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The Logic behind Feynman's Paths
The classical notions of continuity and mechanical causality are left in
order to refor- mulate the Quantum Theory starting from two principles: I) the
intrinsic randomness of quantum process at microphysical level, II) the
projective representations of sym- metries of the system. The second principle
determines the geometry and then a new logic for describing the history of
events (Feynman's paths) that modifies the rules of classical probabilistic
calculus. The notion of classical trajectory is replaced by a history of
spontaneous, random an discontinuous events. So the theory is reduced to
determin- ing the probability distribution for such histories according with
the symmetries of the system. The representation of the logic in terms of
amplitudes leads to Feynman rules and, alternatively, its representation in
terms of projectors results in the Schwinger trace formula.Comment: 15 pages, contribution to Mario Castagnino Festschrif
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
Speakable in Quantum Mechanics
At the 1927 Como conference Bohr spoke the now famous words "It is wrong to
think that the task of physics is to find out how nature is. Physics concerns
what we can say about nature." However, if the Copenhagen interpretation really
holds on to this motto, why then is there this feeling of conflict when
comparing it with realist interpretations? Surely what one can say about nature
should in a certain sense be interpretation independent. In this paper I take
Bohr's motto seriously and develop a quantum logic that avoids assuming any
form of realism as much as possible. To illustrate the non-triviality of this
motto a similar result is first derived for classical mechanics. It turns out
that the logic for classical mechanics is a special case of the derived quantum
logic. Finally, some hints are provided in how these logics are to be used in
practical situations and I discuss how some realist interpretations relate to
these logics
Quantum theory without Hilbert spaces
Quantum theory does not only predict probabilities, but also relative phases
for any experiment, that involves measurements of an ensemble of systems at
different moments of time. We argue, that any operational formulation of
quantum theory needs an algebra of observables and an object that incorporates
the information about relative phases and probabilities. The latter is the
(de)coherence functional, introduced by the consistent histories approach to
quantum theory. The acceptance of relative phases as a primitive ingredient of
any quantum theory, liberates us from the need to use a Hilbert space and
non-commutative observables. It is shown, that quantum phenomena are adequately
described by a theory of relative phases and non-additive probabilities on the
classical phase space. The only difference lies on the type of observables that
correspond to sharp measurements. This class of theories does not suffer from
the consequences of Bell's theorem (it is not a theory of Kolmogorov
probabilities) and Kochen- Specker's theorem (it has distributive "logic"). We
discuss its predictability properties, the meaning of the classical limit and
attempt to see if it can be experimentally distinguished from standard quantum
theory. Our construction is operational and statistical, in the spirit of
Kopenhagen, but makes plausible the existence of a realist, geometric theory
for individual quantum systems.Comment: 32 pages, Latex, 4 figures. Small changes in the revised version,
comments and references added; essentially the version to appear in Found.
Phy
Is mereology empirical? Composition for fermions
How best to think about quantum systems under permutation invariance is a
question that has received a great deal of attention in the literature. But
very little attention has been paid to taking seriously the proposal that
permutation invariance reflects a representational redundancy in the formalism.
Under such a proposal, it is far from obvious how a constituent quantum system
is represented. Consequently, it is also far from obvious how quantum systems
compose to form assemblies, i.e. what is the formal structure of their
relations of parthood, overlap and fusion.
In this paper, I explore one proposal for the case of fermions and their
assemblies. According to this proposal, fermionic assemblies which are not
entangled -- in some heterodox, but natural sense of 'entangled' -- provide a
prima facie counterexample to classical mereology. This result is puzzling;
but, I argue, no more intolerable than any other available interpretative
option.Comment: 24 pages, 1 figur
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