The existence of Gravitational Waves was proved by A. Einstein in his General Theory of Relativity in 1917. The Theory of Relativity represents events happening in a four-dimension space and describes these waves as "ripples in space-time".

It is well known in Physics that "carrying energy" is the main task of waves (acoustic, electromagnetic, sea waves, and so on), and Gravitational Waves are no exception to this. The generation of Gravitational Waves is due to the collapsing and/or the explosion of celestial bodies having strong gravitational fields. As during such events a change in the gravitational field takes place, Gravitational Waves carrying (gravitational) energy are generated, in order to re-establish the equilibrium conditions. For example, when there is the collapsing of a celestial body, its gravitational energy increases and, consequently, a gravitational wave dragging gravitational energy from the surrounding environment is generated.

It is difficult to interpret what we have just said if, as it happens in today's Physics, in the environment there is the "vacuum" and, therefore, it is "empty-of-gravity" too.

We are trying to explain hereunder how, according to our opinion, Gravitational Waves are generated. It is obvious that it is not possible to understand Gravitational Waves (e.g. dynamic gravity), without understanding first of all what is and how the Gravity (e.g. static gravity) acts.

What is Gravity? Which is the mechanism acting on bodies through the Force of Gravity? As we know, Gravity is something static that it is concentrated around bodies, that is to say around protons and neutrons, exerting an attractive force on the nearby bodies. We also know that the bigger is a body, that is to say with more matter, the higher is its Force of Gravity. Furthermore, we know another important fact today: if the matter of the same body is concentrated into a smaller volume (e.g. collapsed), it results that its Force of Gravity is higher.

Because of this latter fact, Newton's Universal Law of Gravitation is passing through a crisis as, in the well known formula representing it, only the amount of matter (that is, its mass) is represented, while there is no indication of how it is arranged in space.

To "rescue" Newton's Law, Physicians have "invented" the "dark" matter. That is to say, a sort of not well defined substance that, according to the gravitation point of view, behaves like true matter, while according both to the mechanic and electromagnetic point of view, it corresponds to "nothing" or little more. And also, to enable further working of Newton's Law for celestial structures of large size, it is necessary that such a "dark" matter might not concentrated in the centre of these ones, as it should be more predictable, but in peripheral areas! For example, to be able to explain the higher orbital velocity of the outer stars in a galaxy, the "dark" matter might form a sort of halo around the same galaxy.

We have also known, not for a long time, that celestial structures of smaller size than a galaxy, such as the Solar System, might need "dark" matter too. Space-crafts Pioneer 10 and 11 launched in the 70ies, that today are tens AU far (1 AU=distance Sun-Earth), undergo a higher deceleration than as foreseen by Newton's Law. In other words, it is as if these space-crafts, while further going away, were crossing a region rich in "dark" matter!

Today's Physics states that there is no transmission medium for the electric, the magnetic or the gravitational forces, the main forces of Nature, and the Force of Gravity is explained by a mysterious "action-at-a-distance" among the bodies. The explanation given by General Theory of Relativity, in terms of a "curvature of space-time", has not improved this situation.

We do not like of the "dark" matter, as well as the action-at-a-distance. Therefore, we have looked for an explanation of Gravity which had to be not only more satisfactory but, also, more convenient, being willing to give up a formula such as Newton's Law which is, however, aesthetically effective.

In our opinion Gravity and Gravitational Waves, such as many other matters of Physics, can be well understood in agreeing that space is not "empty" but it has its own electric, magnetic and gravitational properties which depend on its density, δ.

Into such a "physical" space, into which all the matter is plunged, take place the electric, magnetic and gravitational energies. The latter one being represented by its state of contraction, such that in one cubic meter it is directly proportional to the mass of space therein contained.

According to its nature, matter produces a thickening of the "physical" space around itself. The more matter there is in a given region, the higher is this thickening, and the same amount of matter concentrated in a smaller volume produces a higher thickening of the space. Therefore, the Force of Gravity can be represented by gradient of density of the "physical" space, but can even guess something more: we can imagine it as a (super)fluid and introduce the gradient of (gravitational) pressure, as we are used to do in Fluid Mechanics where: d p = c2 *d δ, with c being the propagation speed of (gravitational) waves. In this way, we can imagine the Force of Gravity as the Archimede's buoyant force exerted on the bodies by the "physical" space and, simply, states that:

"... a body immersed into a gravitational field (e.g. a region of "physical space" where there is a gradient of density and, therefore, of pressure) experiences a thrust force in the same direction as the gradient itself and in a directly proportional way as said gradient ..."

and, as Archimede's buoyant force F is directly proportional to the volume, V, of "displaced" fluid by the body: F = - V * d p/d r = - V * c2 *d δ/d r. the force of gravity depends on the mass, V * δ, of "physical" space "displaced" by the matter itself and not by the amount of matter the body is made of!

By taking into account the fundamental property of the "physical" space: δ * c3 = constant one obtains: F = V * δ * d c2/d r. Therefore, the difference of the (gravitational) potential between Point 1 and Point 2 becomes: U1 - U2 = 3/2 * ( c12 - c22 ).

After "physical" space density, speed-of-light become the second most important parameters to represent Gravity. The third parameter, that is the characteristic dimension, ξ, of space-particles (e.g. the side lenght of the cube) comes from the Planck constant, h, through the relation: h = 1/4 * δ * c * ξ4. But, that's another story.

A collapsed celestial body, such as a quasar, produces a more intense gravitational field because of its gradient of density is higher than the un-collapsed one having same matter. In this way, super-massive objects are no more needed to get high gravitational fields. For example, a quasar placed in the centre of a giant elliptic galaxy may well have a mass (that is, matter) that can be even a small fraction of its hosting galaxy, provided the former one occupies a very small volume of space. In other words, the quasar would be made of "collapsed" matter namely, a matter that has, no more, any electromagnetic energy. Therefore, to justify the huge gravitational fields that exist around some celestial structures such as, for example, galaxy clusters, not large amount of "dark" matter but small amount "collapsed" (true) matter is required.

After these thoughts about Gravity, we can go back to Gravitational Waves.

What would happen to the Solar System in case of, for any reason, the Sun would start collapsing so that its dimensions reduce to such a value that space density increases by 1,000 times, that is the speed-of-light reduces 10 times? First of all, a (negative) gravitational wave, propagating from the Sun outwards, would be produced which drags the space needed to increase its gravitational field. This wave, propagating from the Sun outwards, would invest planets and other celestial bodies in the area, dragging also them towards the Sun, taking place into orbits by 10 times smaller, in accordance, with their 10 times smaller orbital velocity.

Being on the Earth, what could we perceive? Probably, if the collapsing occurs slowly, very little or nothing.

Namely, as matter plunged into the "physical" space "adapts" to it in varying its dimensions inversely proportional to the cubic root of its density, the Earth too and all what is on it will undergo a contraction similar to the one experienced by the Sun. We also will undergo the same reduction in our dimensions, with our "sample meter" reduced too!

How will our clocks behave? Clocks will go on working as before, as these instruments are not affected by the gravitational field. Therefore, we will not perceive any variation in the orbit period of the planets, whose orbit speed will be reduced too. The same will be experienced by the speedometer on board our cars, which will continue to give us the same indications as before, as the diameter of the wheels will be reduced too!

All other measuring instruments we dispose of, will undergo the same change. For example, in electric circuits, voltages and currents will be reduced but, as voltmeters and amperometers have undergone a similar contraction, they will always continue to measure the same values as before. Our computers as well as power plants will continue to work as before and the effective frequency of the grid will still be 50 Hz! Also the light emitted by the Sun will reduce its wave lenght but as the speed-of-light, too, will go undergo the same reduction, its frequency does not change and we will continue to see things around us having same colours.

What would it happen if after collapsing the Sun would suddenly "disappear", "buried" within the space? The thickened space (that is, its gravitational field!) will never be able to "go away" with it. Due to the fact that the matter of Sun retaining it is suddenly missing, the space will undergo an expansion in order to re-establish the equilibrium with the surrounding space. In other words, a positive (contraction) gravitational wave will be generated, quite like a tsunami, which will disperse the gravitational field "released" by the Sun.

When such a gravitational wave passes through the Solar System, the planets will be driven apart from each other and from the place where there was the Sun. Once the gravitational wave extinguishes and the space all around is back on rest, the planets will not undergo the Sun's force of gravity any more, so that their motion will change dramatically; they will arrange into new orbits depending on the residual gravitational field they produce, starting, therefore, to rotate one around the other, as it happens with the stars of a globular mass, with Jupiter and Saturn trying to set in the centre, because of their higher mass.

The gravitational wave will, therefore, produces an expansion of the Solar System, that is to say a (local) micro-expansion of the Universe. Now, try to imagine how much thickened space take place around a very old quasar living in the centre of a giant elliptic galaxy or inside a cluster of galaxies. If, by chance, one of these super-massive objects collapses and "disappears", the amount of space released would produce a much larger expansion. But, if only few hundreds of these objects are collapsing and "disappearing" every year, here and there in the Universe, the expansion rate would, on a very large scale, be quite continuous and we would see celestial objects going away from us at a rate, more or less, directly proportional to the distance, as represented by the well known Hubble's Law.

With the existence of the "physical" space, therefore, the "dark" energy is no more needed to explain the expansion of the Universe, as this would occur to the expense of the (huge) gravitational energy that quasars accumulate during their long existence.

We want to conclude remarking the important concept stated above: when space density varies, the speed-of-light, varies too at a rate which is directly proportional to the physical dimensions of each body. And, as the length of interferometers vary in the same way, when a gravitational wave arrives, these instruments cannot notice, more or less, anything. Now, you also know why, notwithstanding the enormous efforts made to build bigger and bigger and more and more expensive interferometers, these instruments will never be able to detect Gravitational Waves.


Rome, August, 2006