22,678 research outputs found
Choice of Consistent Family, and Quantum Incompatibility
In consistent history quantum theory, a description of the time development
of a quantum system requires choosing a framework or consistent family, and
then calculating probabilities for the different histories which it contains.
It is argued that the framework is chosen by the physicist constructing a
description of a quantum system on the basis of questions he wishes to address,
in a manner analogous to choosing a coarse graining of the phase space in
classical statistical mechanics. The choice of framework is not determined by
some law of nature, though it is limited by quantum incompatibility, a concept
which is discussed using a two-dimensional Hilbert space (spin half particle).
Thus certain questions of physical interest can only be addressed using
frameworks in which they make (quantum mechanical) sense. The physicist's
choice does not influence reality, nor does the presence of choices render the
theory subjective. On the contrary, predictions of the theory can, in
principle, be verified by experimental measurements. These considerations are
used to address various criticisms and possible misunderstandings of the
consistent history approach, including its predictive power, whether it
requires a new logic, whether it can be interpreted realistically, the nature
of ``quasiclassicality'', and the possibility of ``contrary'' inferences.Comment: Minor revisions to bring into conformity with published version.
Revtex 29 pages including 1 page with figure
The C-metric as a colliding plane wave space-time
It is explicitly shown that part of the C-metric space-time inside the black
hole horizon may be interpreted as the interaction region of two colliding
plane waves with aligned linear polarization, provided the rotational
coordinate is replaced by a linear one. This is a one-parameter generalization
of the degenerate Ferrari-Ibanez solution in which the focussing singularity is
a Cauchy horizon rather than a curvature singularity.Comment: 6 pages. To appear in Classical and Quantum Gravit
Consistent histories, quantum truth functionals, and hidden variables
A central principle of consistent histories quantum theory, the requirement
that quantum descriptions be based upon a single framework (or family), is
employed to show that there is no conflict between consistent histories and a
no-hidden-variables theorem of Bell, and Kochen and Specker, contrary to a
recent claim by Bassi and Ghirardi. The argument makes use of ``truth
functionals'' defined on a Boolean algebra of classical or quantum properties.Comment: Latex 10 pages, no figure
Quantum Measurements Are Noncontextual
Quantum measurements are noncontextual, with outcomes independent of which
other commuting observables are measured at the same time, when consistently
analyzed using principles of Hilbert space quantum mechanics rather than
classical hidden variables.Comment: Minor update of previous version, with comments on the BKS theorem
added towards the en
Quantum Information: What Is It All About?
This paper answers Bell's question: What does quantum information refer to?
It is about quantum properties represented by subspaces of the quantum Hilbert
space, or their projectors, to which standard (Kolmogorov) probabilities can be
assigned by using a projective decomposition of the identity (PDI or framework)
as a quantum sample space. The single framework rule of consistent histories
prevents paradoxes or contradictions. When only one framework is employed,
classical (Shannon) information theory can be imported unchanged into the
quantum domain. A particular case is the macroscopic world of classical physics
whose quantum description needs only a single quasiclassical framework.
Nontrivial issues unique to quantum information, those with no classical
analog, arise when aspects of two or more incompatible frameworks are compared.Comment: 14 pages. v2:Minor changes in title, abstract, Sec. 7. References
added and correcte
Consistent Histories and Quantum Reasoning
A system of quantum reasoning for a closed system is developed by treating
non-relativistic quantum mechanics as a stochastic theory. The sample space
corresponds to a decomposition, as a sum of orthogonal projectors, of the
identity operator on a Hilbert space of histories. Provided a consistency
condition is satisfied, the corresponding Boolean algebra of histories, called
a {\it framework}, can be assigned probabilities in the usual way, and within a
single framework quantum reasoning is identical to ordinary probabilistic
reasoning. A refinement rule, which allows a probability distribution to be
extended from one framework to a larger (refined) framework, incorporates the
dynamical laws of quantum theory. Two or more frameworks which are incompatible
because they possess no common refinement cannot be simultaneously employed to
describe a single physical system.Comment: Latex, 31 page
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