483 research outputs found
Relational Parametricity and Separation Logic
Separation logic is a recent extension of Hoare logic for reasoning about
programs with references to shared mutable data structures. In this paper, we
provide a new interpretation of the logic for a programming language with
higher types. Our interpretation is based on Reynolds's relational
parametricity, and it provides a formal connection between separation logic and
data abstraction
Quantum Particles as Conceptual Entities: A Possible Explanatory Framework for Quantum Theory
We put forward a possible new interpretation and explanatory framework for
quantum theory. The basic hypothesis underlying this new framework is that
quantum particles are conceptual entities. More concretely, we propose that
quantum particles interact with ordinary matter, nuclei, atoms, molecules,
macroscopic material entities, measuring apparatuses, ..., in a similar way to
how human concepts interact with memory structures, human minds or artificial
memories. We analyze the most characteristic aspects of quantum theory, i.e.
entanglement and non-locality, interference and superposition, identity and
individuality in the light of this new interpretation, and we put forward a
specific explanation and understanding of these aspects. The basic hypothesis
of our framework gives rise in a natural way to a Heisenberg uncertainty
principle which introduces an understanding of the general situation of 'the
one and the many' in quantum physics. A specific view on macro and micro
different from the common one follows from the basic hypothesis and leads to an
analysis of Schrodinger's Cat paradox and the measurement problem different
from the existing ones. We reflect about the influence of this new quantum
interpretation and explanatory framework on the global nature and evolutionary
aspects of the world and human worldviews, and point out potential explanations
for specific situations, such as the generation problem in particle physics,
the confinement of quarks and the existence of dark matter.Comment: 45 pages, 10 figure
An anthology of non-local QFT and QFT on noncommutative spacetime
Ever since the appearance of renormalization theory there have been several
differently motivated attempts at non-localized (in the sense of not generated
by point-like fields) relativistic particle theories, the most recent one being
at QFT on non-commutative Minkowski spacetime. The often conceptually
uncritical and historically forgetful contemporary approach to these problems
calls for a critical review the light of previous results on this subject.Comment: 33 pages tci-latex, improvements of formulations, shortening of
sentences, addition of some reference
Higher Theory and the Three Problems of Physics
According to the Butterfield--Isham proposal, to understand quantum gravity
we must revise the way we view the universe of mathematics. However, this paper
demonstrates that the current elaborations of this programme neglect quantum
interactions. The paper then introduces the Faddeev--Mickelsson anomaly which
obstructs the renormalization of Yang--Mills theory, suggesting that to
theorise on many-particle systems requires a many-topos view of mathematics
itself: higher theory. As our main contribution, the topos theoretic framework
is used to conceptualise the fact that there are principally three different
quantisation problems, the differences of which have been ignored not just by
topos physicists but by most philosophers of science. We further argue that if
higher theory proves out to be necessary for understanding quantum gravity, its
implications to philosophy will be foundational: higher theory challenges the
propositional concept of truth and thus the very meaning of theorising in
science.Comment: 23 pages, 1 table
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