7,330 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
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
Unimodular loop quantum gravity and the problems of time
We develop the quantization of unimodular gravity in the Plebanski and
Ashtekar formulations and show that the quantum effective action defined by a
formal path integral is unimodular. This means that the effective quantum
geometry does not couple to terms in the expectation value of the
energy-momentum tensor proportional to the metric tensor. The path integral
takes the same form as is used to define spin foam models, with the additional
constraint that the determinant of the four metric is constrained to be a
constant by a gauge fixing term. We also review the proposal of Unruh, Wald and
Sorkin- that the hamiltonian quantization yields quantum evolution in a
physical time variable equal to elapsed four volume-and discuss how this may be
carried out in loop quantum gravity. This then extends the results of
arXiv:0904.4841 to the context of loop quantum gravity.Comment: 14 pages lagex, no figure
Irreducible decomposition of Gaussian distributions and the spectrum of black-body radiation
It is shown that the energy of a mode of a classical chaotic field, following
the continuous exponential distribution as a classical random variable, can be
uniquely decomposed into a sum of its fractional part and of its integer part.
The integer part is a discrete random variable (we call it Planck variable)
whose distribution is just the Bose distribution yielding the Planck law of
black-body radiation. The fractional part is the dark part (we call is dark
variable) with a continuous distribution, which is, of course, not observed in
the experiments. It is proved that the Bose distribution is infinitely
divisible, and the irreducible decomposition of it is given. The Planck
variable can be decomposed into an infinite sum of independent binary random
variables representing the binary photons (more accurately photo-molecules or
photo-multiplets) of energies 2^s*h*nu with s=0,1,2... . These binary photons
follow the Fermi statistics. Consequently, the black-body radiation can be
viewed as a mixture of statistically and thermodynamically independent fermion
gases consisting of binary photons. The binary photons give a natural tool for
the dyadic expansion of arbitrary (but not coherent) ordinary photon
excitations. It is shown that the binary photons have wave-particle
fluctuations of fermions. These fluctuations combine to give the wave-particle
fluctuations of the original bosonic photons expressed by the Einstein
fluctuation formula.Comment: 29 page
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