This article has the following sections.
A Ritzian Interpretation of Variable Stars
Non-pulsating Cepheid Variables
Ritzian Gamma-Ray Bursts
Ultra High Energy Cosmic Rays
Unsung Binaries and de Sitter's Whimsical Images?
GRB 790731 and omega Geminorum
A Ritzian Interpretation of Variable Stars1 - 2 - 3 - 4
An enlargement on 1987-1989 researches by V.I. Sekerin
and M.S. Serbulenko
Copyright © 1999-2004 - Robert S. Fritzius
This article is written under the presumption that the constancy of the "measured" speed of light by all observers (in vacuo) is an unresolved issue. The author favors Ritz's use of c+v relativity but with the reservation that extinction (Tolman or Ewald-Oseen), i.e., the speed of light eventually reaches a terminal speed with respect to any given medium, has to be taken into account. De Sitter's (1913) argument against Ritz is used as a theoretical springboard from which to examine currently published observations of what are thought to be radially pulsating variable stars. High-angular-resolution photographs of these variables obtained from the Hubble Space Telescope (HST), the very large array (VLA) radio telescope(s), the growing family of very large telescopes (VLTs), and/or the publication of light curves along with phase-matched spectroscopic line profiles (absorption and emission) can be used to resolve the c+v question.
[Ritz's c+v variable speed of hypothesis is not the same as the Variable Speed of Light (VSL) ideas of João Magueijo. In Ritz's theory, the speed of light "c" is a constant with respect to emission sources, but the source velocities are vectorially additive with it; i.e., c' = c+v. To this writer's knowledge, Magueijo does not get into non-cosmological periodic speed of light variations (This note was reworked on 12 May 2003.) ]
In 1908 Walter Ritz formulated an emission theory
of general electrodynamics(1).
in which the velocity of a light source is vectorially
additive to the velocity of the light emitted by it, i.e.,
the velocity of light is c + v. That aspect of
Ritz's theory does not hold for macroscopic-scale paths in
dispersive media such as the earth's atmosphere. Ritz was
aware of the problem, and intended to revise his theory,
but he died in 1909 and didn't get to do the revision. The
theory, as it stands, may still find application on
intermolecular and atomic scales and for modest distances
in highly rarefied regions in the interstellar medium.
This article deals primarily with the latter case. For
example, the light curves in the figure to the left were
produced by a computer program which simulates the orbit
of one component of a spectroscopic binary. (The color
gradations were added manually.) The program uses c +
v relativity to calculate the light travel time to
various extinction distances. The vectorial addition of
the star's instantaneous orbital velocity with that of
light (in the direction of the observer) produces
arrival-time modulation, which leads to "observed"
intensity and color modulation.
In 1913 Willem de Sitter urged abandonment of the Ritz theory because binary stars (the interstellar medium scenario) failed to show the predicted c + v effects(2). De Sitter's binary star argument was along the following lines.
The addition of the velocity of a visible component of a
binary star to the velocity of its light emitted in the
direction of an observer would allow slower light (c -
v) from one side of the orbit (when the component
was traveling away from the observer) to be overtaken by
the faster light (c + v) from one half orbit later
(when the component was traveling toward the observer). At
the right distance this effect could cause the visible
component to periodically be seen at two different
locations simultaneously and generally would lead to
apparent observational departures from Keplerian motion.
(The expression to compute the overtaking distance, which
is a function of orbit period and orbital speed, is
Actually de Sitter focused mainly on spectroscopically double stars (with parallaxes on the order of 0.1 arc sec and less) and with the idea that their conformance with Keplerian motion (based on radial velocity measurements alone) was to be taken as evidence against the Ritz theory. See: Binary Stars as Evidence against Ritz's Relativity. [Added 15 May 2004. Updated 14 Dec 2009.]
Ritz had already alluded to this kind of possibility. In his 1908 paper he said:
|"I would like to remark that if P' is animated by an oscillatory movement and if the distance PP' is sufficiently large, it is possible that the waves starting at moments t'(1), t'(2), ... where the speed of P' had different values v'(1), v'(2), ..., will arrive at P simultaneously because of the difference of their speed of propagation. In practice this case will be presented only in Optics." (W. Ritz, Ann. Chim. Phys., 13, 145 (1908): pp. 213-214.)|
Contrary to the de Sitter claim, and to other arguments
recently, John Fox(3) found that visible binary stars do not
offer evidence against the Ritz theory. He takes this
stand on the basis of
Tolman's extinction theorem (3a)(*), i.e., the absorption
of electromagnetic radiation by electrical charges in a
leads to a terminal speed for light with respect
to the medium.
The Ewald-Oseen extinction theorems (3b) are
related to this idea.
Fox states that one extinction length in our local
is estimated to be on the order of one light year. His
however, suggest that extinction distances may be much
shorter than our
current estimates. (Reference to be added.)
In the binary star case, bound atomic charges in the
interstellar environment within a light year or less of
the binary star absorb and re-emit the light from each
visible component, so that beyond five extinction lengths
the re-emitted light travels at the speed of light with
the bulk motion of the interstellar medium.
(*) Fox attributed this action to Richard Tolman, but Tolman strictly dealt with an abrupt change from c to -c, during light's perpendicular reflection from a mirror. Tolman and de Sitter seem to have thought that interstellar gas, as well as the Earth's atmosphere, had no effect on the speed of light. [This correction was added on 27 Jul 2004. Tweaked on 07 Mar 2006.]
In 1987 Vladimir Sekerin of Novosibirsk, Siberia, in an article titled Gnosiological Peculiarities in the Interpretations of Observations (For Example the Observation of Binary Stars)(4), showed that when we consider the distances (binary-to-observer) required for de Sitter's "whimsical" images effect to manifest themselves that the angular resolution of our best telescopes (1987) are insufficient for us to resolve them.
An English translation of Sekerin's paper is on this website.
Sekerin does not address extinction effects but he claims that de Sitter's hypothetical c + v binary star scenario provides an alternate explanation for the periodic light and apparent radial velocity variations of periodic variable stars which he says are really spectroscopic binaries. Because these images can't be resolved we won't see a visible component at two locations simultaneously, rather, we will get periodic variations in light intensity and color. The following derivation shows how to compute the distance necessary for the faster light to exactly overtake the slower light of one half orbital period earlier.
We set the time interval (t1) required for the slower light (visible component receding from observer) to reach the observer at distance (L), to be:
and time interval (t2) which is the sum of the time for one half orbit (T) plus the time for the faster light (component approaching observer) to travel the same distance L:
For t1 = t2 we have:
Re-arranging and solving for L we get:
In the following text and figures Lo will represent the exact overtaking distance in the derivation above and L will represent the observer's fraction of or multiple of the distance Lo from the binary.
Robert Fritzius email@example.com