57 research outputs found
Embedding QM into an objective framework
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.Comment: 8 page
A survey of the ESR model for an objective reinterpretation of quantum mechanics
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 raise still unsolved
problems, as the objectification problem in the quantum theory of measurement.
The extended semantic realism (ESR) model offers a possible way out from these
difficulties by embedding the mathematical formalism of QM into a broader
mathematical formalism and reinterpreting quantum probabilities as conditional
on detection rather than absolute. The embedding allows to recover the formal
apparatus of QM within the ESR model, and the reinterpretation of QM allows to
construct a noncontextual hidden variables theory which justifies the
assumptions introduced in the ESR model and proves its objectivity. According
to the ESR model both linear and nonlinear time evolution occur, depending on
the physical environment, as in QM. In addition, the ESR model, though
objective, implies modified Bell's inequalities that do not conflict with QM,
supplies different mathematical representations of proper and improper
mixtures, provides a general framework in which the local interpretations of
the GHZ experiment obtained by other authors are recovered and explained, and
supports an interpretation of quantum logic which avoids the introduction of
the problematic notion of quantum truth.Comment: 12 page
A Pragmatic Interpretation of Quantum Logic
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 that are empirically justified or
unjustified in the framework of quantum mechanics. According to this
interpretation, QL formalizes properties of the metalinguistic notion of
empirical justification within 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. By the way, some elucidations of
the standard notion of quantum truth are also obtained.
Key words: pragmatics, quantum logic, quantum mechanics, justifiability,
global pluralism.Comment: Third version: 20 pages. Sects. 1, 2, and 4 rewritten and improved.
Explanations adde
A Semantic Approach to the Completeness Problem in Quantum Mechanics
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 the notions of semantic objectivity and
semantic completeness of the physical theory can be introduced and inquired. In
particular, standard QM adopts a verificationist theory of truth that implies
its semantic nonobjectivity; moreover, we show in this paper that standard QM
is semantically complete, which matches Bohr's thesis. On the other hand, one
of the authors has provided a Semantic Realism (or SR) interpretation of QM
that adopts a Tarskian theory of truth as correspondence for the observative
language of QM (which was previously mantained to be impossible); according to
this interpretation QM is semantically objective, yet incomplete, which matches
EPR's thesis. Thus, standard QM and the SR interpretation of QM come to
opposite conclusions. These can be reconciled within an integrationist
perspective that interpretes non-Tarskian theories of truth as theories of
metalinguistic concepts different from truth.Comment: 19 pages. Further revision. Proof of Theorem 3.2.1 simplified,
Section 3.5 amended, minor changes in several sections. Accepted for
publication in Foundations of Physic
On the Notion of Proposition in Classical and Quantum Mechanics
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 interpretation of propositions
problematical. The difficulty can be removed by adopting the objective
interpretation of QM proposed by one of the authors (semantic realism, or SR,
interpretation). In this case, a unified perspective can be adopted for QM and
classical mechanics (CM), and a simple first order predicate calculus L(x) with
Tarskian semantics can be constructed such that one can associate a physical
proposition (i.e., a set of physical states) with every sentence of L(x). The
set of all physical propositions is partially ordered and contains a
subset of testable physical propositions whose order structure
depends on the criteria of testability established by the physical theory. In
particular, turns out to be a Boolean lattice in CM, while it can
be identified with QL in QM. Hence the propositions of QL can be associated
with sentences of L(x), or also with the sentences of a suitable quantum
language , and the structure of QL characterizes the notion of
testability in QM. One can then show that the notion of quantum truth does not
conflict with the classical notion of truth within this perspective.
Furthermore, the interpretation of QL propounded here proves to be equivalent
to a previous pragmatic interpretation worked out by one of the authors, and
can be embodied within a more general perspective which considers states as
first order predicates of a broader language with a Kripkean semantics.Comment: 22 pages. To appear in "The Foundations of Quantum Mechanics:
Historical Analysis and Open Questions-Cesena 2004", C. Garola, A. Rossi and
S. Sozzo Eds., World Scientific, Singapore, 200
Generalized Observables, Bell's Inequalities and Mixtures in the ESR Model for QM
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 research on this topic. We
attain in a new, shortened way a mathematical representation of the generalized
observables introduced by the ESR model and a generalization of the projection
postulate of elementary QM. Basing on these results we prove that the
Bell-Clauser-Horne-Shimony-Holt (BCHSH) inequality, a modified BCHSH inequality
and quantum predictions hold together in the ESR model because they refer to
different parts of the picture of the physical world supplied by the model.
Then we show that a new mathematical representation of mixtures must be
introduced in the ESR model which does not coincide with the standard
representation in QM and avoids some deep problems that arise from the
representation of mixtures provided by QM. Finally we get a nontrivial
generalization of the Luders postulate, which is justified in a special case by
introducing a reasonable physical assumption on the evolution of the compound
system made up of the measured system and the measuring apparatus.Comment: 24 pages, 1 figure, Found. Phy
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