The theoretical apparatus of semantic realism: A new language for classical and quantum physics

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 dichotomy are criticizable, and many quantum paradoxes can be attributed to it. We discuss a new viewpoint in this paper (semantic realism, or briefly SR), which applies both to classical physics (CP) and to QP. and is characterized by the attempt of giving up verificationism without adopting ontological realism. As a first step, we construct a formalized observative language L endowed with a correspondence truth theory. Then, we state a set of axioms by means of L which hold both in CP and in QP. and construct a further language L_v which can express bothtestable andtheoretical properties of a given physical system. The concepts ofmeaning andtestability do not collapse in L and L_e hence we can distinguish between semantic and pragmatic compatibility of physical properties and define the concepts of testability and conjoint testability of statements of L and L_e. In this context a new metatheoretical principle (MGP) is stated, which limits the validity of empirical physical laws. By applying SR (in particular. MGP) to QP, one can interpret quantum logic as a theory of testability in QP, show that QP is semantically incomplete, and invalidate the widespread claim that contextuality is unavoidable in QP. Furthermore. SR introduces some changes in the conventional interpretation of ideal measurements and Heisenbergs uncertainty principle.     

On the logical foundations of the Jauch-Piron approach to quantum physics

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 structure of the JP theory by means ofL _e . Finally, we show that the JP syntactic system can be endowed with an intended interpretation, which yields a physical model of the system. A mathematical model endowed with a physical interpretation is given which establishes (in the usual sense of the model theory) the coherence of the JP syntactic system.     

MGP Versus Kochen–Specker Condition in Hidden Variables Theories

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 one to introduce a class of hidden parameters theories in which contextuality can, in principle, be avoided, since the proofs of the Bell–Kochen–Specker theorem break down. A simple model recently provided by the author for an objective interpretation of quantum mechanics can be looked at as a noncontextual hidden parameters theory, which shows that such theories actually exist.     

Semantic realism versus EPR-Like paradoxes: The Furry,Bohm-Aharonov,and Bell paradoxes

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, we consider the Bell-Kochen-Specker und the Bell theorems that should prove that QP is inherently contextual and nonlocal, respectively, and show that they can be invalidated in the SR approach. This removes the seeming contradiction between the basic assumptions of SR and QP, and proves that some problematic features that are usually attributed to QP, us contextuality and nonlocality, occur because of the adoption of a verificationist position, from one side, and from an insufficient adherence to the operational principles that have inspired QP itself, from the other side.     

Semantic Realism: A New Philosophy for Quantum Physics

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 analternative viewpoint, according to which evennontestable statements made up of individually testablestatements have a meaning, but quantum laws are notnecessarily true in physical contexts that QP itselfclassifies as nonaccessible. This viewpoint produces a new interpretation of QP which preserves itsformal structure and observational interpretation, butinvalidates those theorems that aim to prove suchpuzzling features of this theory as nonlocality and contextuality (Bell and Bell-Kochen-Speckertheorems).     

Quantum logics seen as quantum testability theories

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 can be interpreted as quantum physical theories of the metalinguistic concept of testability in the framework of a suitable classical language (with Tarskian semantics).     

Semantic incompleteness of quantum physics and EPR-like paradoxes

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 paradoxes that seem to follow from the analysis of the Einstein, Podolsky, and Rosen (EPR) thought experiment. Some recent results are summarized (in particular, the semantical incompleteness of QP) obtained by the author in the framework of the aforesaid approach, and it is shown that they can be used in order to deal with some EPR-like paradoxes. Thus one can legitimately affirm that at least some of them can be a consequence of semantical ambiguities and of the acceptance of a philosophical dichotomy which is not logically unavoidable.     

Analysis of the Einstein-Podolsky-Rosen experiment by relativistic quantum logic

The EPR experiment is investigated within the abstract language of relativistic quantum physics (relativistic quantum logic). First we show that the principles of reality (R) and locality (L) contradict the validity principle (Q) of quantum physics. A reformulation of this argument is then given in terms of relativistic quantum logic which is based on the principlesR andQ. It is shown that the principleL must be replaced by a convenient relaxation ¯L, by which the contradiction can be eliminated. On the other hand this weak locality principle ¯L does not contradict Einstein causality and is thus in accordance with special relativity.     

Classical foundations of quantum logic

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 is put forward forL which is compatible with a physical interpretation and embodies a truth theory which provides the statistical quantifiers with properties that fit their interpretation; in this framework, the truth mode of physical laws is suitably characterized and a probability-frequency correlation principle is established. By making use ofL and , a set of basic physical laws is stated that hold both in classical physics (CP) and in quantum physics (QP), which allow the selection of suitable subsets of primitive predicates ofL (the set _P of pure states; the sets _o and _E of operational and exact effects, respectively) and the introduction on these subsets of binary relations (a preclusion relation # on _P , an order relation < on _E . By assuming further physical laws, ( _E , <) turns out to be a complete orthocomplemented lattice [mixtures and atomicity of ( _E , <) also can be introduced by means of suitable physical assumptions]. Two languagesL _E ^x andL _E ^S are constructed that can be mapped intoL; the mapping induces on them mathematical structures, some kind of truth function, an interpretation. The formulas ofL _E ^x can be interpreted as statements about properties of a physical object, and the truth function onL _E ^x is two valued. The formulas ofL _E ^S can be endowed with two different interpretations as statements about the frequency of some physical property in some class (state) of physical objects; consequently, a two-valued truth function and a multivalued fuzzy-truth function are defined onL _E ^S . In all cases the algebras of propositions of these logics are complete orthocomplemented lattices isomorphic to ( _E , <). These results hold both in CP and in QP; further physical assumptions endow the lattice ( _E , <), henceL _E ^x andL _E/S , with further properties, such as distributivity in CP and weak modularity and covering law in QP. In the latter case,L _E ^S andL _E ^S , together with their interpretations, can be considered different models of the same basic mathematical structure, and can be identified with standard (elementary) quantum logics. These are therefore founded on the classical extended languageL with semantic model .     

Physical Propositions and Quantum Languages

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 obtained by selecting a subset of p-testable propositions within the Boolean lattice of all propositions associated with sentences of ℒ(x). Yet, the aforesaid semantics is incompatible with the standard interpretation of quantum mechanics (QM) because of known no-go theorems. But if one accepts our criticism of these theorems and the ensuing SR (semantic realism) interpretation of QM, the incompatibility disappears, and the classical and quantum notions of truth can coexist, since they refer to different metalinguistic concepts (truth and verifiability according to QM, respectively). Moreover one can construct a quantum language ℒ _TQ (x) whose Lindenbaum–Tarski algebra is isomorphic to QL, the sentences of which state (testable) properties of individual samples of physical systems, while standard QL does not bear this interpretation.     

Quantum physics as a particular domain of probabilistic physics

Quantum physics (QP) is meant as a whole science having both theoretical and experimental parts. The subjects of these parts in any science are entirely different. The experimental part deals with really existing particular objects (concrete objects), whereas the theoretical part refers to the so-calledabstract objects which are used in our considerations only. The necessity of a strict distinction between concrete and abstract objects is a crucialkey methodological principle (KMP). This principle allows one to construct the science of probability (probabilistics) whose theoretical and experimental parts are, respectively,probability theory andexperimental statistics, Probabilistics suggests two methods of solving probabilistic problems: theclassical method and thequantum approach. The application of probabilistics to physics leads toprobabilistic physics, whose two interconnected particular domains,classical statistical physics (CSP) and QP, result, respectively, from the treatment of macrosystems by the classical method and of microsystems by the quantum approach. The mathematical peculiarities of QP stem from the pertinent ones in probabilistics itself. Having been constructed as a particular domain of probabilistic physics, QP needs no artificial interpretation. Many quantum-related issues and paradoxes are thereby easily settled.     

Weak Value,Quasiprobability and Bohmian Mechanics

We clarify the significance of quasiprobability (QP) in quantum mechanics that is relevant in describing physical quantities associated with a transition process. Our basic quantity is Aharonov’s weak value, from which the QP can be defined up to a certain ambiguity parameterized by a complex number. Unlike the conventional probability, the QP allows us to treat two noncommuting observables consistently, and this is utilized to embed the QP in Bohmian mechanics such that its equivalence to quantum mechanics becomes more transparent. We also show that, with the help of the QP, Bohmian mechanics can be recognized as an ontological model with a certain type of contextuality.     

Semantic incompleteness of quantum physics

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 property which characterizes it in QP, and that the set of all properties whose truth value can be predicted for a physical object in the stateS coincides with the set of all properties which are certainly true or certainly false inS. These results lead us to introduce a notion of compatibility between states which can be applied to the EPR experiment, in order to prove that no quantum paradox follows from it if our interpretation of states and physical properties is accepted.     

Symmetries of physical theories

A physical theory is, by definition, a complete orthomodular atomic lattice having the covering property. GivenL a quantum logic andS _L the set of all its states, a theorem is proved which asserts that, if certain reasonable assumptions concerningS _L are satisfied, then for any bijective convex mappingU: S _LS_L, satisfying also certain physically meaningful conditions, there exists a unique automorphismV: L L such thatU(p)=p oV ^–1 for allp S _L.     

Quantum Set Theory

The complete orthomodular lattice of closed subspaces of a Hilbert space is considered as the logic describing a quantum physical system, and called a quantum logic. G. Takeuti developed a quantum set theory based on the quantum logic. He showed that the real numbers defined in the quantum set theory represent observables in quantum physics. We formulate the quantum set theory by introducing a strong implication corresponding to the lattice order, and represent the basic concepts of quantum physics such as propositions, symmetries, and states in the quantum set theory.     

Quantum Physics with Neutrons: From Spinor Symmetry to Kochen-Specker Phenomena

In 1974 perfect crystal interferometry has been developed and immediately afterwards the 4π-symmetry of spinor wave-functions has been verified. The new method opened a new access to the observation of intrinsic quantum phenomena. Spin-superposition, quantum state reconstruction and quantum beat effects are examples of such investigations. In this connection efforts have been made to separate and measure various dynamical and geometrical phases. Non-cyclic and non-adiabatic topological phases have been identified and their stability against various fluctuations and dissipative forces has been investigated by means of ultra-cold neutrons. An entanglement between different degrees of freedom of a single neutron system demonstrated the contextuality feature of quantum mechanics. In its continuation this yields to Kochen-Specker theorem like investigations providing a new basis for information processing and for the understanding of quantum physics in general. All investigations show the equivalence of various phase spaces and show how physical phenomena are correlated by quantum laws. Some curiosa occurred during the experiments and some epistemological aspects will be discussed as well.     

Logics for quantum mechanics

The two concepts of probability used in physics are analyzed from the formal and the material points of view. The standard theory corresponds toprob ₁ (probability of the coexistence of two properties). A general logicomathematical theory ofprob ₂ (probability of transition between states) is presented in axiomatic form. The underlying state algebra is neither Boolean nor Birkhoff-von Neumann but partial Boolean. In the Boolean subalgebras,prob ₁ theory holds. The theory presented contains the logicomathematical foundations of quantum mechanics and, as degenerate cases, the theories of stochastic games and of Markov chains.     

Quantum Non-Gravity and Stellar Collapse

Observational indications combined with analyses of analogue and emergent gravity in condensed matter systems support the possibility that there might be two distinct energy scales related to quantum gravity: the scale that sets the onset of quantum gravitational effects E_BE_{\rm B} (related to the Planck scale) and the much higher scale E_LE_{\rm L} signalling the breaking of Lorentz symmetry. We suggest a natural interpretation for these two scales: E_LE_{\rm L} is the energy scale below which a special relativistic spacetime emerges, E_BE_{\rm B} is the scale below which this spacetime geometry becomes curved. This implies that the first ‘quantum’ gravitational effect around E_BE_{\rm B} could simply be that gravity is progressively switched off, leaving an effective Minkowski quantum field theory up to much higher energies of the order of E_LE_{\rm L}. This scenario may have important consequences for gravitational collapse, inasmuch as it opens up new possibilities for the final state of stellar collapse other than an evaporating black hole.     

Towards a Resolution of Dilemma: Nonlocality or Nonobjectivity?

This paper discusses a possible resolution of the nonobjectivity-nonlocality dilemma in quantum mechanics in the light of experimental tests of the Bell inequality for two entangled photons and a Bell-like inequality for a single neutron. My conclusion is that these experiments show that quantum mechanics is nonobjective: that is, the values of physical observables cannot be assigned to a system before measurement. Bell’s assumption of nonlocality has to be rejected as having no direct experimental confirmation, at least thus far. I also consider the relationships between nonobjectivity and contextuality. Specifically, I analyze the impact of the Kochen-Specker theorem on the problem of contextuality of quantum observables. I argue that, just as von Neumann’s “no-go” theorem, the Kochen-Specker theorem is based on assumptions that do not correspond to the real physical situation. Finally, I present a theory of measurement based on a classical, purely wave model (pre-quantum classical statistical field theory), a model that reproduces quantum probabilities. In this model continuous fields are transformed into discrete clicks of detectors. While this model is classical, it is nonobjective. In this case, nonobjectivity is the result of the dependence of experimental outcomes on the context of measurement, in accordance with Bohr’s view.     

Electromagnetic momentum in frontiers of modern physics

We review the role of the momentum of the electromagnetic (EM) fields P _e in several areas of modern physics. P _e represents the EM interaction in equations for matter and light waves propagation. As an application of wave propagation properties, a first order optical experiment which tests the speed of light in moving rarefied gases is presented. Within a classical context, the momentum P _e appears also in proposed tests of EM interactions involving open currents and angular momentum conservation laws. Moreover, P _e is the link to the unitary vision of the quantum effects of the Aharonov-Bohm (AB) type and, for several of these effects, the strength of P _e is evaluated. These effects provide a quantum approach to evaluate the limit of the photon mass m _ph. A new effect of the AB type, together with the scalar AB effect, provides the basis for table-top experiments which yield the limit m _ph = 9.4 × 10⁻⁵²g, a value that improves the results achieved with recent classical and quantum approaches.