8,680 research outputs found

### Variability of fundamental constants

If the fine structure constant is not really constant, is this due to a
variation of $e$, $\hbar$, or $c$? 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
($V$). Such a lowest limit $V$, 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 ($v\approx V$), 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

### The Maxwell Lagrangian in purely affine gravity

The purely affine Lagrangian for linear electrodynamics, that has the form of
the Maxwell Lagrangian in which the metric tensor is replaced by the
symmetrized Ricci tensor and the electromagnetic field tensor by the tensor of
homothetic curvature, is dynamically equivalent to the Einstein-Maxwell
equations in the metric-affine and metric formulation. We show that this
equivalence is related to the invariance of the Maxwell Lagrangian under
conformal transformations of the metric tensor. We also apply to a purely
affine Lagrangian the Legendre transformation with respect to the tensor of
homothetic curvature to show that the corresponding Legendre term and the new
Hamiltonian density are related to the Maxwell-Palatini Lagrangian for the
electromagnetic field. Therefore the purely affine picture, in addition to
generating the gravitational Lagrangian that is linear in the curvature,
justifies why the electromagnetic Lagrangian is quadratic in the
electromagnetic field.Comment: 9 pages; published versio

### Cosmological Constant and Noncommutative Spacetime

We show that the cosmological constant appears as a Lagrange multiplier if
nature is described by a canonical noncommutative spacetime. It is thus an
arbitrary parameter unrelated to the action and thus to vacuum fluctuations.
The noncommutative algebra restricts general coordinate transformations to
four-volume preserving noncommutative coordinate transformations. The
noncommutative gravitational action is thus an unimodular noncommutative
gravity. We show that spacetime noncommutativity provides a very natural
justification to an unimodular gravity solution to the cosmological problem. We
obtain the right order of magnitude for the critical energy density of the
universe if we assume that the scale for spacetime noncommutativity is the
Planck scale.Comment: 7 page

### Dynamics of Einstein - de Haas Effect: Application to Magnetic Cantilever

Local time-dependent theory of Einstein - de Haas effect is developed. We
begin with microscopicinteractions and derive dynamical equations that couple
elastic deformations with internal twists due to spins. The theory is applied
to the description of the motion of a magnetic cantilever caused by the
oscillation of the domain wall. Theoretical results are compared with a recent
experiment on Einstein - de Haas effect in a microcantilever.Comment: 7 PR pages, 5 figures, submitted to PR

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