Abstract
.GINGER (Gyroscopes IN General Relativity) is a proposal for an Earth-based experiment to measure the Lense-Thirring (LT) and de Sitter effects. GINGER is based on ring lasers, which are the most sensitive inertial sensors to measure the rotation rate of the Earth. We show that two ring lasers, one at maximum signal and the other horizontal, would be the simplest configuration able to retrieve the GR effects. Here, we discuss this configuration in detail showing that it would have the capability to test LT effect at 1%, provided the accuracy of the scale factor of the instrument at the level of 1 part in 1012 is reached. In principle, one single ring laser could do the test, but the combination of the two ring lasers gives the necessary redundancy and the possibility to verify that the systematics of the lasers are sufficiently small. The discussion can be generalised to seismology and geodesy and it is possible to say that signals 10-12 orders of magnitude below the Earth rotation rate can be studied; the proposed array can be seen as the basic element of multi-axial systems, and the generalisation to three dimensions is feasible adding one or two devices and monitoring the relative angles between different ring lasers. This simple array can be used to measure with very high precision the amplitude of angular rotation rate (the length of the day, LOD), its short term variations, and the angle between the angular rotation vector and the horizontal ring laser. Finally this experiment could be useful to probe gravity at fundamental level giving indications on violations of Einstein Equivalence Principle and Lorenz Invariance and possible chiral effects in the gravitational field.
Highlights
Ring Lasers Gyroscopes (RL) are high-sensitivity devices widely used to measure absolute rotation rates, exploiting the Sagnac effect [1,2]
We show that two ring lasers, one at maximum signal and the other horizontal, would be the simplest configuration able to retrieve the General Relativity (GR) effects
The discussion can be generalised to seismology and geodesy and it is possible to say that signals 10–12 orders of magnitude below the Earth rotation rate can be studied; the proposed array can be seen as the basic element of multi-axial systems, and the generalisation to three dimensions is feasible adding one or two devices and monitoring the relative angles between different ring lasers
Summary
The graph is not to scale and it gives a pictorial view of the relative orientations of the different components. It is shown that it is possible to reconstruct the angle between the horizontal RL and the angular rotation vector with very high precision This is a major point: each measurement is affected by changes in the orientation of the area versor, the higher the sensitivity the higher the precision required in the relative angles: for example, 2 · 10−9 rad error in orientation is equivalent to a. Let us consider the special case in which RL1 is closely aligned with the total axis of rotation (ΩT ); in this case the angle ζ1 1, assuming that γ is known with the error δγ (ζ1 = γ + δγ − ζ); substituting in eq (2), it is possible to show that the error δζ depends at first order on the product ζ1 · δγ, δζγ cot(ζ) · ζ1 × δγ,. The experimental requirements for GR test will be discussed
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