and quantum mechanics, that upset the world view provided by XIXth century physics. But every physicist knows how difficult it may be to explain the basic aspects of these theories to people having a non-physical professional training. The main reas...

We prove that the general scheme for physical theories that we have called semantic realism(SR) in some previous papers copes successfully with a number of EPR-like paradoxes when applied to quantum physics (QP). In particular, we consider the old arguments by Furry and Bohm- Aharonov and show that they are not valid within a SR framework. Moreover...

The standard interpretation of quantum physics (QP) and some recent generalizations of this theory rest on the adoption of a rerificationist theory of truth and meaning, while most proposals for modifying and interpreting QP in a realistic way attribute an ontological status to theoretical physical entities (ontological realism). Both terms of this...

An approach to quantum physics (QP) is proposed that is characterized by the attempt to give up the verificationist theory of truth underlying the standard interpretation of QP. As a first step, anobservatively minimal language L is constructed that is endowed with a Tarskian truth theory. Then, a set of axioms is stated by means of L that hold bot...

We construct an extension P of the standard language of classical propositional logic by adjoining to the alphabet of a new category of logical-pragmatic signs. The well formed formulas of are calledradical formulas (rfs) of P;rfs preceded by theassertion sign constituteelementary assertive formulas of P, which can be connected together by means of...

A typical sample of Bell's inequality is proved to require, besides the standard assumptions on realism and locality, the adoption of a metatheoretical classical principle for interpreting quantum laws. A new principle is proposed which is consistent with the operational philosophy of quantum physics; it is then shown that, whenever the latter prin...

Bell’s theorem is proved to rest on a metatheoretical assumption (MCP) regarding the validity of physical laws that is compatible with the worldview of Classical Physics, not with the worldview of Quantum Physics (QP). A new general principle (MGP) is stated here that is consistent with the basic operational philosophy of QP. By using MGP, which do...

In The Foundations of Quantum Mechanics - Historical Analysis and Open Questions, leading Italian researchers involved in different aspects of the foundations and history of quantum mechanics are brought together in an interdisciplinary debate. The book therefore presents an invaluable overview of the state of Italian work in the field at this mome...

A metatheoretical generalized principle (MGP) is stated that formalizes an operational non-standard way of looking at the laws of physics. In quantum physics MGP leads to the invalidation of Bell's inequality without renouncing a minimal form of realism or locality. Therefore, the violation of Bell's inequality predicted by quantum physics does not...

In the approach to quantum physics (QP) forwarded by the author ana priori formalization of the observative language of the theory is yielded. It is shown here that this formalization allows one to avoid both ontological realism and verificationism, which are the philosophically opposed positions that are usually assumed in the debate on the parado...

We forward an epistemological perspective regarding non-classical logics which restores the universality of logic in accordance with the thesis of global pluralism. In this perspective every non-classical truth-theory is actually a theory of some metalinguistic concept which does not coincide with the concept of truth (described by Tarski's truth t...

We confute logical relativism and forward an alternative epistemological thesis according to which nonstandard truth-theories are considered theories of some metalinguistic concepts which do not coincide with truth, this latter concept being exhaustively described by Tarski's truth theory. We illustrate our viewpoint by showing that quantum logics...

We discuss the completeness of quantum physics (QP) from a nonrealistic viewpoint. To this end we make use of the formalized languageL for QP that we introduced in a recent paper and show that QP is incomplete both in an intuitive sense and in a more formal logical sense. We also show that a pure state is not physically equivalent to the physical p...

We construct a languageL for a classical first-order predicate calculus with monadic predicates only, extended by means of a family of statistical quantifiers. Then, a formal semantic model We construct a languageL for a classical first-order predicate calculus with monadic predicates only, extended by means of a family of statistical quantifiers....

We make a critical analysis of the basic concepts of the Jauch-Piron (JP) approach to quantum physics. Then, we exhibit a formalized presentation of the mathematical structure of the JP theory by introducing it as a completely formalized syntactic system, i.e., we construct a formalized languageL e and formally state the logical-deductive structur...

We study the characterization of the 13 cases obtained in the classification of the irreducible linear–antilinear representations of semigroups in a finite-dimensional vector space X over an algebraically closed field K with a conjugation j (generalized Frobenius–Schur–Wigner, or FS×W, classification). It has already been shown that each case can b...

It has been proposed that some posets of quantum logic could be embedded into lattices in order to recover the lattice structure avoiding the introduction of ad hoc axioms. We consider here the embedding s of any posetS into the complete lattice s of its closed ideals (normal embedding ofS) and show that s can be characterized (up to a lattice isom...

We consider the set E of all the yes-no experiments that can be performed on a given physical system and the related posets (ℰ, ≤) of the «effects» and (ℒ,, ≤) of the «propositions», illustrate by means of examples the relations ≤ and {precedes or equal to} and give counterexamples for properties that one might suspect to hold in (ℰ, {precedes or e...

We reconsider a well-known classification, due to Wigner, of the unitary–antiunitary finite-dimensional irreducible group representations within a somewhat generalized mathematical framework, where, in particular, any algebraically closed field K with an involutory automorphism j is considered in place of the complex field C. We show that each case...

We analyze some commutation properties of the sets of mappings of a vector space X over a division ring K with a conjugation j which are relevant when studying symmetries in quantum mechanics and in elementary-particle physics. The first part of the paper is devoted to the “linear-antilinear centralizer” c, i.e. to the group of the linear and antil...

We briefly analyze two partial order relations that are usually introduced in quantum logic by making use of the concepts of yes-no experiment and of preparation as fundamental. We show that two distinct posetsE andL can be defined, the latter being identifiable with the lattice of quantum logic. We consider the posetE and find that it contains a s...

A proposition of Autonne , Frobenius and Schur concerning the equivalence of any unitary finite-dimensional complex group representation to a real representation and a related classification of such complex representations are both generalized to every family U of arbitrary mappings in any vector space over a (commutative or non-commutative) field...

Summary We consider the method originally developed by Kemble and Dunham to find approximate solutions to the Schrödinger equation, inside the W. K. B. method, using complex integration techniques. We generalize it in order to afford the discussion about any degree of approximation whatsoever. We briefly apply the method to scattering theory, bound...