11 research outputs found
Research of Gravitation in Flat Minkowski Space
In this paper it is introduced and studied an alternative theory of
gravitation in flat Minkowski space. Using an antisymmetric tensor, which is
analogous to the tensor of electromagnetic field, a non-linear connection is
introduced. It is very convenient for studying the perihelion/periastron shift,
deflection of the light rays near the Sun and the frame dragging together with
geodetic precession, i.e. effects where angles are involved. Although the
corresponding results are obtained in rather different way, they are the same
as in the General Relativity. The results about the barycenter of two bodies
are also the same as in the General Relativity. Comparing the derived equations
of motion for the -body problem with the Einstein-Infeld-Hoffmann equations,
it is found that they differ from the EIH equations by Lorentz invariant terms
of order .Comment: 28 page
Continuity of the Maximum-Entropy Inference
We study the inverse problem of inferring the state of a finite-level quantum
system from expected values of a fixed set of observables, by maximizing a
continuous ranking function. We have proved earlier that the maximum-entropy
inference can be a discontinuous map from the convex set of expected values to
the convex set of states because the image contains states of reduced support,
while this map restricts to a smooth parametrization of a Gibbsian family of
fully supported states. Here we prove for arbitrary ranking functions that the
inference is continuous up to boundary points. This follows from a continuity
condition in terms of the openness of the restricted linear map from states to
their expected values. The openness condition shows also that ranking functions
with a discontinuous inference are typical. Moreover it shows that the
inference is continuous in the restriction to any polytope which implies that a
discontinuity belongs to the quantum domain of non-commutative observables and
that a geodesic closure of a Gibbsian family equals the set of maximum-entropy
states. We discuss eight descriptions of the set of maximum-entropy states with
proofs of accuracy and an analysis of deviations.Comment: 34 pages, 1 figur