24 research outputs found
Bell-Type Quantum Field Theories
In [Phys. Rep. 137, 49 (1986)] John S. Bell proposed how to associate
particle trajectories with a lattice quantum field theory, yielding what can be
regarded as a |Psi|^2-distributed Markov process on the appropriate
configuration space. A similar process can be defined in the continuum, for
more or less any regularized quantum field theory; such processes we call
Bell-type quantum field theories. We describe methods for explicitly
constructing these processes. These concern, in addition to the definition of
the Markov processes, the efficient calculation of jump rates, how to obtain
the process from the processes corresponding to the free and interaction
Hamiltonian alone, and how to obtain the free process from the free Hamiltonian
or, alternatively, from the one-particle process by a construction analogous to
"second quantization." As an example, we consider the process for a second
quantized Dirac field in an external electromagnetic field.Comment: 53 pages LaTeX, no figure
Decoherence in a Two Slit Diffraction Experiment with Massive Particles
Matter-wave interferometry has been largely studied in the last few years.
Usually, the main problem in the analysis of the diffraction experiments is to
establish the causes for the loss of coherence observed in the interference
pattern. In this work, we use different type of environmental couplings to
model a two slit diffraction experiment with massive particles. For each model,
we study the effects of decoherence on the interference pattern and define a
visibility function that measures the loss of contrast of the interference
fringes on a distant screen. Finally, we apply our results to the experimental
reported data on massive particles .Comment: 6 pages, 3 figure
Collapse models with non-white noises II: particle-density coupled noises
We continue the analysis of models of spontaneous wave function collapse with
stochastic dynamics driven by non-white Gaussian noise. We specialize to a
model in which a classical "noise" field, with specified autocorrelator, is
coupled to a local nonrelativistic particle density. We derive general results
in this model for the rates of density matrix diagonalization and of state
vector reduction, and show that (in the absence of decoherence) both processes
are governed by essentially the same rate parameters. As an alternative route
to our reduction results, we also derive the Fokker-Planck equations that
correspond to the initial stochastic Schr\"odinger equation. For specific
models of the noise autocorrelator, including ones motivated by the structure
of thermal Green's functions, we discuss the qualitative and qantitative
dependence on model parameters, with particular emphasis on possible
cosmological sources of the noise field.Comment: Latex, 43 pages; versions 2&3 have minor editorial revision
The Point Processes of the GRW Theory of Wave Function Collapse
The Ghirardi-Rimini-Weber (GRW) theory is a physical theory that, when
combined with a suitable ontology, provides an explanation of quantum
mechanics. The so-called collapse of the wave function is problematic in
conventional quantum theory but not in the GRW theory, in which it is governed
by a stochastic law. A possible ontology is the flash ontology, according to
which matter consists of random points in space-time, called flashes. The joint
distribution of these points, a point process in space-time, is the topic of
this work. The mathematical results concern mainly the existence and uniqueness
of this distribution for several variants of the theory. Particular attention
is paid to the relativistic version of the GRW theory that I developed in 2004.Comment: 72 pages LaTeX, 3 figure
f(R) Quantum Cosmology
We have quantized a flat cosmological model in the context of the metric f(R)
models, using the causal Bohmian quantum theory. The equations are solved and
then we have obtained how the quantum corrections influence the classical
equations.Comment: 6 figures. to appear in General Relativity and Cosmology, 200
The effect of spontaneous collapses on neutrino oscillations
We compute the effect of collapse models on neutrino oscillations. The effect
of the collapse is to modify the evolution of the `spatial' part of the wave
function, which indirectly amounts to a change on the flavor components. In
many respects, this phenomenon is similar to neutrino propagation through
matter. For the analysis we use the mass proportional CSL model, and perform
the calculation to second order perturbation theory. As we will show, the CSL
prediction is very small - mainly due to the very small mass of neutrinos - and
practically undetectable.Comment: 24 pages, RevTeX. Updated versio
Quantum mechanics: Myths and facts
A common understanding of quantum mechanics (QM) among students and practical
users is often plagued by a number of "myths", that is, widely accepted claims
on which there is not really a general consensus among experts in foundations
of QM. These myths include wave-particle duality, time-energy uncertainty
relation, fundamental randomness, the absence of measurement-independent
reality, locality of QM, nonlocality of QM, the existence of well-defined
relativistic QM, the claims that quantum field theory (QFT) solves the problems
of relativistic QM or that QFT is a theory of particles, as well as myths on
black-hole entropy. The fact is that the existence of various theoretical and
interpretational ambiguities underlying these myths does not yet allow us to
accept them as proven facts. I review the main arguments and counterarguments
lying behind these myths and conclude that QM is still a
not-yet-completely-understood theory open to further fundamental research.Comment: 51 pages, pedagogic review, revised, new references, to appear in
Found. Phy
Against the 'No-Go' Philosophy of Quantum Mechanics
In the area of the foundations of quantum mechanics a true industry appears to have developed in the last decades, with the aim of proving as many results as possible concerning what there cannot be in the quantum realm. In principle, the significance of proving ‘no-go’ results should consist in clarifying the fundamental structure of the theory, by pointing out a class of basic constraints that the theory itself is supposed to satisfy. In the present paper I will discuss some more recent no-go claims and I will argue against the deep significance of these results, with a two-fold strategy. First, I will consider three results concerning respectively local realism, quantum covariance and predictive power in quantum mechanics, and I will try to show how controversial the main conditions of the negative theorem turn out to be – something that strongly undermines the general relevance of these theorems. Second, I will try to discuss what I take to be a common feature of these theoretical enterprises, namely that of aiming at establishing negative results for quantum mechanics in absence of a deeper understanding of the overall ontological content and structure of the theory. I will argue that the only way toward such an understanding may be to cast in advance the problems in a clear and well-defined interpretational framework – which in my view means primarily to specify the ontology that quantum theory is supposed to be about – and after to wonder whether problems that seemed worth pursuing still are so in the framework
Benefits of Objective Collapse Models for Cosmology and Quantum Gravity
We display a number of advantages of objective collapse theories for the resolution of long-standing problems in cosmology and quantum gravity. In particular, we examine applications of objective reduction models to three important issues: the origin of the seeds of cosmic structure, the problem of time in quantum gravity and the information loss paradox; we show how reduction models contain the necessary tools to provide solutions for these issues. We wrap up with an adventurous proposal to relate the spontaneous collapse events of objective collapse models to microscopic virtual black holes