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• OPTICAL REFERENCE GEOMETRY FOR STATIONARY AND AXIALLY SYMMETRIC SPACETIMES M.A. Abramowicz, P. Nurowski, N. Wex, Class.Quantum.Grav., 12, 1467-1472 (1995)

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Gravity power in the Universe

Despite the profound progress in describing the gravity phenomenon that was achieved early in our century by Albert Einstein, several important aspects of gravity's nature remain not sufficiently understood. We still do not know how gravity operates on the level of elementary particles and we do not quite understand the origin of inertia. This does not mean, as some use to say, that gravity is a mystery. Quite the contrary - a great many of very specific conclusions deduced from Einstein's general theory of relativity and directly relevant for planets, stars and galaxies have been observationally confirmed with an impressive accuracy. Numerous difficult tests that Einstein's theory has brilliantly passed made us firmly convinced that Einstein was fundamentally right.

Studies of effects of gravity have always been enjoying a very distinguished status in astronomy. Indeed, one may say that modern astronomy was created three hundred years ago by Isaak Newton as an application of his law of universal gravitation. Newton explained the motions of heavenly bodies by universal gravity, and by doing this he introduced gravity to the centre of astronomers' work. Gravity is very much the central issue also for the present generation of astrophysicists who have been using high-tech spacecraft to reveal some most amazing aspects of very strong gravity. Thus, we have learnt about quasars - huge black holes which release gravitational energy of matter thousand times more efficiently than in the nuclear explosions; pulsars - stars smashed by the extreme strength of the gravitational field into balls measuring twenty kilometers across; and gamma ray bursts - gravitationally driven explosions which are so powerful that they are seen from vast distances halfway throughout the whole Universe. The extreme conditions of compactness, speed, temperature, and strength that are found in these objects, cannot be dreamt of even in the most technologically advanced experiments on Earth.

Strong gravity that plays the dominant role in these spectacular phenomena is described by the Einstein general theory of relativity. According to Einstein, gravity is an effect of the curvature of spacetime, and the curvature is caused by the presence of matter. For astrophysicists today the concept of the strong spacetime curvature near black holes and pulsars is not anymore strange or confusing. Rather, it is familiar and natural. However, very often effects of the curvature are extremely difficult to calculate and for this reason supercomputer simulations of the strong gravity has became a rapidly growing research area. The other fascinating intellectual challenges are connected with understanding how in pulsars' interiors the strong gravity cooperates with the laws governing elementary particles, and with studying the very complex, indeed chaotic, behaviour of turbulence, viscosity and heat transport in the super-hot matter close to black holes.

Inertial forces, origin of inertia, quantum gravity

According to the famous First Law which provides the very foundation for Newton's dynamics, bodies that are subjected to no action of applied forces do rest or move with a constant speed in a fixed direction. This means that all bodies have a truly remarkable property - a natural resistance to changes in speed or direction. Newton called this property the {\it inertia of matter}. You will most probably be very surprised to know that still today no physicist can honestly say what the reason for the origin of matter's inertia is.

Indeed, the problem of the origin of inertia has been at the centre of an acute controversy for more than three centuries. It arises from a seemingly simple and innocent question. The First Law speaks about the constant speed and the fixed direction. One may ask: constant speed, but with respect to what, fixed direction, but with respect to what? Indeed, both speed and direction are always related to something. When travelling through a dense motionless fog on a plane that moves at a constant speed and in a fixed direction with respect to the Earth, the passangers inside the plane have no way to distinguish between real and apparent motion. They cannot know whether they are hoovering in the motionless fog, being motionless themselves, or whether perhaps they are speeding at a thrilling 900 km/hour. If the plane, however, changes speed or turns, the passangers are immediately alert of these changes. They feel forces: a push in the back when the plane accelerates, and a push to the left when the plane banks making a turn to the right. The passangers may see this as a beautiful confirmation of the First Law: `` Obviously, - say the passangers - the forces applied by the engines of the plane do change the plane's direction and speed with respect to the Earth. If not for the fog, we it would be able to measure directly the changes of speed and direction with respect to the Earth and confirm the First Law with great precision.'' Suppose that already a long time ago, and unknowingly to the passangers, their plane had been moved far away from the Earth and it is now travelling between stars somewhere in the Galaxy. There is still a dense fog around, but there is no Earth nearby to help define directions. When the plane accelerates or turns, the passangers still feel exactly the same forces as they felt previously, being close to the Earth. How could they explain that? ``Oh, well - they would probably say - the Earth does not matter, the plane changes the speed and direction with respect to the stars in the Galaxy. This is why we feel the inertial forces. If not the fog which prevents us from seeing the stars, we could use the stars as reference points and measure the changes of speed and direction. The measurements would surely agree with the First Law. By the way, if you say now that the plane is already outside the Galaxy and it is travelling through this damn fog in the intergalactic space, speed and direction may be related to the distant galaxies. We feel the inertial forces because the plane accelerates with respect to these distant galaxies. The First Law still holds.'' And now comes the point. Suppose that there are no distant galaxies, that the Universe the passangers could see outside their plane cointains nothing but fog that in all circumstances, always and everywhere, looks the same, and thus cannot be used as reference. In such an empty Universe, there is no way to measure (or for that matter define) speed and direction. Would the passangers still feel inertial forces when the engines of the plane are on?

Newton's answer to this question was - yes, they will. Probably most of the physicists today think that the answer should however be - no, they will not. For Newton, inertia of matter was related to space itself. In his view, it was not neccessary to relate motion to some specific bodies really existing somewhere in the Universe, because the motion could always be related to some properties of space, to the very fabric of the vacuum. In the modern view, the inertia of a particular body is due to a kind of gravitational interaction of the body in question with all other bodies in the whole Universe. This view is called the Mach Principle and was brilliatly advocated by the Austrian philosopher Ernst Mach, who worked at the beginning of the century in Vienna. Early in his development of the general theory of relativity, Albert Einstein was deeply influenced by Mach's ideas.

The observed Universe is very uniform and contains a very large number of bodies. According to the Mach principle, their enormously big mass should dominate the properties of inertia - influence of the nearby bodies should be negligible in comparison. Let us take just one example of how the Mach Priciple works. From observations we know that properties of the very distant Universe do not depend on the direction. In particular, we see the same number of the most distant galaxies in whatever direction we look at. This explains why the properties of inertia also do not depend on direction. In particular, this explains why the same force is needed to accelerate an electron to the same final velocity in whatever direction we try.

The Mach principle also has a strong predictive power, which indeed appealed to many physicists including Einstein. If centrifugal force, for example, is due to the rotation of the body with respect to the whole Universe, we should observe the centrifugal force also when the whole Universe rotates around the body - as far as the relative motion is concerned, these two situations are identical. We cannot, of course, change the rotation of the whole Universe, but we may try to measure the centrifugal force induced by the rotation of a large, nearby mass. According to the Mach Principle the induced force must be minute, very small indeed, but non-zero. Einstein's general theory of relativity, predicts the existence of this Machian (some say Machismo, or even Machissmo) effect and allows us to calculate its exact magnitude, but the effect has not yet been measured in a direct experiment.

The very strong gravity of the black hole matches the influence of the distant matter. Thus, some of the Machian effects should be strong close to the black holes. The most spectacular example that was found recently through calculations based on Einstein's theory, is that the centrifugal force points, for bodies circling close enough to the black hole, to the centre of their circular motion.

I am deeply convinced that both Newton's and Mach's ideas are fundamentally right. In my opinion, when somebody contrasts these ideas, a rather important point is missed. Newton's critics claim that there should be no inertia in an empty Universe, but what does this exactly mean? How anything could be measured in an empty Universe? Surely, one needs at least light to see the results of the measurements! However, if light was there, the problem changes: one can use the optical reference geometry - indeed the light trajectories in space - to define speed and direction. Locally, the light trajectories in vacuum are probably determined by quantum processes, independent from the classical gravity. In this way, some kind of the fabric of the Absolute Space forseen by Newton, may be locally determined by the quantum structure of the vacuum. Then the Mach Principle changes its relevance: it becomes interesting in the context of the Quantum Gravity and may be stated as the question: why the local fabric of space given by the quantum structure of the vacuum agrees with the distribution of the most distant galaxies? That is the question...