526 research outputs found
Why Quantum Theory is Possibly Wrong
Quantum theory is a tremendously successful physical theory, but nevertheless
suffers from two serious problems: the measurement problem and the problem of
interpretational underdetermination. The latter, however, is largely overlooked
as a genuine problem of its own. Both problems concern the doctrine of realism,
but pull, quite curiously, into opposite directions. The measurement problem
can be captured such that due to scientific realism about quantum theory common
sense anti-realism follows, while theory underdetermination usually counts as
an argument against scientific realism. I will also consider the more refined
distinctions of ontic and epistemic realism and demonstrate that quantum theory
in its most viable interpretations conflicts with at least one of the various
realism claims. A way out of the conundrum is to come to the bold conclusion
that quantum theory is, possibly, wrong (in the realist sense)
Unsharp Quantum Reality
The positive operator (valued) measures (POMs) allow one to generalize the notion of observable beyond the traditional one based on projection valued measures (PVMs). Here, we argue that this generalized conception of observable enables a consistent notion of unsharp reality and with it an adequate concept of joint properties. A sharp or unsharp property manifests itself as an element of sharp or unsharp reality by its tendency to become actual or to actualize a specific measurement outcome. This actualization tendency-or potentiality-of a property is quantified by the associated quantum probability. The resulting single-case interpretation of probability as a degree of reality will be explained in detail and its role in addressing the tensions between quantum and classical accounts of the physical world will be elucidated. It will be shown that potentiality can be viewed as a causal agency that evolves in a well-defined way
There exist non orthogonal quantum measurements that are perfectly repeatable
We show that, contrarily to the widespread belief, in quantum mechanics
repeatable measurements are not necessarily described by orthogonal
projectors--the customary paradigm of "observable". Nonorthogonal
repeatability, however, occurs only for infinite dimensions. We also show that
when a non orthogonal repeatable measurement is performed, the measured system
retains some "memory" of the number of times that the measurement has been
performed.Comment: 4 pages, 1 figure, revtex4, minor change
Information theoretic approach to single-particle and two-particle interference in multi-path interferometers
We propose entropic measures for the strength of single-particle and
two-particle interference in interferometric experiments where each particle of
a pair traverses a multi-path interferometer. Optimal single-particle
interference excludes any two-particle interference, and vice versa. We report
an inequality that states the compromises allowed by quantum mechanics in
intermediate situations, and identify a class of two-particle states for which
the upper bound is reached. Our approach is applicable to symmetric two-partite
systems of any finite dimension.Comment: RevTex 4, 4 pages, 2 figure
Jacobi's Principle and the Disappearance of Time
Jacobi's action principle is known to lead to a problem of time. For example,
the timelessness of the Wheeler-DeWitt equation can be seen as resulting from
using Jacobi's principle to define the dynamics of 3-geometries through
superspace. In addition, using Jacobi's principle for non-relativistic
particles is equivalent classically to Newton's theory but leads to a
time-independent Schrodinger equation upon Dirac quantization. In this paper,
we study the mechanism for the disappearance of time as a result of using
Jacobi's principle in these simple particle models. We find that the path
integral quantization very clearly elucidates the physical mechanism for the
timeless of the quantum theory as well as the emergence of duration at the
classical level. Physically, this is the result of a superposition of clocks
which occurs in the quantum theory due to a sum over all histories.
Mathematically, the timelessness is related to how the gauge fixing functions
impose the boundary conditions in the path integral.Comment: Published version. Significant amendments to presentation. 27 page
EPR, Bell, and Quantum Locality
Maudlin has claimed that no local theory can reproduce the predictions of
standard quantum mechanics that violate Bell's inequality for Bohm's version
(two spin-half particles in a singlet state) of the Einstein-Podolsky-Rosen
problem. It is argued that, on the contrary, standard quantum mechanics itself
is a counterexample to Maudlin's claim, because it is local in the appropriate
sense (measurements at one place do not influence what occurs elsewhere there)
when formulated using consistent principles in place of the inconsistent
appeals to "measurement" found in current textbooks. This argument sheds light
on the claim of Blaylock that counterfactual definiteness is an essential
ingredient in derivations of Bell's inequality.Comment: Minor revisions to previous versio
A quantum logical and geometrical approach to the study of improper mixtures
We study improper mixtures from a quantum logical and geometrical point of
view. Taking into account the fact that improper mixtures do not admit an
ignorance interpretation and must be considered as states in their own right,
we do not follow the standard approach which considers improper mixtures as
measures over the algebra of projections. Instead of it, we use the convex set
of states in order to construct a new lattice whose atoms are all physical
states: pure states and improper mixtures. This is done in order to overcome
one of the problems which appear in the standard quantum logical formalism,
namely, that for a subsystem of a larger system in an entangled state, the
conjunction of all actual properties of the subsystem does not yield its actual
state. In fact, its state is an improper mixture and cannot be represented in
the von Neumann lattice as a minimal property which determines all other
properties as is the case for pure states or classical systems. The new lattice
also contains all propositions of the von Neumann lattice. We argue that this
extension expresses in an algebraic form the fact that -alike the classical
case- quantum interactions produce non trivial correlations between the
systems. Finally, we study the maps which can be defined between the extended
lattice of a compound system and the lattices of its subsystems.Comment: submitted to the Journal of Mathematical Physic
Type-Decomposition of a Pseudo-Effect Algebra
The theory of direct decomposition of a centrally orthocomplete effect
algebra into direct summands of various types utilizes the notion of a
type-determining (TD) set. A pseudo-effect algebra (PEA) is a (possibly)
noncommutative version of an effect algebra. In this article we develop the
basic theory of centrally orthocomplete PEAs, generalize the notion of a TD set
to PEAs, and show that TD sets induce decompositions of centrally orthocomplete
PEAs into direct summands.Comment: 18 page
The Definition of Mach's Principle
Two definitions of Mach's principle are proposed. Both are related to gauge
theory, are universal in scope and amount to formulations of causality that
take into account the relational nature of position, time, and size. One of
them leads directly to general relativity and may have relevance to the problem
of creating a quantum theory of gravity.Comment: To be published in Foundations of Physics as invited contribution to
Peter Mittelstaedt's 80th Birthday Festschrift. 30 page
Types of quantum information
Quantum, in contrast to classical, information theory, allows for different
incompatible types (or species) of information which cannot be combined with
each other. Distinguishing these incompatible types is useful in understanding
the role of the two classical bits in teleportation (or one bit in one-bit
teleportation), for discussing decoherence in information-theoretic terms, and
for giving a proper definition, in quantum terms, of ``classical information.''
Various examples (some updating earlier work) are given of theorems which
relate different incompatible kinds of information, and thus have no
counterparts in classical information theory.Comment: Minor changes so as to agree with published versio
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