46,323 research outputs found
A river model of space
Within the theory of general relativity gravitational phenomena are usually
attributed to the curvature of four-dimensional spacetime. In this context we
are often confronted with the question of how the concept of ordinary physical
three-dimensional space fits into this picture. In this work we present a
simple and intuitive model of space for both the Schwarzschild spacetime and
the de Sitter spacetime in which physical space is defined as a specified set
of freely moving reference particles. Using a combination of orthonormal basis
fields and the usual formalism in a coordinate basis we calculate the physical
velocity field of these reference particles. Thus we obtain a vivid description
of space in which space behaves like a river flowing radially toward the
singularity in the Schwarzschild spacetime and radially toward infinity in the
de Sitter spacetime. We also consider the effect of the river of space upon
light rays and material particles and show that the river model of space
provides an intuitive explanation for the behavior of light and particles at
and beyond the event horizons associated with these spacetimes.Comment: 22 pages, 5 figure
Einstein's "Zur Elektrodynamik..." (1905) Revisited, with Some Consequences
Einstein, in his "Zur Elektrodynamik bewegter Korper", gave a physical
(operational) meaning to "time" of a remote event in describing "motion" by
introducing the concept of "synchronous stationary clocks located at different
places". But with regard to "place" in describing motion, he assumed without
analysis the concept of a system of co-ordinates. In the present paper, we
propose a way of giving physical (operational) meaning to the concepts of
"place" and "co-ordinate system", and show how the observer can define both the
place and time of a remote event. Following Einstein, we consider another
system "in uniform motion of translation relatively to the former". Without
assuming "the properties of homogeneity which we attribute to space and time",
we show that the definitions of space and time in the two systems are linearly
related. We deduce some novel consequences of our approach regarding
faster-than-light observers and particles, "one-way" and "two-way" velocities
of light, symmetry, the "group property" of inertial reference frames, length
contraction and time dilatation, and the "twin paradox". Finally, we point out
a flaw in Einstein's argument in the "Electrodynamical Part" of his paper and
show that the Lorentz force formula and Einstein's formula for transformation
of field quantities are mutually consistent. We show that for faster-than-light
bodies, a simple modification of Planck's formula for mass suffices. (Except
for the reference to Planck's formula, we restrict ourselves to Physics of
1905.)Comment: 55 pages, 4 figures, accepted for publication in "Foundations of
Physics
Post-Newtonian limitations on measurement of the PPN parameters caused by motion of gravitating bodies
We derive explicit Lorentz-invariant solution of the Einstein and null
geodesic equations for data processing of the time delay and ranging
experiments in gravitational field of moving gravitating bodies of the solar
system - the Sun and major planets. We discuss general-relativistic
interpretation of these experiments and the limitations imposed by motion of
the massive bodies on measurement of the parameters gamma_{PPN}, beta_{PPN} and
delta_{PPN} of the parameterized post-Newtonian formalism.Comment: 17 pages, 1 figure; accepted for publication to MNRA
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