17,832 research outputs found
Variability of fundamental constants
If the fine structure constant is not really constant, is this due to a
variation of , , or ? It is argued that the only reasonable
conclusion is a variable speed of light.Comment: preliminary draft, comments welcom
Lorentz group theory and polarization of the light
Some facts of the theory of the Lorentz group are specified for looking at
the problems of light polarization optics in the frames of vector
Stokes-Mueller and spinor Jones formalism. In view of great differences between
properties of isotropic and time-like vectors in Special Relativity we should
expect principal differences in describing completely polarized and partly
polarized light. In particular, substantial differences are revealed when
turning to spinor techniques in the context of the polarized light. Because
Jones complex formalism has close relation to spinor objects of the Lorentz
group, within the field of the light polarization we could have physical
realizations on the optical desk of some subtle topological distinctions
between orthogonal L_{+}^{\uparrow} =SO_{0}(3.1) and spinor SL(2.C) groups.
These topological differences of the groups find their corollaries in the
problem of the so-called spinor structure of physical space-time, some new
points are considered.Comment: 17 pages. Talk given at 16 International Seminar: NCPS, May 19-22,
2009, Minsk. A shorter vertion published as a journal pape
Doubly Special Relativity with a minimum speed and the Uncertainty Principle
The present work aims to search for an implementation of a new symmetry in
the space-time by introducing the idea of an invariant minimum speed scale
(). Such a lowest limit , being unattainable by the particles, represents
a fundamental and preferred reference frame connected to a universal background
field (a vacuum energy) that breaks Lorentz symmetry. So there emerges a new
principle of symmetry in the space-time at the subatomic level for very low
energies close to the background frame (), providing a fundamental
understanding for the uncertainty principle, i.e., the uncertainty relations
should emerge from the space-time with an invariant minimum speed.Comment: 10 pages, 8 figures, Correlated paper in:
http://www.worldscientific.com/worldscinet/ijmpd?journalTabs=read. arXiv
admin note: substantial text overlap with arXiv:physics/0702095,
arXiv:0705.4315, arXiv:0709.1727, arXiv:0805.120
Moving Observers in an Isotropic Universe
We show how the anisotropy resulting from the motion of an observer in an
isotropic universe may be determined by measurements. This provides a means to
identify inertial frames, yielding a simple resolution to the twins paradox of
relativity theory. We propose that isotropy is a requirement for a frame to be
inertial; this makes it possible to relate motion to the large scale structure
of the universe.Comment: 8 pages, 1 figure, with minor typographical correctio
The evolution of radiation towards thermal equilibrium: A soluble model which illustrates the foundations of Statistical Mechanics
In 1916 Einstein introduced the first rules for a quantum theory of
electromagnetic radiation, and he applied them to a model of matter in thermal
equilibrium with radiation to derive Planck's black-body formula. Einstein's
treatment is extended here to time-dependent stochastic variables, which leads
to a master equation for the probability distribution that describes the
irreversible approach of Einstein's model towards thermal equilibrium, and
elucidates aspects of the foundation of statistical mechanics. An analytic
solution of this equation is obtained in the Fokker-Planck approximation which
is in excellent agreement with numerical results. At equilibrium, it is shown
that the probability distribution is proportional to the total number of
microstates for a given configuration, in accordance with Boltzmann's
fundamental postulate of equal a priori probabilities for these states. While
the counting of these configurations depends on particle statistics- Boltzmann,
Bose-Einstein, or Fermi-Dirac - the corresponding probability is determined
here by the dynamics which are embodied in the form of Einstein's quantum
transition probabilities for the emission and absorption of radiation. In a
special limit, it is shown that the photons in Einstein's model can act as a
thermal bath for the evolution of the atoms towards the canonical equilibrium
distribution of Gibbs. In this limit, the present model is mathematically
equivalent to an extended version of the Ehrenfests' ``dog-flea'' model, which
has been discussed recently by Ambegaokar and Clerk
On the Trace-Free Einstein Equations as a Viable Alternative to General Relativity
The quantum field theoretic prediction for the vacuum energy density leads to
a value for the effective cosmological constant that is incorrect by between 60
to 120 orders of magnitude. We review an old proposal of replacing Einstein's
Field Equations by their trace-free part (the Trace-Free Einstein Equations),
together with an independent assumption of energy--momentum conservation by
matter fields. While this does not solve the fundamental issue of why the
cosmological constant has the value that is observed cosmologically, it is
indeed a viable theory that resolves the problem of the discrepancy between the
vacuum energy density and the observed value of the cosmological constant.
However, one has to check that, as well as preserving the standard cosmological
equations, this does not destroy other predictions, such as the junction
conditions that underlie the use of standard stellar models. We confirm that no
problems arise here: hence, the Trace-Free Einstein Equations are indeed viable
for cosmological and astrophysical applications.Comment: Substantial changes from v1 including added author, change of title
and emphasis of the paper although all original results of v1. remai
Noncommutative General Relativity
We define a theory of noncommutative general relativity for canonical
noncommutative spaces. We find a subclass of general coordinate transformations
acting on canonical noncommutative spacetimes to be volume-preserving
transformations. Local Lorentz invariance is treated as a gauge theory with the
spin connection field taken in the so(3,1) enveloping algebra. The resulting
theory appears to be a noncommutative extension of the unimodular theory of
gravitation. We compute the leading order noncommutative correction to the
action and derive the noncommutative correction to the equations of motion of
the weak gravitation field.Comment: v2: 10 pages, Discussion on noncommutative coordinate transformations
has been changed. Corresponding changes have been made throughout the pape
Applications of Ideas from Random Matrix Theory to Step Distributions on "Misoriented" Surfaces
Arising as a fluctuation phenomenon, the equilibrium distribution of
meandering steps with mean separation on a "tilted" surface can be
fruitfully analyzed using results from RMT. The set of step configurations in
2D can be mapped onto the world lines of spinless fermions in 1+1D using the
Calogero-Sutherland model. The strength of the ("instantaneous",
inverse-square) elastic repulsion between steps, in dimensionless form, is
. The distribution of spacings between neighboring
steps (analogous to the normalized spacings of energy levels) is well described
by a {\it "generalized" Wigner surmise}: . The value of is taken to best fit the data;
typically . The procedure is superior to conventional
Gaussian and mean-field approaches, and progress is being made on formal
justification. Furthermore, the theoretically simpler step-step distribution
function can be measured and analyzed based on exact results. Formal results
and applications to experiments on metals and semiconductors are summarized,
along with open questions. (conference abstract)Comment: 7 pages, 2 figures; based on talk presented at TH-2002, UNESCO,
Paris, July 2002; to be published in Ann. Henri Poincare
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