Analysis of the Anomalous Brillet and Hall Experimental Result

Abstract

The persistent, second order, anomalous signal found in the Brillet and Hall experiment is derived by applying 4D differential geometry in the rotating earth frame. By incorporating the off diagonal time-space components of the rotating frame metric directly into the analysis, rather than arbitrarily transforming them away, one finds a signal dependence on the surface speed of the earth due to rotation about its axis. This leads to a Brillet-Hall signal prediction in remarkably close agreement with experiment. No signal is predicted from the speed of the earth in solar or galactic orbit, as the associated metric for gravitational orbit has no off diagonal component. To corroborate this result, a repetition by other experimentalists of the Brillet-Hall experiment, in which the test apparatus turns with respect to the earth surface, is urged.

Relativistic Rotation: A Comparison of Theories

“…Thus, the round trip speed of light in any direction orthogonal to the rotating frame local velocity is c. (A more sophisticated analysis leading to this result can be found in Ref. [40], p. 130.)…”

“…11 for an explanation of how this earth frame signal effectively averaged out to zero for the cosmic light speed isotropy result.) Most subsequent researchers have considered this signal to be anomalous, though others [39] , [16] , [40] have suggested that something significant may be behind it, i.e., true light speed anisotropy due to idiosyncrasies of rotating frames.…”

“…Klauber [16] , [40] , [44] analyzed relativistic rotation using a fully differential geometric approach. He started with the widely used transformation to a rotating frame (21), i.e.,…”

Derivation of the General Case Sagnac Result Using Non-Time-Orthogonal Analysis

“…where, e 1 and e 2 here do not, in general, have to be orthogonal, e i andê i point in the same direction for each index i, and carets over component indices indicate physical components. Substituting (25) into (27), one readily…”

“…When this is done, not only can the Sagnac effect be derived (as shown below), but all other observed rotating frame effects can be, as well. (See Klauber [15] , [16] , [20] , [21] , [22] , [23] , [24] , [25].) Further, the geometric foundation of relativity theory remains intact.…”