7.1 Introduction

It was clear to Einstein that, due to their extreme weakness,1 of the order of (v/c)5, there was no hope of detecting gravitational waves in Earth-based laboratories; after some years he reconsidered the whole matter coming to the conclusion that gravitational waves actually do not exist, being simply gauge artifacts. In 1936, together with Nathan Rosen,2 Einstein wrote a paper containing such a conclusion and sent it for publication to the Physical Review. The article was rejected. Quite angrily Einstein withdrew the manuscript and published it on the Journal of the Franklin Institute with a less provoking title [3].

In the following years Einstein reconsidered once again the matter and, together with Infeld and Hoffmann, developed a systematic post-Newtonian expansion of the field equations of General Relativity, showing that wave radiation does not appear up to the (v/c)4 order. Yet at the next order, (v/c)5, waves pop up and follow the quadrupole formula (7.1.1), as demonstrated by Hu in a 1947 paper [4].

7.1.1 The Idea of GW Detectors

The first attempts to construct experimental apparats able to detect gravitational waves are due to the American physicist Joseph Weber, the founder of laser and maser physics.3 In the years 1955–1956, Weber worked at the Institute for Advanced Studies of Princeton with John Archibald Wheeler4 and developed the project of a

1As we are going to show in the present chapter the 1918 Einstein formula for the emission power can be retrieved from first principles (see (7.3.94)) and precisely involves the ratio of actual velocities with respect to the speed light raised to power five.

2Nathan Rosen, (Brooklyn 1909, Haifa 1995) was the author, together with Einstein and Podolsky of the famous 1935 paper where the possibility that Quantum Mechanics might be incomplete was put forward. In the EPR paper the existence of hidden variables was conjectured and the probabilistic interpretation of Quantum Mechanics questioned. Yet, as it is widely known, all experimental tests have always confirmed Quantum Mechanics and rejected any competitor theory.

3Joseph Weber (1919–2000) was an American physicist. Born in Paterson, New Jersey, he died in Pittsburgh, Pennsylvania. After serving in the Navy during war-times, where he studied electronics, Weber graduated from the University of Maryland at College Park and obtained his Ph.D. with a thesis on microwave spectroscopy. In 1952 he gave a public lecture in Ottawa where he laid down the principles behind the construction of what were later called lasers and masers. These ideas were developed simultaneously by Charles Townes, Nikolay Basov, and Aleksandr Prokhorov, who built working prototypes of these devices, and received the Nobel Prize for this work in 1964.

4John Archibald Wheeler (July 9, 1911–April 13, 2008) was an eminent American theoretical physicist. He ranks among the later collaborators of Albert Einstein and includes Richard Feynman, Kip Thorne, Hugh Everett and Tullio Regge among his Ph.D. students. He tried to achieve Einstein’s vision of a unified field theory. He is also known for having coined the terms black hole and wormhole. As many other American physicists Wheeler participated in the Manhattan Project for the construction of the Atomic Bomb. For a few decades, General Relativity was somewhat neglected by the main stream of Physics, being detached from experiment. Wheeler was a key figure in the revival of the subject, leading the school at Princeton, while Dennis Sciama and Yakov Zel’dovich developed the subject in Cambridge and Moscow. The work of Wheeler and his students contributed greatly to the golden age of General Relativity.

Fig. 7.1 The antenna Explorer is a cylinder of Al5056, it weights 2300 kg, it is 3 meter long and it has a diameter of 60 cm. It is cooled at the temperature of liquid helium (4.2 K) and it operates at the temperature of 2 K, which is reached by lowering the pressure on the liquid helium reservoir. Its resonance frequencies are around 906 and 923 Hz

gravitational antenna made of a resonant metallic bar, which he further improved during a long visit at the University of Leiden in the Netherlands. In the early 1960s Weber developed the first wave detectors and began publishing papers where he claimed evidence of such a detection. In 1972 one of Weber’s bar detectors was sent to the moon on the Apollo 17th lunar mission.

Weber’s claims were received with high skepticism by the scientific community and the systematic error inherent to the large noise of his detectors was demonstrated to invalidate his conclusions. Notwithstanding the fact that his efforts were inconclusive, Weber is nonetheless credited as the father of gravitational wave experiments.

The lead in this direction was then taken by the Italians under the stimulus of Edoardo Amaldi. The idea of starting an experiment aiming to detect GW in Rome was stimulated by the Course on Experimental Tests of Gravitational Theories held in summer 1961 at the Scuola Internazionale E. Fermi in Varenna, where the problem was discussed by J. Weber. The program remained rather vague for practical reasons until 1968, when W. Fairbank spent a few months in Rome at G. Careri’s low temperature laboratory. When Fairbank mentioned his intention of starting the development of a low temperature gravitational antenna, Careri, who was informed for long time of the interest of Edoardo Amaldi in the subject, suggested a first direct contact. A group formed by Edoardo Amaldi, Massimo Cerdonio, Renzo Marconero and Guido Pizzella was created and a long term research project started which eventually resulted in the creation of the sophisticated, ultra-cryogenic, barantennae, nowadays operating in the sites of CERN and of the National Laboratories of Frascati, respectively known as Explorer, Nautilus and Auriga (Fig. 7.1).

The operating concept of bar-antennae is extremely simple. A gravitational wave is a propagating deformation of space-time geometry, which induces a vibrating deformation of macroscopic objects. Orthogonal directions, in the plane transverse to the propagation direction of the wave, are alternatively stretched and compressed. Correspondingly, the bar should be compressed and stretched: if the wave frequency is close to its resonance frequency, the bar will resonate and the resonance can be detected by means of sophisticated electronics. The problem is just that of sensitivity. The space displacements to be measured are of the order of 10−18–10−20 cm.