114 research outputs found
Hidden Variables or Positive Probabilities?
Despite claims that Bell's inequalities are based on the Einstein locality
condition, or equivalent, all derivations make an identical mathematical
assumption: that local hidden-variable theories produce a set of
positive-definite probabilities for detecting a particle with a given spin
orientation. The standard argument is that because quantum mechanics assumes
that particles are emitted in a superposition of states the theory cannot
produce such a set of probabilities. We examine a paper by Eberhard, and
several similar papers, which claim to show that a generalized Bell inequality,
the CHSH inequality, can be derived solely on the basis of the locality
condition, without recourse to hidden variables. We point out that these
authors nonetheless assumes a set of positive-definite probabilities, which
supports the claim that hidden variables or "locality" is not at issue here,
positive-definite probabilities are. We demonstrate that quantum mechanics does
predict a set of probabilities that violate the CHSH inequality; however these
probabilities are not positive-definite. Nevertheless, they are physically
meaningful in that they give the usual quantum-mechanical predictions in
physical situations. We discuss in what sense our results are related to the
Wigner distribution.Comment: 19 pages, 2 ps files This is a second replacement. In this version we
include an analysis of yet another version of Bell's theorem which has been
brought to our attention. We also discuss in what sense our results are
related to the Wigner distributio
Time and Spacetime: The Crystallizing Block Universe
The nature of the future is completely different from the nature of the past.
When quantum effects are significant, the future shows all the signs of quantum
weirdness, including duality, uncertainty, and entanglement. With the passage
of time, after the time-irreversible process of state-vector reduction has
taken place, the past emerges, with the previous quantum uncertainty replaced
by the classical certainty of definite particle identities and states. The
present time is where this transition largely takes place, but the process does
not take place uniformly: Evidence from delayed choice and related experiments
shows that isolated patches of quantum indeterminacy remain, and that their
transition from probability to certainty only takes place later. Thus, when
quantum effects are significant, the picture of a classical Evolving Block
Universe (`EBU') cedes place to one of a Crystallizing Block Universe (`CBU'),
which reflects this quantum transition from indeterminacy to certainty, while
nevertheless resembling the EBU on large enough scales.Comment: 25 Pages. 3 figure
A Simple Derivation of the Gertsenshtein Effect
As shown by Gertsenshtein in 1961, an external magnetic field can catalyze
the mixing of graviton and photon states in a manner analogous to
neutrino-flavor oscillations. We first present a straightforward derivation of
the mechanism by a method based on unpublished notes of Freeman Dyson. We next
extend his method to include boundary conditions and retrieve the results of
Boccaletti et al. from 1970. We point out that, although the coupling between
the graviton and photon states is extremely weak, the large magnetic fields
around neutron stars G make the Gertsenshtein effect a plausible
source of gravitons. We also point out that axion-photon mixing, a subject of
active current research, is essentially the same process as the Gertsenshtein
effect, and so the general mechanism may be of broad astrophysical and
cosmological interest.Comment: 14 pages, no figures. V2: references added, section 4 expande
The Lorentz Force and the Radiation Pressure of Light
In order to make plausible the idea that light exerts a pressure on matter,
some introductory physics texts consider the force exerted by an
electromagnetic wave on an electron. The argument as presented is both
mathematically incorrect and has several serious conceptual difficulties
without obvious resolution at the classical, yet alone introductory, level. We
discuss these difficulties and propose an alternate demonstration.Comment: More or less as in AJ
"Quantum Interference with Slits" Revisited
Marcella [arXiv:quant-ph/0703126] has presented a straightforward technique
employing the Dirac formalism to calculate single- and double-slit interference
patterns. He claims that no reference is made to classical optics or scattering
theory and that his method therefore provides a purely quantum mechanical
description of these experiments. He also presents his calculation as if no
approximations are employed. We show that he implicitly makes the same
approximations found in classical treatments of interference and that no new
physics has been introduced. At the same time, some of the quantum mechanical
arguments Marcella gives are, at best, misleading.Comment: 11 pages, 3 figure
Instability of Extremal Relativistic Charged Spheres
With the question, ``Can relativistic charged spheres form extremal black
holes?" in mind, we investigate the properties of such spheres from a classical
point of view. The investigation is carried out numerically by integrating the
Oppenheimer-Volkov equation for relativistic charged fluid spheres and finding
interior Reissner-Nordstr\"om solutions for these objects. We consider both
constant density and adiabatic equations of state, as well as several possible
charge distributions, and examine stability by both a normal mode and an energy
analysis. In all cases, the stability limit for these spheres lies between the
extremal () limit and the black hole limit (). That is, we find
that charged spheres undergo gravitational collapse before they reach ,
suggesting that extremal Reissner-Nordtr\"om black holes produced by collapse
are ruled out. A general proof of this statement would support a strong form of
the cosmic censorship hypothesis, excluding not only stable naked
singularities, but stable extremal black holes. The numerical results also
indicate that although the interior mass-energy obeys the usual stability limit for the Schwarzschild interior solution, the gravitational
mass does not. Indeed, the stability limit approaches as .
In the Appendix we also argue that Hawking radiation will not lead to an
extremal Reissner-Nordstr\"om black hole. All our results are consistent with
the third law of black hole dynamics, as currently understood
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