978-1-4673-8292-2/16/$31.00 ©2016 IEEE Laboratory tests of a high-precision laser interferometry readout for the GG experiment in space Marco Pisani and Massimo Zucco INRIM-Istituto Nazionale di Ricerca Metrologica Via delle Cacce 91, Torino, Italy Email: marco.pisani@inrim.it massimo.zucco@inrim.it Anna M. Nobili Department of Physics “E. Fermi” University of Pisa and INFN-Istituto Nazionale di Fisica Nucleare Largo B. Pontecorvo 3, 56127 Pisa, Italy Email: anna.nobili@unipi.it Abstract—On 25 April the Microscope satellite was successfully launched to test the weak equivalence principle, which is the founding pillar of General Relativity, to to 1 part in 10 15 (100- fold improvement). A possible violation will potentially be a major discovery and call for urgent checking. The GG (“Galileo Galilei”) satellite experiment can do that with one hundred times better precision, to 10 -17 . To do that GG is required to measure the relative displacements of two concentric test cylinders with a precision of about half a picometer at the frequency of 1 Hz.A laser interferometry gauge has been designed for this purpose and is under development at INRIM with a required noise level of 1 pm √ Hz at 1 Hz. We report recent experimental results which demonstrate that the requirement can be met with a free running laser (no frequency lock needed) and consequent reduced complexity. I. I NTRODUCTION In a gravitational field all bodies fall with the same ac- celeration regardless of their mass and composition. This is the Universality of Free Fall-UFF (also known as the Weak Equivalence Principle-WEP). As stated by Einstein in his 1916 paper “The foundation of the general theory of relativity”[1], this ‘fact of nature’ is at the foundation of the General theory of Relativity (GR) and must therefore be firmly supported by experiments. In 1916 Einstein brought as experimental evidence the best tests of his time carried out in Budapest by Lor` and von E¨ otv¨ os and his group, referring to the great accuracy of these tests in a specific footnote of his paper. The results of E¨ otv¨ os were indeed astonishing. While all his predecessors since Galileo had suspended different test masses from pendulums, E¨ otv¨ os had the great intuition of coupling them by suspension on a single torsion balance, and in so doing improved the precision of the test by three orders of magnitude. One century later the best controlled laboratory tests of UFF-WEP are still provided by torsion balances, now rotating in order to modulate the signal and up-covert its frequency to higher values (the higher the better) where thermal noise, elec- tronics noise and other noise sources are known to be smaller. In a remarkable series of experiments with slowly rotating torsion balances the E¨ ot-Wash group of Eric Adelberger at the University of Washington has confirmed UFF-WEP to 1 part in 10 13 in the gravitational field of the Earth [2], [3]. A similar result has been obtained for the Moon and the Earth falling in the gravitational field of the Sun by laser ranging to the retroreflectors left by the astronauts on the surface of the Moon ([4], [5]). Gravity is the only fundamental force of nature to obey the equivalence principle. The equivalence principle is therefore at the crossroad between General Relativity and the Standard Model of particle physics, and for this reason a huge amount of theoretical work has been carried out in trying to establish at which level a breakdown –if any– should occur. Till now these efforts have failed to provide us with a firm target. Thus, similarly to Einstein and E¨ otv¨ os one hundred years ago, we consider the best tests available and how they can be further improved, A violation of UFF-WEP would signal that either GR needs fixing, or a new force of nature has been found. Either way it would be a scientific revolution. This is why experimentalists have tried to test it with better and better precision whenever the possibility for an improvement has arisen. Tests of the Universality of Free Fall are quantified by the fractional differential acceleration η = Δa a (1) between two test masses of different composition as they fall in the gravitational field of a source body with the average acceleration a (the “driving signal”). The physical observable quantity is the differential acceleration Δa of the falling masses relative to each other, pointing to the center of mass of the source body (e.g. the Earth). For UFF-WEP to hold it must be η =0; the lower the value of η, the more sensitive is the test. For the same experimental sensitivity to Δa, the higher the driving acceleration a (at the denominator of (1)), the more sensitive is the test. If the test masses are suspended inside a satellite orbiting the Earth at low altitude rather than being on a torsion balance on the ground, the gain due to the driving 260