237 research outputs found
The Quantum Mechanical Arrows of Time
The familiar textbook quantum mechanics of laboratory measurements
incorporates a quantum mechanical arrow of time --- the direction in time in
which state vector reduction operates. This arrow is usually assumed to
coincide with the direction of the thermodynamic arrow of the quasiclassical
realm of everyday experience. But in the more general context of cosmology we
seek an explanation of all observed arrows, and the relations between them, in
terms of the conditions that specify our particular universe. This paper
investigates quantum mechanical and thermodynamic arrows in a time-neutral
formulation of quantum mechanics for a number of model cosmologies in fixed
background spacetimes. We find that a general universe may not have well
defined arrows of either kind. When arrows are emergent they need not point in
the same direction over the whole of spacetime. Rather they may be local,
pointing in different directions in different spacetime regions. Local arrows
can therefore be consistent with global time symmetry.Comment: 9 pages, 4 figures, revtex4, typos correcte
Unitarity and Causality in Generalized Quantum Mechanics for Non-Chronal Spacetimes
Spacetime must be foliable by spacelike surfaces for the quantum mechanics of
matter fields to be formulated in terms of a unitarily evolving state vector
defined on spacelike surfaces. When a spacetime cannot be foliated by spacelike
surfaces, as in the case of spacetimes with closed timelike curves, a more
general formulation of quantum mechanics is required. In such generalizations
the transition matrix between alternatives in regions of spacetime where states
{\it can} be defined may be non-unitary. This paper describes a generalized
quantum mechanics whose probabilities consistently obey the rules of
probability theory even in the presence of such non-unitarity. The usual notion
of state on a spacelike surface is lost in this generalization and familiar
notions of causality are modified. There is no signaling outside the light
cone, no non-conservation of energy, no ``Everett phones'', and probabilities
of present events do not depend on particular alternatives of the future.
However, the generalization is acausal in the sense that the existence of
non-chronal regions of spacetime in the future can affect the probabilities of
alternatives today. The detectability of non-unitary evolution and violations
of causality in measurement situations are briefly considered. The evolution of
information in non-chronal spacetimes is described.Comment: 40pages, UCSBTH92-0
Conditional probabilities in Ponzano-Regge minisuperspace
We examine the Hartle-Hawking no-boundary initial state for the Ponzano-Regge
formulation of gravity in three dimensions. We consider the behavior of
conditional probabilities and expectation values for geometrical quantities in
this initial state for a simple minisuperspace model consisting of a
two-parameter set of anisotropic geometries on a 2-sphere boundary. We find
dependence on the cutoff used in the construction of Ponzano-Regge amplitudes
for expectation values of edge lengths. However, these expectation values are
cutoff independent when computed in certain, but not all, conditional
probability distributions. Conditions that yield cutoff independent expectation
values are those that constrain the boundary geometry to a finite range of edge
lengths. We argue that such conditions have a correspondence to fixing a range
of local time, as classically associated with the area of a surface for
spatially closed cosmologies. Thus these results may hint at how classical
spacetime emerges from quantum amplitudes.Comment: 26 pages including 10 figures, some reorganization in the
presentation of results, expanded discussion of results in the context of 2+1
gravity in the Witten variables, 3 new reference
Exterior and interior metrics with quadrupole moment
We present the Ernst potential and the line element of an exact solution of
Einstein's vacuum field equations that contains as arbitrary parameters the
total mass, the angular momentum, and the quadrupole moment of a rotating mass
distribution. We show that in the limiting case of slowly rotating and slightly
deformed configuration, there exists a coordinate transformation that relates
the exact solution with the approximate Hartle solution. It is shown that this
approximate solution can be smoothly matched with an interior perfect fluid
solution with physically reasonable properties. This opens the possibility of
considering the quadrupole moment as an additional physical degree of freedom
that could be used to search for a realistic exact solution, representing both
the interior and exterior gravitational field generated by a self-gravitating
axisymmetric distribution of mass of perfect fluid in stationary rotation.Comment: Latex, 15 pages, 3 figures, final versio
Do macroscopic properties dictate microscopic probabilities?
Aharonov and Reznik have recently (in quant-ph/0110093) argued that the form
of the probabilistic predictions of quantum theory can be seen to follow from
properties of macroscopic systems. An error in their argument is identified.Comment: LaTeX, 6 pages, no figure
The quasiclassical realms of this quantum universe
The most striking observable feature of our indeterministic quantum universe
is the wide range of time, place, and scale on which the deterministic laws of
classical physics hold to an excellent approximation. This essay describes how
this domain of classical predictability of every day experience emerges from a
quantum theory of the universe's state and dynamics.Comment: 24 pages, revtex4, minor change
Canonical Partition Functions for Parastatistical Systems of any order
A general formula for the canonical partition function for a system obeying
any statistics based on the permutation group is derived. The formula expresses
the canonical partition function in terms of sums of Schur functions. The only
hitherto known result due to Suranyi [ Phys. Rev. Lett. {\bf 65}, 2329 (1990)]
for parasystems of order two is shown to arise as a special case of our general
formula. Our results also yield all the relevant information about the
structure of the Fock spaces for parasystems.Comment: 9 pages, No figures, Revte
Spacetime Information
In usual quantum theory, the information available about a quantum system is
defined in terms of the density matrix describing it on a spacelike surface.
This definition must be generalized for extensions of quantum theory which do
not have a notion of state on a spacelike surface. It must be generalized for
the generalized quantum theories appropriate when spacetime geometry fluctuates
quantum mechanically or when geometry is fixed but not foliable by spacelike
surfaces. This paper introduces a four-dimensional notion of the information
available about a quantum system's boundary conditions in the various sets of
decohering histories it may display. The idea of spacetime information is
applied in several contexts: When spacetime geometry is fixed the information
available through alternatives restricted to a spacetime region is defined. The
information available through histories of alternatives of general operators is
compared to that obtained from the more limited coarse- grainings of
sum-over-histories quantum mechanics. The definition of information is
considered in generalized quantum theories. We consider as specific examples
time-neutral quantum mechanics with initial and final conditions, quantum
theories with non-unitary evolution, and the generalized quantum frameworks
appropriate for quantum spacetime. In such theories complete information about
a quantum system is not necessarily available on any spacelike surface but must
be searched for throughout spacetime. The information loss commonly associated
with the ``evolution of pure states into mixed states'' in black hole
evaporation is thus not in conflict with the principles of generalized quantum
mechanics.Comment: 47pages, 2 figures, UCSBTH 94-0
The use of exp(iS[x]) in the sum over histories
The use of as the generic form for a sum over histories in
configuration space is discussed critically and placed in its proper context.
The standard derivation of the sum over paths by discretizing the paths is
reviewed, and it is shown that the form is justified only
for Schrodinger-type systems which are at most second order in the momenta.
Extending this derivation to the relativistic free particle, the causal Green's
function is expressed as a sum over timelike paths, and the Feynman Green's
function is expressed both as a sum over paths which only go one way in time
and as a sum over paths which move forward and backward in time. The weighting
of the paths is shown not to be in any of these cases. The role
of the inner product and the operator ordering of the wave equation in defining
the sum over histories is discussed.Comment: 22 pages, Latex, Imperial-TP-92-93-4
Consistent Histories in Quantum Cosmology
We illustrate the crucial role played by decoherence (consistency of quantum
histories) in extracting consistent quantum probabilities for alternative
histories in quantum cosmology. Specifically, within a Wheeler-DeWitt
quantization of a flat Friedmann-Robertson-Walker cosmological model sourced
with a free massless scalar field, we calculate the probability that the
univese is singular in the sense that it assumes zero volume. Classical
solutions of this model are a disjoint set of expanding and contracting
singular branches. A naive assessment of the behavior of quantum states which
are superpositions of expanding and contracting universes may suggest that a
"quantum bounce" is possible i.e. that the wave function of the universe may
remain peaked on a non-singular classical solution throughout its history.
However, a more careful consistent histories analysis shows that for arbitrary
states in the physical Hilbert space the probability of this Wheeler-DeWitt
quantum universe encountering the big bang/crunch singularity is equal to
unity. A quantum Wheeler-DeWitt universe is inevitably singular, and a "quantum
bounce" is thus not possible in these models.Comment: To appear in Foundations of Physics special issue on quantum
foundation
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