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 $P^{f}$ of all physical propositions is partially ordered and contains a subset $P^{f}_{T}$ of testable physical propositions whose order structure depends on the criteria of testability established by the physical theory. In particular, $P^{f}_{T}$ 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 $L_{TQ}(x)$, 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 $\hbar\rightarrow 0$ 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