14 research outputs found
Astrophysical and Cosmological Tests of Quantum Theory
We discuss several proposals for astrophysical and cosmological tests of
quantum theory. The tests are motivated by deterministic hidden-variables
theories, and in particular by the view that quantum physics is merely an
effective theory of an equilibrium state. The proposed tests involve searching
for nonequilibrium violations of quantum theory in: primordial inflaton
fluctuations imprinted on the cosmic microwave background, relic cosmological
particles, Hawking radiation, photons with entangled partners inside black
holes, neutrino oscillations, and particles from very distant sources.Comment: 25 pages. Amendment to section 7. Contribution to: "The Quantum
Universe", special issue of Journal of Physics A, dedicated to Prof. G.-C.
Ghirardi on the occasion of his seventieth birthda
Inflationary Cosmology as a Probe of Primordial Quantum Mechanics
We show that inflationary cosmology may be used to test the statistical
predictions of quantum theory at very short distances and at very early times.
Hidden-variables theories, such as the pilot-wave theory of de Broglie and
Bohm, allow the existence of vacuum states with non-standard field fluctuations
('quantum nonequilibrium'). We show that inflationary expansion can transfer
microscopic nonequilibrium to macroscopic scales, resulting in anomalous power
spectra for the cosmic microwave background. The conclusions depend only weakly
on the details of the de Broglie-Bohm dynamics. We discuss, in particular, the
nonequilibrium breaking of scale invariance for the primordial (scalar) power
spectrum. We also show how nonequilibrium can generate primordial perturbations
with non-random phases and inter-mode correlations (primordial
non-Gaussianity). We address the possibility of a low-power anomaly at large
angular scales, and show how it might arise from a nonequilibrium suppression
of quantum noise. Recent observations are used to set an approximate bound on
violations of quantum theory in the early universe.Comment: 44 pages. Minor changes in v
Bell nonlocality, signal locality and unpredictability (or What Bohr could have told Einstein at Solvay had he known about Bell experiments)
The 1964 theorem of John Bell shows that no model that reproduces the
predictions of quantum mechanics can simultaneously satisfy the assumptions of
locality and determinism. On the other hand, the assumptions of \emph{signal
locality} plus \emph{predictability} are also sufficient to derive Bell
inequalities. This simple theorem, previously noted but published only
relatively recently by Masanes, Acin and Gisin, has fundamental implications
not entirely appreciated. Firstly, nothing can be concluded about the
ontological assumptions of locality or determinism independently of each other
-- it is possible to reproduce quantum mechanics with deterministic models that
violate locality as well as indeterministic models that satisfy locality. On
the other hand, the operational assumption of signal locality is an empirically
testable (and well-tested) consequence of relativity. Thus Bell inequality
violations imply that we can trust that some events are fundamentally
\emph{unpredictable}, even if we cannot trust that they are indeterministic.
This result grounds the quantum-mechanical prohibition of arbitrarily accurate
predictions on the assumption of no superluminal signalling, regardless of any
postulates of quantum mechanics. It also sheds a new light on an early stage of
the historical debate between Einstein and Bohr.Comment: Substantially modified version; added HMW as co-autho
De Broglie-Bohm Guidance Equations for Arbitrary Hamiltonians
In a pilot-wave theory, an individual closed system is described by a
wavefunction and configuration . The evolution of the wavefunction
and configuration are respectively determined by the Schr\"odinger and guidance
equations. The guidance equation states that the velocity field for the
configuration is given by the quantum current divided by the density
. We present the currents and associated guidance equations for
any Hamiltonian given by a differential operator. These are derived directly
from the Schr\"odinger equation, and also as Noether currents arising from a
global phase symmetry associated with the wavefunction in configuration space.Comment: 22 pages, no figures, LaTex; v3 minor corrections; v2 minor
correction
Einstein, incompleteness, and the epistemic view of quantum states
Does the quantum state represent reality or our knowledge of reality? In
making this distinction precise, we are led to a novel classification of hidden
variable models of quantum theory. Indeed, representatives of each class can be
found among existing constructions for two-dimensional Hilbert spaces. Our
approach also provides a fruitful new perspective on arguments for the
nonlocality and incompleteness of quantum theory. Specifically, we show that
for models wherein the quantum state has the status of something real, the
failure of locality can be established through an argument considerably more
straightforward than Bell's theorem. The historical significance of this result
becomes evident when one recognizes that the same reasoning is present in
Einstein's preferred argument for incompleteness, which dates back to 1935.
This fact suggests that Einstein was seeking not just any completion of quantum
theory, but one wherein quantum states are solely representative of our
knowledge. Our hypothesis is supported by an analysis of Einstein's attempts to
clarify his views on quantum theory and the circumstance of his otherwise
puzzling abandonment of an even simpler argument for incompleteness from 1927.Comment: 18 pages, 8 figures, 1 recipe for cupcakes; comments welcom
A Dirac sea pilot-wave model for quantum field theory
We present a pilot-wave model for quantum field theory in which the Dirac sea
is taken seriously. The model ascribes particle trajectories to all the
fermions, including the fermions filling the Dirac sea. The model is
deterministic and applies to the regime in which fermion number is
superselected. This work is a further elaboration of work by Colin, in which a
Dirac sea pilot-wave model is presented for quantum electrodynamics. We extend
his work to non-electromagnetic interactions, we discuss a cut-off
regularization of the pilot-wave model and study how it reproduces the standard
quantum predictions. The Dirac sea pilot-wave model can be seen as a possible
continuum generalization of a lattice model by Bell. It can also be seen as a
development and generalization of the ideas by Bohm, Hiley and Kaloyerou, who
also suggested the use of the Dirac sea for the development of a pilot-wave
model for quantum electrodynamics.Comment: 41 pages, no figures, LaTex, v2 minor improvements and addition
Quartic quantum theory: an extension of the standard quantum mechanics
We propose an extended quantum theory, in which the number K of parameters
necessary to characterize a quantum state behaves as fourth power of the number
N of distinguishable states. As the simplex of classical N-point probability
distributions can be embedded inside a higher dimensional convex body of mixed
quantum states, one can further increase the dimensionality constructing the
set of extended quantum states. The embedding proposed corresponds to an
assumption that the physical system described in N dimensional Hilbert space is
coupled with an auxiliary subsystem of the same dimensionality. The extended
theory works for simple quantum systems and is shown to be a non-trivial
generalisation of the standard quantum theory for which K=N^2. Imposing certain
restrictions on initial conditions and dynamics allowed in the quartic theory
one obtains quadratic theory as a special case. By imposing even stronger
constraints one arrives at the classical theory, for which K=N.Comment: 30 pages in latex with 6 figures included; ver.2: several
improvements, new references adde