GINGER

General Relativity is a theory of gravity and it attributes to the gravitational interaction a nature quite different from that of all other fundamental forces of nature. GR in fact expresses gravity as a geometrical property of a 4-dimensional manifold: the space-time. The behavior of any freely falling body as well as of any field, such as electromagnetism (or the weak or strong forces), depends, as a consequence, on the curvature of space-time, which in turn is determined by the presence of matter and fields. The geometric nature of GR, besides being very elegant and powerful, poses various problems to the whole framework of present theoretical physics, the main troubles coming from the enduring conflict with quantum mechanics. That conflict shows up at extremely high interaction energies (and extremely short distances) which means that the experimental investigation thereupon is very difficult being restricted to the observation, as far as possible, of the initial stages of the life of the universe. For this very reason it is however of paramount importance to test all aspects of the gravitational interaction as described by GR in order to verify the completeness and correctness of the theory in all its implications. Turning then the attention to areas where actual experiments are possible we find a peculiar effect, which accompanies the gravitational field of a rotating body. That something special had to be expected there, had already been supposed before relativity, at the end of the 19^{th} century, just by analogy with Maxwell’s electromagnetism. Since Newton’s gravitational field of a rotating sphere looks like the electric field of a spherical charge distribution, shouldn’t a rotating massive sphere show a “magnetic” component of its gravitational field, just as it happens with a rotating charged sphere? Classically there is no way to produce such an effect, but GR dose indeed predict the presence of an additional contribution to the gravitational field, coming from the motion of the source and in particular from its *rotation* (uniform rectilinear motion can be globally eliminated by a simple Lorentz transformation; this is not the case for rotations). In practice, at least in its lowest approximation description, the additional contribution makes a rotating mass similar to a bar magnet or a finite cylindrical coil carrying current. A little massive body in the surroundings, if it moves, will feel both a gravito*electric * force attracting it toward the central mass, and a gravito*magnetic * force pulling it aside, working as the Lorentz force acting on a charge moving in a magnetic field. The presence of the gravitomagnetic field was discussed by Einstein in 1913, before the formal completion of GR, and was explored, in its effects, by Hans Lense and his student Joseph Thirring a few years later, this is the reason why we know today the typical gravitomagnetic *frame dragging *also as the *Lense-Thirring *effect (LT). Despite having been pointed out very early, the effect if very difficult to verify, since in all ordinary situations (in practice always, just excepting neutron stars and black holes) it is extremely weak: on earth the transverse “Lorentz” acceleration is at least as small as one thousandth of a billionth of the gravitoelectric Newtonian acceleration.

So far, the limited number of experiments that have been performed have been based on the fact that, according to GR, a gyroscope is gravitationally the analog of a magnet, so it is expected to interact with the rotating earth as a magnet (having to conserve its angular momentum) would do with another bigger magnet. In practice, a peculiar precession rate is expected. The test gyroscope may be a small one (actually four) carried by a spacecraft orbiting the earth, as it was the case of the GP-B experiment. Or it may be as big as the moon on its orbit around the earth (lunar laser ranging); or the LAGEOS I and LAGEOS II satellites in their orbits; or the orbit of the dedicated LARES satellite, now flying. This type of experiments has confirmed LT within an accuracy of 10% (LAGEOS I and II; GP-B was within 19%) and are expected (LARES) to achieve a few % (possibly 1%) accuracy.

There is however another interesting possibility. The space-time containing a steadily rotating mass acquires a chiral symmetry about the time axis, besides the obvious rotation symmetry around the rotation axis. If we now consider a closed path in space and send along it two entities (they may be anything: continuous waves, objects, pulses…) in opposite directions, the time each of them will take to complete the tour and come back to the starting point, will be different even though their local velocity (the velocity with respect to the immediate surroundings at rest) will have been kept fixed and equal for both during the whole journey.

This is also true for light, which is moreover a perfect probe for relativity, since its local velocity is always *c*. If we use two continuous counter-propagating beams, a stationary condition is attained where the difference in the time of flight is reflected in the fact that each separate beam slightly adjusts its frequency in order to achieve its own static state. The two beams are superposed and have now different frequencies despite having been generated by the same source. The amplitude of the compound signal will be modulated by a beat, whose frequency (much smaller than the ones of the two beams) turns out to be proportional to the angular momentum of the central body whose rotation is responsible for the asymmetry in the propagation. Reading the beat frequency out is then possible to measure the strength of the gravitomagnetic field and ultimately the LT effect. Unfortunately things are not that easy, because, as mentioned above, the gravitomagnetic field depends in part also on the reference frame one uses. In practice, if the observer (the laboratory) is rotating on its own with respect to the “fixed stars”, his rotation provides a kinematical contribution to the gravitomagnetic field and induces a time of flight difference between co-rotating and counter-rotating beams. The kinematical rotation effect is known as the *Sagnac effect. * Unfortunately, for a laboratory fixed to the rotating earth, the Sagnac effect turns out to be approximately one billion times bigger than the Lense-Thirring contribution.

In a few lines we have explained how a *ring-laser *works and why such devices are now widely used as compact commercial rotation sensors, replacing old mechanical gyroscopes. In order to reveal the Lense-Thirring effect (as well as another GR effect, called geodetic precession), an extremely high sensitivity is required. The best research ring-laser in the world is, at the moment, the G ring in Wettzell (Bavaria) whose accuracy is less than an order of magnitude above the threshold for the detection of LT. The GINGER experiment (to be deployed at the LNGS) is meant to attain a sensitivity a couple of orders of magnitude *below* that threshold. It will be a three-dimensional array of square loops of light, not less than six meters side. The three-dimensional configuration will allow for the independent measurement of the three space components of the gravitomagnetic field. The result is within reach of the present laser technologies, however it will require much ingenuity and care in the design and building of the apparatus. The expected performance of the instrument will have to face the quantum noise in the laser and the long term stability, the behavior of the mirrors at the corners of the squares and especially the fact that differential deformations of each ring (for mechanical or thermal reasons) can easily overwhelm the sought for signal.

The problem can be dealt with either by an extremely rigid set up (which is the solution adopted for G-Wettzell) or pursuing a dynamical stability of the geometry of the rings, which is the way adopted for GINGER. In practice, the length of the main diagonals of each ring will be controlled by means of additional laser cavities and piezoelectric actuators moving the mirrors in order to counter any small drift of mechanical or thermal origin and keeping the length of the perimeter fixed.

At the moment the path towards the full implementation of GINGER is at an intermediate stage, where to devices, GP2 and GINGERino, have been realized, the former in Pisa and the latter at the LNGS. The two instruments are being used in order to test technologies and methods and in particular to characterize the LNGS location from the viewpoint of environmental rotations and to optimize the technique of the dynamical control of the perimeter. The program is advancing according to the predefined road map and will soon lead to the actual building of the full GINGER and to the terrestrial measurement of the LT effect with an accuracy better than 1%.