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 derived below.) 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. In closing, he did mention two visual binaries, delta Equulei and zeta Herculis, without calling attention to their apparently very high eccentricities. See English translations of Physik. Zeitschr. 14, 429 (1913) and Physik. Zeitschr. 14, 1267 (1913) [Added 15 May 2004. Updated 4 June 2004.]

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 advanced more 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 and re-radiation of electromagnetic radiation by electrical charges in a dispersive medium 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 interstellar medium, is estimated to be on the order of one light year. His laboratory tests, 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 respect to 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. * * * Misspelled keywords: atronomical 1 - 2 - 3 - 4 - Next