Do bodies of different composition fall with the same acceleration in a gravitational field? If not, the so called Equivalence Principle (EP) is violated. The Equivalence Principle, expressed by Galileo and later reformulated by Newton, was assumed by Einstein as the founding Principle of General Relativity, so far the most widely accepted theory of gravitation. In fact, it is not a Principle but a starting hypothesis unique to Gravity: no Equivalence Principle holds for the other fundamental forces of Nature (the electromagnetic, weak and strong interactions) and almost all theories trying to unify gravity with these forces require an EP violation, thus indicating that General Relativity may not be the final truth on gravitation, just as Newton’s theory of gravitation was proved by Einstein not to be the final truth at the beginning of 1900. All tests of General Relativity, except those on the Equivalence Principle, are concerned with specific predictions of the theory; instead, EP tests probe its basic assumption, and this is why they are a much more powerful instrument of investigation. A high accuracy, unquestionable, experimental result on the Equivalence Principle - no matter whether it is confirmed or violated - will be a crucial asset for a long time to come. And this is how it has to be, because physics is an experimental science in which any theory, in spite of its internal consistency and beauty, has to confront experiments, and ultimately will stand or fall depending solely on experimental results.

Galileo questioned Aristotle’s statement that heavier bodies should fall faster than lighter ones, arguing instead that all bodies fall at equal speeds regardless of their mass (which he proved by reasoning) and composition (which he proved by experiments). Galileo's formulation of the universality of free fall, which lately became known as the Equivalence Principle, was first published in 1638: "…veduto, dico questo, cascai in opinione che se si levasse totalmente la resistenza del mezzo, tutte le materie descenderebbero con eguali velocità " ("... having observed this I came to the conclusion that, if one could totally remove the resistance of the medium, all substances would fall at equal speeds "). It appeared in his Discorsi e dimostrazioni matematiche intorno a due nuove scienze attinenti alla meccanica e ai movimenti locali, which was published outside Italy (in Leiden) few years after completion due to Galileo’s prosecution by the Church of Rome³. Aged 74, Galileo was blind and under house arrest; but the Discorsi are based on much earlier work, mostly on experiments with the inclined plane and the pendulum going back almost 40 years to the time when he was a young lecturer at the University of Pisa, or had just moved to Padova. Galileo was well aware that his experiments with inclined planes and pendula were much more accurate than just dropping masses from a tower; but ideal mass dropping experiments allowed him to express the universality of free fall in a very straightforward manner, not requiring any deep understanding of mechanics. Indeed, no image of science has captured the imagination of ordinary people more than that of Galileo dropping masses from the leaning tower of Pisa, a symbol of the birth of the modern scientific method.

About 80 years after Galileo's first experiments Newton went further, actually recognizing the proportionality of mass and weight. Newton regarded this proportionality as so important that he devoted to it the opening paragraph of the Principia⁴, where he stated: "This quantity that I mean hereafter under the name of ... mass ... is known by the weight ... for it is proportional to the weight as I have found by experiments on pendulums, very accurately made...'' . At the beginning of the 20^th century, almost 300 years since Galileo's work, Einstein realized that because of the proportionality between the gravitational (passive) mass m_g and the inertial mass m_i, the effect of gravitation is locally equivalent to the effect of an accelerated frame, and can be locally cancelled. This is known as the Weak Equivalence Principle which Einstein introduced in 1907⁵ as the "hypothesis of complete physical equivalence" between a gravitational field and an accelerated reference frame: in a freely falling system all masses fall equally fast, hence gravitational acceleration has no local dynamical effects. Therefore, according to Einstein, the effects of gravity are equivalent to the effects of living in a curved space-time. In this sense the Equivalence Principle expresses the very essence of General Relativity and as such it deserves to be tested as accurately as possible. In the last 30 years since the advent of the space age General Relativity has been subjected to extensive experimental testing as never before in its first 50 years of existence, and so far it has come out having no real competitors; the crucial area where experimental gravitation is likely to play an important role is in the verification of the universality of free fall as a test of the weak equivalence principle itself, since it is tantamount to testing whether gravitation can be ascribed to a metric structure of space-time.

such that a non-zero value of h_k would define the violation of equivalence between the inertial and gravitational mass-energy of the k-th type. For instance, the rest mass would contribute (as a fraction of the total) for @ 1; the nuclear binding energy for 8× 10^-3, the mass difference between neutron and proton for 8× 10^-4 (A-Z) (A  being the number of protons plus neutrons and  Z  the number of protons in the nucleus), the electrostatic energy of repulsion in the nuclei for 6× 10^-4 Z² A^-4/3, the mass of electrons for 5× 10^-4 Z, the antiparticles for @ 10^-7, the weak interactions responsible of b decay for @ 10^-11. From the point of view of conventional field theory, the verification of all these separate "Equivalence Principles" corresponds to a very peculiar coupling of each field to gravity; whether and why it should be so in all cases is a mystery. Let us consider the case of antiparticles. A peculiarity of gravity, strictly related to the Equivalence Principle, is that there is so far no evidence for antigravity, namely for the possibility that matter is gravitationally repelled by antimatter. A negative ratio of inertial to gravitational mass would obviously violate the Equivalence Principle and forbid any metric theory of gravity. Yet, there are theoretical formulations which would naturally lead to antigravity. Unfortunately, while experiments concerning the inertial mass of antiparticles have been highly successful, and these are very accurately known, gravitational experiments (i.e. involving the gravitational mass of antiparticles) are extremely difficult because of the far larger electric effects, such as those due to stray electric fields in walls of the container. In absence of such direct tests, an improvement by several orders of magnitude of current tests of the weak Equivalence Principle with ordinary matter would also be an important constraint as far as the relation between gravity and antimatter is concerned.

No precise target accuracy, at which a violation should occur, has been predicted by these theories; an EP violation is expected, but only below the 10^-12 level reached so far, probably well below it. Whether this is really so, only high accuracy experiments can tell.

The first experimental apparatus to provide very accurate EP tests (to 10^-8-10^-9) was the torsion balance used by Eötvös⁶, at the turn of the 20^th century, and later on by his students⁷. The reason is simple: an EP test requires to detect tiny differences in the accelerations of two test bodies falling in the gravitational field of a source mass. It is therefore a differential experiment, naturally yielding the best sensitivity if performed with a differential apparatus like the torsion balance: no violation, no signal. Although in reality no apparatus is perfectly differential, the advantages are enormous. The next leap in sensitivity (to 10^-11-10^-12) came in the 60s⁸ and early 70s⁹ with the recognition that by taking the Sun as the source mass rather than the Earth, any differential effect on the test bodies of the torsion balance would be modulated by the 24^hr rotation of the Earth on which the experiment sits. Everyone who has attempted to detect a weak signal knows how important modulation is. Indeed, the modulation frequency should be as high as possible, in order to reduce 1/f electronic (and mechanical) noise. Which explains why the best and most reliable results in EP testing (to about 1 part in 10¹²) have been achieved in recent years by the "Eöt-Wash" group at the University of Seattle¹⁰ with a torsion balance placed on a turntable which modulates the signal at 1- 2hr period. An alternative to attempting faster rotation is pursued in India^11,12 by R. Cowsik and his group, based on a much heavier torsion balance (1.5kg) in a very low noise environment (25m under the ground) with very good thermal stability (obtained by means of two, very large, concentric vacuum chambers).

In GG the signal modulation (Figure 2.1) is provided by the 2Hz rotation rate of the entire satellite which encloses the test bodies, about 4 orders of magnitude higher than the modulation frequency of the best ground based experiments. In addition, it is well known since the beginning of the space age that if the test bodies of an EP experiment orbit the Earth the driving signal of a possible EP violation increases by about 3 orders of magnitude, correspondingly increasing the achievable sensitivity in EP testing. Last but not the least, in absence of weight test bodies do not need to be suspended against the 1-g local acceleration of gravity; the largest force acting on the GG test bodies in space is about 10⁸ times smaller than 1-g, which obviously simplifies the experiment. If the risks of working in remote, with no direct access to the apparatus, are minimized by manufacturing and testing a ground based payload prototype (in addition to performing the usual simulation and tests of all space instruments), the advantages of working in space can be fully exploited to improve the current best ground results by 5 orders of magnitude. Even with further progress in ground experiments (e.g. to an accuracy of 1 part in 10¹³, possibly 10¹⁴) the GG small mission would undoubtedly mean a great leap forward, allowing space scientists to probe a totally unknown, highly promising field of physics like no other ground experiment can even dream of.

Surprisingly enough, completely different tests of the Equivalence Principle (for the Earth and the Moon falling towards the Sun) have achieved an accuracy close to that of torsion balance experiments^17,18,19. The Earth- Moon distance is measured by lunar laser ranging (LLR) to the corner cube laser reflectors left by the astronauts on the surface of the Moon, accurate to better than 1cm. Were the Earth and the Moon to be attracted differently by the Sun because of their different composition (1/3 iron core and 2/3 silicate mantle the Earth; entirely silicate mantle the Moon), a physical model based on conventional Newtonian gravity with general relativistic corrections would not be able to make predictions reconcilable with the observed LLR data. This is an EP for different composition, but also for gravitational self- energy effects in the Earth (testing gravity's pull on gravitational energy), effects which are obviously absent in test bodies of laboratory size. According to Einstein, all forms of matter and energy, including the gravitational binding energy, accelerate at the same rate in a uniform gravitational field, and the gravitational binding energy of the Earth amounts to 5× 10^-10 of its mass and is therefore not negligible to the current achieved accuracy.

1.2 The Technological Goal