1,182 research outputs found
Between Laws and Models: Some Philosophical Morals of Lagrangian Mechanics
I extract some philosophical morals from some aspects of Lagrangian
mechanics. (A companion paper will present similar morals from Hamiltonian
mechanics and Hamilton-Jacobi theory.) One main moral concerns methodology:
Lagrangian mechanics provides a level of description of phenomena which has
been largely ignored by philosophers, since it falls between their accustomed
levels--``laws of nature'' and ``models''. Another main moral concerns
ontology: the ontology of Lagrangian mechanics is both more subtle and more
problematic than philosophers often realize.
The treatment of Lagrangian mechanics provides an introduction to the subject
for philosophers, and is technically elementary. In particular, it is confined
to systems with a finite number of degrees of freedom, and for the most part
eschews modern geometry. But it includes a presentation of Routhian reduction
and of Noether's ``first theorem''.Comment: 106 pages, no figure
The non-relativistic limit of (central-extended) Poincare group and some consequences for quantum actualization
The nonrelativistic limit of the centrally extended Poincar\'e group is
considered and their consequences in the modal Hamiltonian interpretation of
quantum mechanics are discussed [ O. Lombardi and M. Castagnino, Stud. Hist.
Philos. Mod. Phys 39, 380 (2008) ; J. Phys, Conf. Ser. 128, 012014 (2008) ].
Through the assumption that in quantum field theory the Casimir operators of
the Poincar\'e group actualize, the nonrelativistic limit of the latter group
yields to the actualization of the Casimir operators of the Galilei group,
which is in agreement with the actualization rule of previous versions of modal
Hamiltonian interpretation [ Ardenghi et al., Found. Phys. (submitted)
Recovering the quantum formalism from physically realist axioms
We present a heuristic derivation of Born's rule and unitary transforms in
Quantum Mechanics, from a simple set of axioms built upon a physical
phenomenology of quantization. This approach naturally leads to the usual
quantum formalism, within a new realistic conceptual framework that is
discussed in details. Physically, the structure of Quantum Mechanics appears as
a result of the interplay between the quantized number of "modalities"
accessible to a quantum system, and the continuum of "contexts" that are
required to define these modalities. Mathematically, the Hilbert space
structure appears as a consequence of a specific "extra-contextuality" of
modalities, closely related to the hypothesis of Gleason's theorem, and
consistent with its conclusions.Comment: This is an improved version of arXiv:1505.01369 [quant-ph]. In v2
clarifications on the link between axioms and mathematic
Relational Quantum Mechanics
I suggest that the common unease with taking quantum mechanics as a
fundamental description of nature (the "measurement problem") could derive from
the use of an incorrect notion, as the unease with the Lorentz transformations
before Einstein derived from the notion of observer-independent time. I suggest
that this incorrect notion is the notion of observer-independent state of a
system (or observer-independent values of physical quantities). I reformulate
the problem of the "interpretation of quantum mechanics" as the problem of
deriving the formalism from a few simple physical postulates. I consider a
reformulation of quantum mechanics in terms of information theory. All systems
are assumed to be equivalent, there is no observer-observed distinction, and
the theory describes only the information that systems have about each other;
nevertheless, the theory is complete.Comment: Substantially revised version. LaTeX fil
From 2-sequents and Linear Nested Sequents to Natural Deduction for Normal Modal Logics
We extend to natural deduction the approach of Linear Nested Sequents and
2-sequents. Formulas are decorated with a spatial coordinate, which allows a
formulation of formal systems in the original spirit of natural
deduction---only one introduction and one elimination rule per connective, no
additional (structural) rule, no explicit reference to the accessibility
relation of the intended Kripke models. We give systems for the normal modal
logics from K to S4. For the intuitionistic versions of the systems, we define
proof reduction, and prove proof normalisation, thus obtaining a syntactical
proof of consistency. For logics K and K4 we use existence predicates
(following Scott) for formulating sound deduction rules
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