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Compatible Quantum Theory
Formulations of quantum mechanics can be characterized as realistic,
operationalist, or a combination of the two. In this paper a realistic theory
is defined as describing a closed system entirely by means of entities and
concepts pertaining to the system. An operationalist theory, on the other hand,
requires in addition entities external to the system. A realistic formulation
comprises an ontology, the set of (mathematical) entities that describe the
system, and assertions, the set of correct statements (predictions) the theory
makes about the objects in the ontology. Classical mechanics is the prime
example of a realistic physical theory. The present realistic formulation of
the histories approach originally introduced by Griffiths, which we call
'Compatible Quantum Theory (CQT)', consists of a 'microscopic' part (MIQM),
which applies to a closed quantum system of any size, and a 'macroscopic' part
(MAQM), which requires the participation of a large (ideally, an infinite)
system. The first (MIQM) can be fully formulated based solely on the assumption
of a Hilbert space ontology and the noncontextuality of probability values,
relying in an essential way on Gleason's theorem and on an application to
dynamics due in large part to Nistico. The microscopic theory does not,
however, possess a unique corpus of assertions, but rather a multiplicity of
contextual truths ('c-truths'), each one associated with a different framework.
This circumstance leads us to consider the microscopic theory to be physically
indeterminate and therefore incomplete, though logically coherent. The
completion of the theory requires a macroscopic mechanism for selecting a
physical framework, which is part of the macroscopic theory (MAQM). Detailed
definitions and proofs are presented in the appendice
Causal Quantum Theory and the Collapse Locality Loophole
Causal quantum theory is an umbrella term for ordinary quantum theory
modified by two hypotheses: state vector reduction is a well-defined process,
and strict local causality applies. The first of these holds in some versions
of Copenhagen quantum theory and need not necessarily imply practically
testable deviations from ordinary quantum theory. The second implies that
measurement events which are spacelike separated have no non-local
correlations. To test this prediction, which sharply differs from standard
quantum theory, requires a precise theory of state vector reduction.
Formally speaking, any precise version of causal quantum theory defines a
local hidden variable theory. However, causal quantum theory is most naturally
seen as a variant of standard quantum theory. For that reason it seems a more
serious rival to standard quantum theory than local hidden variable models
relying on the locality or detector efficiency loopholes.
Some plausible versions of causal quantum theory are not refuted by any Bell
experiments to date, nor is it obvious that they are inconsistent with other
experiments. They evade refutation via a neglected loophole in Bell experiments
-- the {\it collapse locality loophole} -- which exists because of the possible
time lag between a particle entering a measuring device and a collapse taking
place. Fairly definitive tests of causal versus standard quantum theory could
be made by observing entangled particles separated by light
seconds.Comment: Discussion expanded; typos corrected; references adde
Quantum Systems based upon Galois Fields: from Sub-quantum to Super-quantum Correlations
In this talk we describe our recent work on discrete quantum theory based on
Galois fields. In particular, we discuss how discrete quantum theory sheds new
light on the foundations of quantum theory and we review an explicit model of
super-quantum correlations we have constructed in this context. We also discuss
the larger questions of the origins and foundations of quantum theory, as well
as the relevance of super-quantum theory for the quantum theory of gravity.Comment: 22 pages LaTeX. Uses ws-procs975x65.cls. Contribution to the
Proceedings of the Conference in Honour of the 90th Birthday of Freeman
Dyson, 26-29 August 2013, Institute of Advanced Studies at the Nanyang
Technological University, Singapore. Talk presented by Takeuch
Modal quantum theory
We present a discrete model theory similar in structure to ordinary quantum
mechanics, but based on a finite field instead of complex amplitudes. The
interpretation of this theory involves only the "modal" concepts of possibility
and necessity rather than quantitative probability measures. Despite its
simplicity, our model theory includes entangled states and has versions of both
Bell's theorem and the no cloning theorem.Comment: Presented at the 7th Workshop on Quantum Physics and Logic, Oxford
University (29-30 May 2010). Revised 1 Aug 2011 in response to referee
comment
Quantum theory cannot consistently describe the use of itself
Quantum theory provides an extremely accurate description of fundamental
processes in physics. It thus seems likely that the theory is applicable beyond
the, mostly microscopic, domain in which it has been tested experimentally.
Here we propose a Gedankenexperiment to investigate the question whether
quantum theory can, in principle, have universal validity. The idea is that, if
the answer was yes, it must be possible to employ quantum theory to model
complex systems that include agents who are themselves using quantum theory.
Analysing the experiment under this presumption, we find that one agent, upon
observing a particular measurement outcome, must conclude that another agent
has predicted the opposite outcome with certainty. The agents' conclusions,
although all derived within quantum theory, are thus inconsistent. This
indicates that quantum theory cannot be extrapolated to complex systems, at
least not in a straightforward manner.Comment: 11 + 8 pages, 4 figures; substantially rewritten, including change of
title; close to published versio
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