192,288 research outputs found
On the Meaning of the String-Inspired Noncommutativity and its Implications
We propose an alternative interpretation for the meaning of noncommutativity
of the string-inspired field theories and quantum mechanics. Arguments are
presented to show that the noncommutativity generated in the stringy context
should be assumed to be only between the particle coordinate observables, and
not of the spacetime coordinates. Some implications of this fact for
noncomutative field theories and quantum mechanics are discussed. In
particular, a consistent interpretation is given for the wavefunction in
quantum mechanics. An analysis of the noncommutative theories in the
Schr\"odinger formulation is performed employing a generalized quantum
Hamilton-Jacobi formalism. A formal structure for noncommutative quantum
mechanics, richer than the one of noncommutative quantum field theory, comes
out. Conditions for the classical and commutative limits of these theories have
also been determined and applied in some examples.Comment: References, comments, and footnotes are included; some changes in
section
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
Quantum mechanics, strong emergence and ontological non-reducibility
We show that a new interpretation of quantum mechanics, in which the notion
of event is defined without reference to measurement or observers, allows to
construct a quantum general ontology based on systems, states and events.
Unlike the Copenhagen interpretation, it does not resort to elements of a
classical ontology. The quantum ontology in turn allows us to recognize that a
typical behavior of quantum systems exhibits strong emergence and ontological
non-reducibility. Such phenomena are not exceptional but natural, and are
rooted in the basic mathematical structure of quantum mechanics.Comment: 8 pages, to appear in Foundations of Chemistr
Partial observables
We discuss the distinction between the notion of partial observable and the
notion of complete observable. Mixing up the two is frequently a source of
confusion. The distinction bears on several issues related to observability,
such as (i) whether time is an observable in quantum mechanics, (ii) what are
the observables in general relativity, (iii) whether physical observables
should or should not commute with the Wheeler-DeWitt operator in quantum
gravity. We argue that the extended configuration space has a direct physical
interpretation, as the space of the partial observables. This space plays a
central role in the structure of classical and quantum mechanics and the
clarification of its physical meaning sheds light on this structure,
particularly in context of general covariant physics.Comment: 9 pages, no figures references adde
From Classical to Wave-Mechanical Dynamics
The time-independent Schroedinger and Klein-Gordon equations - as well as any
other Helmholtz-like equation - were recently shown to be associated with exact
sets of ray-trajectories (coupled by a "Wave Potential" function encoded in
their structure itself) describing any kind of wave-like features, such as
diffraction and interference. This property suggests to view Wave Mechanics as
a direct, causal and realistic, extension of Classical Mechanics, based on
exact trajectories and motion laws of point-like particles "piloted" by de
Broglie's matter waves and avoiding the probabilistic content and the
wave-packets both of the standard Copenhagen interpretation and of Bohm's
theory.Comment: 15 pages, 1 figure. Substantial updates. arXiv admin note: text
overlap with arXiv:1310.807
The classical limit as an approximation
I argue that it is possible to give an interpretation of the classical limit of quantum mechanics that results in a partial explanation of the success of classical mechanics. The interpretation is novel in that it allows one to explain the success of the theoretical structure of classical mechanics. This interpretation clarifies the relationship between physical quantities and propositions in quantum theories, and provides a precise notion of a quantum theory holding ``approximately on certain scales"
Quanta Without Quantization
The dimensional properties of fields in classical general relativity lead to
a tangent tower structure which gives rise directly to quantum mechanical and
quantum field theory structures without quantization. We derive all of the
fundamental elements of quantum mechanics from the tangent tower structure,
including fundamental commutation relations, a Hilbert space of pure and mixed
states, measurable expectation values, Schroedinger time evolution, collapse of
a state and the probability interpretation. The most central elements of string
theory also follow, including an operator valued mode expansion like that in
string theory as well as the Virasoro algebra with central charges.Comment: 8 pages, Latex, Honorable Mention 1997 GRG Essa
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