Updating Century Old Relativity Theory
by David Bryan Wallace
Cape Coral, Florida, USA
first draft 2013-12-15
Last Edited 2024-02-18
Declared public domain by the author.
Proper attribution appreciated.
Some readers take umbrage at the suggestion that relativity theory is not perfect. Einstein's special relativity was adequate while detection of motion relative to an absolute rest frame, (a frame of isotropic one-way light speed,) eluded us. Technological advance is bringing that era to an end, and the theory needs modification to accommodate our ability to detect the absolute rest frame and to measure velocity relative to it.
For the most part, physical theory in 1900 was in fairly good order. In electromagnetics, laws of Karl Gauss, André-Marie Ampere and Michael Faraday were recast in a set of partial differential equations presented by James Clerk Maxwell in 1873 as a theory that unified electricity and magnetism into electromagnetism. This theory was tidied up by Oliver Heaviside in 1884 into four “Maxwell's Equations” in the vector calculus formalism now customarily used. The theory implied that light had a constant speed in free space, and, speed being movement relative to something, that implied the existence of a frame of reference then called "the luminiferous ether" but which might have been called “the absolute rest frame.” Elaborations of relatively new atomic theory were developing. Quantum absorption and emission of light were newly discovered.
In 1887, Michelson and Morley[1] had performed an experiment intended to detect relative motion of the earth and the luminiferous ether. They did not find the expected relative motion, and by 1900 there was not yet a generally accepted explanation for the failure. Albert Einstein's special theory of relativity[2], in 1905, assumed that it was impossible to detect motion relative to the luminiferous ether. Although Einstein seems to have believed there was an actual experimental basis for this assumption, there was not. Einstein rightly supposed that attempts to determine velocity relative to the light medium must be equivalent to timing the one way travel of light between synchronized clocks, but he wrongly believed that such attempts had been tried and significantly failed.
The only significant attempts to measure velocity relative to the light medium had been the Michelson-Morley experiment in 1887 and its subsequent replications. The Michelson-Morley experiment involved round trip, not one way, travel of light. It involved neither synchronized clocks nor measurement of elapsed time. Einstein's supposition was sound, timing of light travel in one direction is necessary to detect motion relative to the light medium, but the Michelson-Morley experiment was no such experiment nor was such an experiment possible until much later. The Michelson-Morley experimenters thought it would succeed because they implicitly assumed dimensional invariance of rigid solids, namely the stone slab floated on mercury.
Michelson and Morley calculated that an interferometric length measurement in wavelengths would depend on the velocity of the interferometer relative to the light medium and on its orientation with respect to the motion. Their apparatus compared two interferometers at right angles with a shared light source, each interferometer measuring a length of stone. The apparatus was rotated to interchange the orientations. The expected dependence on orientation was not found because stone contracts to exactly the degree that makes its interferometric length constant, a fact relied on by standards oganizations ISO and NIST for length standardization.
Although many empirical tests of relativity have confirmed some of its predictions, other variants of relativity can also be consistent with the same empirical confirmations. Still, physicists value the special theory so long as they believe synchronization of distant clocks is not possible independent of the frame of reference chosen.
Clarity in our understanding of what we mean by time is essential here. Our usual notion of time is a continuum involving quantifiable intervals. If event A happens before event B we say the time of event A is less than, or before, the time of event B, and we can discuss by how much the times differ. When we say events are simultaneous we mean the time of one event is equal to the time of the other event. Special relativity theory is inconsistent with this fundamental notion of equality. Einstein stated his definition of “simultaneous events” and explicitly declared as an assumption that his definition of simultaneous events satisfies requirements of equality of time, yet in subsequent paragraphs he showed that it does not. Rather than discarding the pragmatic but troublesome definition he concluded that our concept of time is flawed and that time and simultaneity are not definable in an absolute way — that observers in motion relative to each other cannot in general share the same time scale and agree that events separated by distance are simultaneous. So Einstein's special relativity had at an unfortunate cost: time ceased to be well defined.
When Einstein published his special theory of relativity, the standard for time was rotation of the earth. With such a unique standard of time, all that is needed to define time elsewhere is a method of synchronization at a distance. Today, however, the SI definition of time specifies that the standard is an atomic clock at rest. An atomic clock at rest provides an unvarying standard of time, and it can be replicated and located where needed. If atomic clocks separated by distance are capable of maintaining synchronization then detection of the absolute rest frame is possible.
In 1913 a significant paper by astronomer Willem de Sitter[3] included observations concerning the one way travel of light. Titled “Ein astronomischer Beweis für die Konstanz der Lichgeshwindigkeit,” [“An Astronomical Proof of the Constancy of Light Speed,”] it noted that the orbiting of a binary star is a periodic motion that marks time making it observable that light from a distant star travels to Earth at a speed that is constant, not relative to the inertial frame of the star as it approaches nor relative to the inertial frame of the star as it recedes nor relative to the observer moving with rotation and revolution of Earth, but relative to the same inertial frame in every case for any light traversing the same one way path through space. This again shows that there is a unique frame of reference relative to which light speed is the same in every direction consistent with Maxwell's theory, but contradicting Einstein's declaration that the notion of absolute rest is without meaning.
What would modification of Einstein's relativity theory mean for physics? Perhaps not overwhelmingly much. Relativity theory has been a fairly inconsequential part of physics except that the physics community's fondness for it tends to exclude any person who questions the theory. Changes include altered length contraction ratios and elimination of time dilation, seen as distinct from clock rate variation. Except for observations that in some way constitute observations of one way light speed, the principle of invariance seems valid: the same laws of physics hold locally in every inertial frame of reference. Determination of absolute velocity can be undertaken, this time using atomic clocks to time one way light travel. The feasibility of such determination was demonstrated in 1984 by Torr and Kolen[4].
The author, David Bryan Wallace, is a retired mathematics instructor living in Cape Coral, Florida, USA.
[1] Michelson, Albert Abraham & Morley, Edward Williams (1887). “On the Relative Motion of the Earth and the Luminiferous Ether.” American Journal of Science 34: 333-345. online http://en.wikisource.org/wiki/On_the_Relative_Motion_of_the_Earth_and_the_Luminiferous_Ether.
[2] Einstein, Albert, “Zur Elektrodynamik bewegter Körper,” Annalen der Physik 17:891, 1905, “On the Electrodynamics of Moving Bodies,” online in English http://www.fourmilab.ch/etexts/einstein/specrel/www/.
[3] de Sitter, Willem, “Ein astronomischer Beweis für die Konstanz der Lichgeshwindigkeit," Physik. Zeitschr, 14, 429 (1913). “A proof of the constancy of the velocity of light,” Proceedings of the Royal Netherlands Academy of Arts and Sciences 15 (2): 1297-1298, online in English http://www.datasync.com/~rsf1/desit-1e.htm.
[4] Torr, D.G. and Kolen, P. (1984) “An Experiment to Measure Relative Variations in the One-Way Speed of Light.” In: Taylor, B.N. and Phillips, W.D., Eds., Precision Measurements and Fundamental Constants II, Special Publication, 617, pages 675-679.