409 research outputs found
Quantum Mechanics as a Simple Generalization of Classical Mechanics
A motivation is given for expressing classical mechanics in terms of diagonal
projection matrices and diagonal density matrices. Then quantum mechanics is
seen to be a simple generalization in which one replaces the diagonal real
matrices with suitable Hermitian matrices.Comment: 9 pages, LaTe
Freak observers and the measure of the multiverse
I suggest that the factor in the pocket-based measure of the
multiverse, , should be interpreted as accounting for equilibrium
de Sitter vacuum fluctuations, while the selection factor accounts for
the number of observers that were formed due to non-equilibrium processes
resulting from such fluctuations. I show that this formulation does not suffer
from the problem of freak observers (also known as Boltzmann brains).Comment: 6 pages, no figures; references adde
Agnesi Weighting for the Measure Problem of Cosmology
The measure problem of cosmology is how to assign normalized probabilities to
observations in a universe so large that it may have many observations
occurring at many different spacetime locations. I have previously shown how
the Boltzmann brain problem (that observations arising from thermal or quantum
fluctuations may dominate over ordinary observations if the universe expands
sufficiently and/or lasts long enough) may be ameliorated by volume averaging,
but that still leaves problems if the universe lasts too long. Here a solution
is proposed for that residual problem by a simple weighting factor 1/(1+t^2) to
make the time integral convergent. The resulting Agnesi measure appears to
avoid problems other measures may have with vacua of zero or negative
cosmological constant.Comment: 26 pages, LaTeX; discussion is added of how Agnesi weighting appears
better than other recent measure
Noncomminuted lateral end clavicle fractures associated with coracoclavicular ligament disruption: technical considerations for optimal anatomic fixation and stability
Distal clavicle fractures associated with coracoclavicular ligament disruption are potentially unstable and necessitate surgical treatment. Current fixation techniques are nonanatomic and do not address relevant aspects of the pathoanatomy. We have developed a technique that uses a unique combination of implants; this permits minimally invasive fixation and stable reduction with a lateral fragment size as small as 5 mm. The surgical technique consists of (1) neutralization of muscular forces on the proximal fragment using a minimally invasive ligament repair device (TightRope™, Arthrex, FL, USA) and (2) internal fixation using a contour-matched locking plate (2.4 mm LCP(®) Distal radius plates, Synthes, USA). Technical tips to optimize this new procedure are discussed. The technique can be extended to an “arthroscopic-assisted” method involving arthroscopic coracoclavicular fixation followed by a mini-open plate fixation of the clavicular fragments
The Height of a Giraffe
A minor modification of the arguments of Press and Lightman leads to an
estimate of the height of the tallest running, breathing organism on a
habitable planet as the Bohr radius multiplied by the three-tenths power of the
ratio of the electrical to gravitational forces between two protons (rather
than the one-quarter power that Press got for the largest animal that would not
break in falling over, after making an assumption of unreasonable brittleness).
My new estimate gives a height of about 3.6 meters rather than Press's original
estimate of about 2.6 cm. It also implies that the number of atoms in the
tallest runner is very roughly of the order of the nine-tenths power of the
ratio of the electrical to gravitational forces between two protons, which is
about 3 x 10^32.Comment: 12 pages, LaTe
Black Hole Configurations with Total Entropy Less than A/4
If one surrounds a black hole with a perfectly reflecting shell and
adiabatically squeezes the shell inward, one can increase the black hole area A
to exceed four times the total entropy S, which stays fixed during the process.
A can be made to exceed 4S by a factor of order unity before the one enters the
Planck regime where the semiclassical approximation breaks down. One
interpretation is that the black hole entropy resides in its thermal
atmosphere, and the shell restricts the atmosphere so that its entropy is less
than A/4.Comment: 31 pages, LaTe
The Born Rule Dies
The Born rule may be stated mathematically as the rule that probabilities in
quantum theory are expectation values of a complete orthogonal set of
projection operators. This rule works for single laboratory settings in which
the observer can distinguish all the different possible outcomes corresponding
to the projection operators. However, theories of inflation suggest that the
universe may be so large that any laboratory, no matter how precisely it is
defined by its internal state, may exist in a large number of very distantly
separated copies throughout the vast universe. In this case, no observer within
the universe can distinguish all possible outcomes for all copies of the
laboratory. Then normalized probabilities for the local outcomes that can be
locally distinguished cannot be given by the expectation values of any
projection operators. Thus the Born rule dies and must be replaced by another
rule for observational probabilities in cosmology. The freedom of what this new
rule is to be is the measure problem in cosmology. A particular volume-averaged
form is proposed.Comment: LaTeX, 16 pages, typos in Eqs. (4.3) and (6.2) correcte
Bound states and the Bekenstein bound
We explore the validity of the generalized Bekenstein bound, S <= pi M a. We
define the entropy S as the logarithm of the number of states which have energy
eigenvalue below M and are localized to a flat space region of width a. If
boundary conditions that localize field modes are imposed by fiat, then the
bound encounters well-known difficulties with negative Casimir energy and large
species number, as well as novel problems arising only in the generalized form.
In realistic systems, however, finite-size effects contribute additional
energy. We study two different models for estimating such contributions. Our
analysis suggests that the bound is both valid and nontrivial if interactions
are properly included, so that the entropy S counts the bound states of
interacting fields.Comment: 35 page
Semi-classical limit and minimum decoherence in the Conditional Probability Interpretation of Quantum Mechanics
The Conditional Probability Interpretation of Quantum Mechanics replaces the
abstract notion of time used in standard Quantum Mechanics by the time that can
be read off from a physical clock. The use of physical clocks leads to apparent
non-unitary and decoherence. Here we show that a close approximation to
standard Quantum Mechanics can be recovered from conditional Quantum Mechanics
for semi-classical clocks, and we use these clocks to compute the minimum
decoherence predicted by the Conditional Probability Interpretation.Comment: 8 pages, references adde
Hawking Radiation as Tunneling through the Quantum Horizon
Planck-scale corrections to the black-hole radiation spectrum in the
Parikh-Wilczek tunneling framework are calculated. The corrective terms arise
from modifications in the expression of the surface gravity in terms of the
mass-energy of the black hole-emitted particle system. The form of the new
spectrum is discussed together with the possible consequences for the fate of
black holes in the late stages of evaporation.Comment: 13 pages; the contents of this paper overlap somewhat with the
earlier submissions hep-th/0504188 and gr-qc/0505015; (v2) references added
and various cosmetic (but no physics) changes, to appear in JHE
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