On the Theory of the Michelson-Morley Experiment in the Earth's Gravitational Field

Abstract

In this paper we discuss further the expected results for a Michelson-Morley-type experiment with one of the arms in the vertical direction in the Earth's gravitational field. We use a rigid model for the material and we develop a dimensional analysis. Then we show that the iYinge shift due to gravitation is of the order ofwhen the interferometer is rotated through 90". When the length of the arms is Z = 1 m and the wavelength of the light is A = m, one finds Elo-''. From our analysis we prove in a simple way that the equivalence principle cancels the effects of the order of ( G M B I R ~~) ( Z / A ) .

On the Possibility of Observing Negative Shapiro-like Delay Using Michelson–Morley-Type Experiments

“…It is evident from Equation ( 12) that the light signal suffers a negative time delay due to the negative sign in the round bracket, i.e., there occurs a gravitational time advancement. It should also be mentioned that the correction term also follows from dimensional arguments [32]. A curious aspect of Equation ( 12) is that the time advancement factor appears in the first order in µ but in the second order in 1/ρ.…”

Gravitational time advancement and its possible detection

“…Clearly in this case the signal suffers a negative delay due to the negative sign i.e., gravitational time advancement occurs. It is worthwhile to mention that the corrective term follows also from dimensional arguments [8]. Please note that the calculated effect is independent of PPN γ parameter unlike the standard expression for time delay [1,3,4] because we expressed the time delay/advancement results in terms of proper length that includes the γ factor (in a gravitational field physical parameters should be expressed in terms of proper quantities particularly in situations like the present one where proper quantities differ substantially from those of coordinate expressions).…”

Angular Momentum Effects in Michelson–Morley Type Experiments

“…The Michelson-Morley experiment is an interferometric measure and uses light, let us then start from a generic null line element in polar coordinates and within an axially symmetric static field originated by a central body endowed with an angular velocity Ω = dφ/dt: 0 = g tt dt 2 + 2g tφ dtdφ + g rr dr 2 + g θθ dθ 2 + g φφ dφ 2 (1)…”

“…Since then it has been assumed that no anisotropy can be revealed until the frontier of special relativity is crossed. Only in a few cases anisotropies deriving from general relativistic corrections were considered [2] [3], but only caused by the gravitational red shift in non-horizontal arms of the interferometer; Schwarzschild-like corrections do not produce any effect in the horizontal plane.…”