423 research outputs found
Operational Quantum Mechanics, Quantum Axiomatics and Quantum Structures
The role of operational quantum mechanics, quantum axiomatics and quantum
structures in general is presented as a contribution to a compendium on quantum
physics, its history and philosophy.Comment: 6 page
The Linearity of Quantum Mechanics at Stake: The Description of Separated Quantum Entities
We consider the situation of a physical entity that is the compound entity
consisting of two 'separated' quantum entities. In earlier work it has been
proven by one of the authors that such a physical entity cannot be described by
standard quantum mechanics. More precisely, it was shown that two of the axioms
of traditional quantum axiomatics are at the origin of the impossibility for
standard quantum mechanics to describe this type of compound entity. One of
these axioms is equivalent with the superposition principle, which means that
separated quantum entities put the linearity of quantum mechanics at stake. We
analyze the conceptual steps that are involved in this proof, and expose the
necessary material of quantum axiomatics to be able to understand the argumentComment: 29 page
Being and Change: Foundations of a Realistic Operational Formalism
The aim of this article is to represent the general description of an entity
by means of its states, contexts and properties. The entity that we want to
describe does not necessarily have to be a physical entity, but can also be an
entity of a more abstract nature, for example a concept, or a cultural
artifact, or the mind of a person, etc..., which means that we aim at very
general description. The effect that a context has on the state of the entity
plays a fundamental role, which means that our approach is intrinsically
contextual. The approach is inspired by the mathematical formalisms that have
been developed in axiomatic quantum mechanics, where a specific type of quantum
contextuality is modelled. However, because in general states also influence
context -- which is not the case in quantum mechanics -- we need a more general
setting than the one used there. Our focus on context as a fundamental concept
makes it possible to unify `dynamical change' and `change under influence of
measurement', which makes our approach also more general and more powerful than
the traditional quantum axiomatic approaches. For this reason an experiment (or
measurement) is introduced as a specific kind of context. Mathematically we
introduce a state context property system as the structure to describe an
entity by means of its states, contexts and properties. We also strive from the
start to a categorical setting and derive the morphisms between state context
property systems from a merological covariance principle. We introduce the
category SCOP with as elements the state context property systems and as
morphisms the ones that we derived from this merological covariance principle.
We introduce property completeness and state completeness and study the
operational foundation of the formalismComment: 44 page
State property systems and orthogonality
The structure of a state property system was introduced to formalize in a
complete way the operational content of the Geneva-Brussels approach to the
foundations of quantum mechanics, and the category of state property systems
was proven to be equivalence to the category of closure spaces. The first
axioms of standard quantum axiomatics (state determination and atomisticity)
have been shown to be equivalent to the and axioms of closure
spaces, and classical properties to correspond to clopen sets, leading to a
decomposition theorem into classical and purely nonclassical components for a
general state property system. The concept of orthogonality, very important for
quantum axiomatics, had however not yet been introduced within the formal
scheme of the state property system. In this paper we introduce orthogonality
in a operational way, and define ortho state property systems. Birkhoff's well
known biorthogonal construction gives rise to an orthoclosure and we study the
relation between this orthoclosure and the operational orthogonality that we
introduced.Comment: 10 pages, 2 figures, proceeding of the IQSA 2002 conference in Vienn
Interpreting Quantum Particles as Conceptual Entities
We elaborate an interpretation of quantum physics founded on the hypothesis
that quantum particles are conceptual entities playing the role of
communication vehicles between material entities composed of ordinary matter
which function as memory structures for these quantum particles. We show in
which way this new interpretation gives rise to a natural explanation for the
quantum effects of interference and entanglement by analyzing how interference
and entanglement emerge for the case of human concepts. We put forward a scheme
to derive a metric based on similarity as a predecessor for the structure of
'space, time, momentum, energy' and 'quantum particles interacting with
ordinary matter' underlying standard quantum physics, within the new
interpretation, and making use of aspects of traditional quantum axiomatics.
More specifically, we analyze how the effect of non-locality arises as a
consequence of the confrontation of such an emerging metric type of structure
and the remaining presence of the basic conceptual structure on the fundamental
level, with the potential of being revealed in specific situations.Comment: 19 pages, 1 figur
A universe of processes and some of its guises
Our starting point is a particular `canvas' aimed to `draw' theories of
physics, which has symmetric monoidal categories as its mathematical backbone.
In this paper we consider the conceptual foundations for this canvas, and how
these can then be converted into mathematical structure. With very little
structural effort (i.e. in very abstract terms) and in a very short time span
the categorical quantum mechanics (CQM) research program has reproduced a
surprisingly large fragment of quantum theory. It also provides new insights
both in quantum foundations and in quantum information, and has even resulted
in automated reasoning software called `quantomatic' which exploits the
deductive power of CQM. In this paper we complement the available material by
not requiring prior knowledge of category theory, and by pointing at
connections to previous and current developments in the foundations of physics.
This research program is also in close synergy with developments elsewhere, for
example in representation theory, quantum algebra, knot theory, topological
quantum field theory and several other areas.Comment: Invited chapter in: "Deep Beauty: Understanding the Quantum World
through Mathematical Innovation", H. Halvorson, ed., Cambridge University
Press, forthcoming. (as usual, many pictures
Linearity and Compound Physical Systems: The Case of Two Separated Spin 1/2 Entities
We illustrate some problems that are related to the existence of an
underlying linear structure at the level of the property lattice associated
with a physical system, for the particular case of two explicitly separated
spin 1/2 objects that are considered, and mathematically described, as one
compound system. It is shown that the separated product of the property
lattices corresponding with the two spin 1/2 objects does not have an
underlying linear structure, although the property lattices associated with the
subobjects in isolation manifestly do. This is related at a fundamental level
to the fact that separated products do not behave well with respect to the
covering law (and orthomodularity) of elementary lattice theory. In addition,
we discuss the orthogonality relation associated with the separated product in
general and consider the related problem of the behavior of the corresponding
Sasaki projections as partial state space mappingsComment: 25 page
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