3,551 research outputs found
Causality in Time-Neutral Cosmologies
Gell-Mann and Hartle (GMH) have recently considered time-neutral cosmological
models in which the initial and final conditions are independently specified,
and several authors have investigated experimental tests of such models.
We point out here that GMH time-neutral models can allow superluminal
signalling, in the sense that it can be possible for observers in those
cosmologies, by detecting and exploiting regularities in the final state, to
construct devices which send and receive signals between space-like separated
points. In suitable cosmologies, any single superluminal message can be
transmitted with probability arbitrarily close to one by the use of redundant
signals. However, the outcome probabilities of quantum measurements generally
depend on precisely which past {\it and future} measurements take place. As the
transmission of any signal relies on quantum measurements, its transmission
probability is similarly context-dependent. As a result, the standard
superluminal signalling paradoxes do not apply. Despite their unusual features,
the models are internally consistent.
These results illustrate an interesting conceptual point. The standard view
of Minkowski causality is not an absolutely indispensable part of the
mathematical formalism of relativistic quantum theory. It is contingent on the
empirical observation that naturally occurring ensembles can be naturally
pre-selected but not post-selected.Comment: 5 pages, RevTeX. Published version -- minor typos correcte
Quark-lepton symmetry and complementarity
We argue that the difference between the observed approximate quark-lepton
complementarity and the theoretical prediction based on realistic quark-lepton
symmetry within the seesaw mechanism may be adjusted by means of a triplet
contribution in the seesaw formula.Comment: 7 pages, RevTex
Quasiclassical Coarse Graining and Thermodynamic Entropy
Our everyday descriptions of the universe are highly coarse-grained,
following only a tiny fraction of the variables necessary for a perfectly
fine-grained description. Coarse graining in classical physics is made natural
by our limited powers of observation and computation. But in the modern quantum
mechanics of closed systems, some measure of coarse graining is inescapable
because there are no non-trivial, probabilistic, fine-grained descriptions.
This essay explores the consequences of that fact. Quantum theory allows for
various coarse-grained descriptions some of which are mutually incompatible.
For most purposes, however, we are interested in the small subset of
``quasiclassical descriptions'' defined by ranges of values of averages over
small volumes of densities of conserved quantities such as energy and momentum
and approximately conserved quantities such as baryon number. The
near-conservation of these quasiclassical quantities results in approximate
decoherence, predictability, and local equilibrium, leading to closed sets of
equations of motion. In any description, information is sacrificed through the
coarse graining that yields decoherence and gives rise to probabilities for
histories. In quasiclassical descriptions, further information is sacrificed in
exhibiting the emergent regularities summarized by classical equations of
motion. An appropriate entropy measures the loss of information. For a
``quasiclassical realm'' this is connected with the usual thermodynamic entropy
as obtained from statistical mechanics. It was low for the initial state of our
universe and has been increasing since.Comment: 17 pages, 0 figures, revtex4, Dedicated to Rafael Sorkin on his 60th
birthday, minor correction
Fermion Mass Hierarchy in Lifshitz Type Gauge Theory
We study the origin of fermion mass hierarchy and flavor mixing in a Lifshitz
type extension of the standard model including an extra scalar field. We show
that the hierarchical structure can originate from renormalizable interactions.
In contrast to the Froggatt-Nielsen mechanism, the higher the dimension of
associated operators, the heavier the fermion masses. Tiny masses for
left-handed neutrinos are obtained without introducing right-handed neutrinos.Comment: 13 pages; clarifications of some point
Quantum spacetime and the renormalization group: Progress and visions
The quest for a consistent theory which describes the quantum microstructure
of spacetime seems to require some departure from the paradigms that have been
followed in the construction of quantum theories for the other fundamental
interactions. In this contribution we briefly review two approaches to quantum
gravity, namely, asymptotically safe quantum gravity and tensor models, based
on different theoretical assumptions. Nevertheless, the main goal is to find a
universal continuum limit for such theories and we explain how coarse-graining
techniques should be adapted to each case. Finally, we argue that although
seemingly different, such approaches might be just two sides of the same coin.Comment: 14 pages, 4 figures, Proceedings of "Progress and Visions in Quantum
Theory in View of Gravity: Bridging foundations of physics and mathematics",
Leipzig, 201
Decoherent Histories Quantum Mechanics with One 'Real' Fine-Grained History
Decoherent histories quantum theory is reformulated with the assumption that
there is one "real" fine-grained history, specified in a preferred complete set
of sum-over-histories variables. This real history is described by embedding it
in an ensemble of comparable imagined fine-grained histories, not unlike the
familiar ensemble of statistical mechanics. These histories are assigned
extended probabilities, which can sometimes be negative or greater than one. As
we will show, this construction implies that the real history is not completely
accessible to experimental or other observational discovery. However,
sufficiently and appropriately coarse-grained sets of alternative histories
have standard probabilities providing information about the real fine-grained
history that can be compared with observation. We recover the probabilities of
decoherent histories quantum mechanics for sets of histories that are recorded
and therefore decohere. Quantum mechanics can be viewed as a classical
stochastic theory of histories with extended probabilities and a well-defined
notion of reality common to all decoherent sets of alternative coarse-grained
histories.Comment: 11 pages, one figure, expanded discussion and acknowledgment
Neutrino Models of Dark Energy
I consider a scenario proposed by Fardon, Nelson and Weiner where dark energy
and neutrinos are connected. As a result, neutrino masses are not constant but
depend on the neutrino number density. By examining the full equation of state
for the dark sector, I show that in this scenario the dark energy is equivalent
to having a cosmological constant, but one that "runs" as the neutrino mass
changes with temperature. Two examples are examined that illustrate the
principal feautures of the dark sector of this scenario. In particular, the
cosmological constant is seen to be negligible for most of the evolution of the
Universe, becoming inportant only when neutrinos become non-relativistic. Some
speculations on features of this scenario which might be present in a more
realistic theory are also presented.Comment: 12 pages, 6 figures. Added comments on why FNW scenario always leads
to a running cosmological constant and a few references. To be published in
Phys. Rev.
The Invisible Axion and Neutrino Masses
We show that in any invisible axion model due to the effects of effective
non-renormalizable interactions related to an energy scale near the
Peccei-Quinn, grand unification or even the Planck scale, active neutrinos
necessarily acquire masses in the sub-eV range. Moreover, if sterile neutrinos
are also included and if appropriate cyclic symmetries are imposed, it is
possible that some of these neutrinos are heavy while others are light.Comment: An example included and new references added. To appear in PR
String-Inspired Triplet See-Saw from Diagonal Embedding of SU(2)_L in SU(2)_A x SU(2)_B
Motivated by string constructions, we consider a variant on the Type II
see-saw mechanism involving the exchange of triplet representations of SU(2)_L
in which this group arises from a diagonal embedding into SU(2)_A x SU(2)_B. A
natural assignment of Standard Model lepton doublets to the two underlying
gauge groups results in a bimaximal pattern of neutrino mixings and an inverted
hierarchy in masses. Simple perturbations around this leading-order structure
can accommodate the observed pattern of neutrino masses and mixings.Comment: 8 pages; uses RevTe
On the Definition of Decoherence
We examine the relationship between the decoherence of quantum-mechanical
histories of a closed system (as discussed by Gell-Mann and Hartle) and
environmentally-induced diagonalization of the density operator for an open
system. We study a definition of decoherence which incorporates both of these
ideas, and show that it leads to a consistent probabilistic interpretation of
the reduced density operator.Comment: 10 pages, LaTeX, SJSU/TP-93-1
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