70 research outputs found
The basis problem in many-worlds theories
It is emphasized that a many-worlds interpretation of quantum theory exists
only to the extent that the associated basis problem is solved. The core basis
problem is that the robust enduring states specified by environmental
decoherence effects are essentially Gaussian wave packets that form continua of
non-orthogonal states. Hence they are not a discrete set of orthogonal basis
states to which finite probabilities can be assigned by the usual rules. The
natural way to get an orthogonal basis without going outside the Schroedinger
dynamics is to use the eigenstates of the reduced density matrix, and this idea
is the basis of some recent attempts by many-worlds proponents to solve the
basis problem. But these eigenstates do not enjoy the locality and
quasi-classicality properties of the states defined by environmental
decoherence effects, and hence are not satisfactory preferred basis states. The
basis problem needs to be addressed and resolved before a many-worlds-type
interpretation can be said to exist.Comment: This extended version is to be published in The Canadian Journal of
Physic
Decoherence: Concepts and Examples
We give a pedagogical introduction to the process of decoherence - the
irreversible emergence of classical properties through interaction with the
environment. After discussing the general concepts, we present the following
examples: Localisation of objects, quantum Zeno effect, classicality of fields
and charges in QED, and decoherence in gravity theory. We finally emphasise the
important interpretational features of decoherence.Comment: 24 pages, LATEX, 9 figures, needs macro lamuphys.sty, to appear in
the Proceedings of the 10th Born Symposiu
Where has all the information gone?
The existence of spacetime singularities is irrelevant for the irreversible
appearance of black holes. However, confirmation of the latter's unitary
dynamics would require the preparation of a coherent superposition of a
tremendous number of appropriate ``Everett worlds''.Comment: 10 pages, 1 figure, Latex - Invited paper for a special Einstein
issue of Physics Letters
Arrow of time in a recollapsing quantum universe
We show that the Wheeler-DeWitt equation with a consistent boundary condition
is only compatible with an arrow of time that formally reverses in a
recollapsing universe. Consistency of these opposite arrows is facilitated by
quantum effects in the region of the classical turning point. Since
gravitational time dilation diverges at horizons, collapsing matter must then
start re-expanding ``anticausally" (controlled by the reversed arrow) before
horizons or singularities can form. We also discuss the meaning of the
time-asymmetric expression used in the definition of ``consistent histories".
We finally emphasize that there is no mass inflation nor any information loss
paradox in this scenario.Comment: Many conceptual clarifications include
Quantum discreteness is an illusion
I review arguments demonstrating how the concept of "particle" numbers arises
in the form of equidistant energy eigenvalues of coupled harmonic oscillators
representing free fields. Their quantum numbers (numbers of nodes of the wave
functions) can be interpreted as occupation numbers for objects with a formal
mass (defined by the field equation) and spatial wave number ("momentum")
characterizing classical field modes. A superposition of different oscillator
eigenstates, all consisting of n modes having one node, while all others have
none, defines a nondegenerate "n-particle wave function". Other discrete
properties and phenomena (such as particle positions and "events") can be
understood by means of the fast but smooth process of decoherence: the
irreversible dislocalization of superpositions. Any wave-particle dualism thus
becomes obsolete. The observation of individual outcomes of this decoherence
process in measurements requires either a subsequent collapse of the wave
function or a "branching observer" in accordance with the Schr\"odinger
equation - both possibilities applying clearly after the decoherence process.
Any probability interpretation of the wave function in terms of local elements
of reality, such as particles or other classical concepts, would open a
Pandora's box of paradoxes, as is illustrated by various misnomers that have
become popular in quantum theory.Comment: 18 pages. v2: Some text and two references added. v3: Minor changes,
one reference added. v4: 21 pages. Submitted to AmJP (not accepted). v5:
Minor changes (mainly formulations). v6: Accepted by Found.Phys. Final
version is available at http://www.springerlink.co
Symmetries, superselection rules, and decoherence
We discuss the applicability of the programme of decoherence -- emergence of
approximate classical behaviour through interaction with the environment -- to
cases where it was suggested that the presence of symmetries would lead to
exact superselection rules. For this discussion it is useful to make a
distinction between pure symmetries and redundancies, which results from an
investigation into the constraint equations of the corresponding theories. We
discuss, in particular, superpositions of states with different charges, as
well as with different masses, and suggest how the corresponding interference
terms, although they exist in principle, become inaccessible through
decoherence.Comment: 12 pages, LATEX, Report Freiburg THEP-94/3
Following a "Collapsing" Wavefunction
I study the quantum mechanics of a spin interacting with an ``apparatus''.
Although the evolution of the whole system is unitary, the spin evolution is
not. The system is chosen so that the spin exhibits loss of quantum coherence,
or ``wavefunction collapse'', of the sort usually associated with a quantum
measurement. The system is analyzed from the point of view of the spin density
matrix (or ``Schmidt paths''), and also using the consistent histories
approach. These two points of view are contrasted with each other. Connections
between the results and the form of the Hamiltonian are discussed in detail.Comment: 30 pages, plain LaTex, 3 figures in a separate uuencoded fil
Gibbs' paradox and black-hole entropy
In statistical mechanics Gibbs' paradox is avoided if the particles of a gas
are assumed to be indistinguishable. The resulting entropy then agrees with the
empirically tested thermodynamic entropy up to a term proportional to the
logarithm of the particle number. We discuss here how analogous situations
arise in the statistical foundation of black-hole entropy. Depending on the
underlying approach to quantum gravity, the fundamental objects to be counted
have to be assumed indistinguishable or not in order to arrive at the
Bekenstein--Hawking entropy. We also show that the logarithmic corrections to
this entropy, including their signs, can be understood along the lines of
standard statistical mechanics. We illustrate the general concepts within the
area quantization model of Bekenstein and Mukhanov.Comment: Contribution to Mashhoon festschrift, 13 pages, 4 figure
Decoherence and wave function collapse
The possibility of consistency between the basic quantum principles of
quantum mechanics and wave function collapse is reexamined. A specific
interpretation of environment is proposed for this aim and applied to
decoherence. When the organization of a measuring apparatus is taken into
account, this approach leads also to an interpretation of wave function
collapse, which would result in principle from the same interactions with
environment as decoherence. This proposal is shown consistent with the
non-separable character of quantum mechanics
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