373 research outputs found
Quantum Electrodynamics at Large Distances II: Nature of the Dominant Singularities
Accurate calculations of macroscopic and mesoscopic properties in quantum
electrodynamics require careful treatment of infrared divergences: standard
treatments introduce spurious large-distances effects. A method for computing
these properties was developed in a companion paper. That method depends upon a
result obtained here about the nature of the singularities that produce the
dominant large-distance behaviour. If all particles in a quantum field theory
have non-zero mass then the Landau-Nakanishi diagrams give strong conditions on
the singularities of the scattering functions. These conditions are severely
weakened in quantum electrodynamics by effects of points where photon momenta
vanish. A new kind of Landau-Nakanishi diagram is developed here. It is geared
specifically to the pole-decomposition functions that dominate the macroscopic
behaviour in quantum electrodynamics, and leads to strong results for these
functions at points where photon momenta vanish.Comment: 40 pages, 11 encapsulated postscript figures, latexed,
math_macros.tex can be found on Archive. full postscript available from
http://theorl.lbl.gov/www/theorgroup/papers/35972.p
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
Consistent Quantum Counterfactuals
An analysis using classical stochastic processes is used to construct a
consistent system of quantum counterfactual reasoning. When applied to a
counterfactual version of Hardy's paradox, it shows that the probabilistic
character of quantum reasoning together with the ``one framework'' rule
prevents a logical contradiction, and there is no evidence for any mysterious
nonlocal influences. Counterfactual reasoning can support a realistic
interpretation of standard quantum theory (measurements reveal what is actually
there) under appropriate circumstances.Comment: Minor modifications to make it agree with published version. Latex 8
pages, 2 figure
On the Consequences of Retaining the General Validity of Locality in Physical Theory
The empirical validity of the locality (LOC) principle of relativity is used
to argue in favour of a local hidden variable theory (HVT) for individual
quantum processes. It is shown that such a HVT may reproduce the statistical
predictions of quantum mechanics (QM), provided the reproducibility of initial
hidden variable states is limited. This means that in a HVT limits should be
set to the validity of the notion of counterfactual definiteness (CFD). This is
supported by the empirical evidence that past, present, and future are
basically distinct. Our argumentation is contrasted with a recent one by Stapp
resulting in the opposite conclusion, i.e. nonlocality or the existence of
faster-than-light influences. We argue that Stapp's argumentation still depends
in an implicit, but crucial, way on both the notions of hidden variables and of
CFD. In addition, some implications of our results for the debate between Bohr
and Einstein, Podolsky and Rosen are discussed.Comment: revtex, 11 page
Bell inequalities for continuous-variable correlations
We derive a new class of correlation Bell-type inequalities. The inequalities
are valid for any number of outcomes of two observables per each of n parties,
including continuous and unbounded observables. We show that there are no
first-moment correlation Bell inequalities for that scenario, but such
inequalities can be found if one considers at least second moments. The
derivation stems from a simple variance inequality by setting local commutators
to zero. We show that above a constant detector efficiency threshold, the
continuous variable Bell violation can survive even in the macroscopic limit of
large n. This method can be used to derive other well-known Bell inequalities,
shedding new light on the importance of non-commutativity for violations of
local realism.Comment: 4 pages, 1 figure. v2: New results on detector efficiencies and
macroscopic limit, new co-author, changed title and abstract, changed figure,
added journal reference and DO
Minimum detection efficiency for a loophole-free atom-photon Bell experiment
In Bell experiments, one problem is to achieve high enough photodetection to
ensure that there is no possibility of describing the results via a local
hidden-variable model. Using the Clauser-Horne inequality and a two-photon
non-maximally entangled state, a photodetection efficiency higher than 0.67 is
necessary. Here we discuss atom-photon Bell experiments. We show that, assuming
perfect detection efficiency of the atom, it is possible to perform a
loophole-free atom-photon Bell experiment whenever the photodetection
efficiency exceeds 0.50.Comment: REVTeX4, 4 pages, 1 figur
Lorentz-covariant quantum mechanics and preferred frame
In this paper the relativistic quantum mechanics is considered in the
framework of the nonstandard synchronization scheme for clocks. Such a
synchronization preserves Poincar{\'e} covariance but (at least formally)
distinguishes an inertial frame. This enables to avoid the problem of a
noncausal transmision of information related to breaking of the Bell's
inequalities in QM. Our analysis has been focused mainly on the problem of
existence of a proper position operator for massive particles. We have proved
that in our framework such an operator exists for particles with arbitrary
spin. It fulfills all the requirements: it is Hermitean and covariant, it has
commuting components and moreover its eigenvectors (localised states) are also
covariant. We have found the explicit form of the position operator and have
demonstrated that in the preferred frame our operator coincides with the
Newton--Wigner one. We have also defined a covariant spin operator and have
constructed an invariant spin square operator. Moreover, full algebra of
observables consisting of position operators, fourmomentum operators and spin
operators is manifestly Poincar\'e covariant in this framework. Our results
support expectations of other authors (Bell, Eberhard) that a consistent
formulation of quantum mechanics demands existence of a preferred frame.Comment: 21 pages, LaTeX file, no figure
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