Dear Member,

I enclose a copy of the Society’s lecture programme for the 2005/2006 session. The first lecture takes place on Thursday the 22nd September and will be on The Cassini Huygens Mission by Nick Achilleos of Imperial College.

Council for 2005/6

Membership of Council for this year is:
President - Professor Robert Weale
Secretary – Julie Atkinson
Treasurer – Peter Wallis
Membership Secretary – Elisabeth Fischer
Programme Secretary – Jim Brightwell
Ordinary members – Simon Lang, Eric Morgan, John Oakes, Michael Sabel, Betty Weale.

Doug Daniels

Gravity or Gravitation is probably the most fundamental force in nature. It is the mutual attractive force exhibited by all material bodies. Gravity is the force which keeps the planets orbiting the sun, the force that anchors us to the surface of the earth, the force that holds galaxies together and it is the force that causes massive stars to collapse into ‘Black Holes’ from which nothing, not even light can escape. Gravity is all pervasive in the Universe and it is a force that we still do not entirely understand.

In the early 17th century it was established that the planets of our Solar System orbited the sun, and Kepler formulated his famous laws of planetary motion between 1609 and 1619 to describe their motions, but the forces responsible for these motions were not at all understood. Galileo had an inkling of an idea when he dropped unequal weights from the leaning tower of Pisa, observing that they hit the ground simultaneously, and he also conducted experiments with inclined planes, but it was Isaac Newton who formulated the basic laws of gravitation in 1687.

Everyone is familiar with the story (probably untrue), of how Newton observed an apple falling from a tree and experienced a ‘eureka moment.’ Newton’s work, however inspired, established the basic law of gravitation, which states that: “The force of attraction between two bodies is equal to the product of their masses and is inversely proportional to the square of the distance between them” This is expressed mathematically as:

F=Gm₁m₂/d²

G, the constant of proportionality, is the Gravitational Constant, often called Big G. Newton demonstrated that the gravitational force acts from the centre of mass and on a line joining the centres of the two bodies concerned. The gravitational constant can also be defined as: ‘The force of attraction between two bodies of unit mass separated by unit distance.’ It has been calculated to be equal to:

6.672 x 10^-11 N m² kg^-2

But there is still some uncertainty about this value and we still do not have a precise value for ‘Big G’. The Brans-Dicke theory of gravitation predicts that the value of G will decrease with time by about one part in 1010 but so far this has not been substantiated.

Had Newton actually observed an apple falling from a tree, and I am sure he must have done so at some time, he might well have pondered that it took the entire mass of the earth to dislodge it. This suggests that the forces holding the apple on the tree are orders of magnitude greater than the force of gravity which was pulling it off! In fact, gravity is the weakest force in nature, far weaker than the Strong, Electromagnetic and Weak nuclear forces acting within the cells of the stem. These forces, however, operate over very small distances whereas gravity operates over incredibly vast distances. But you might well dispute the weakness of gravity if you climb a tree to pick an apple and accidentally fall out of it!

Newton’s laws of gravitation hold for most circumstances but they were to be challenged by Einstein’s General Theory of Relativity published in 1915, following on from his Special Theory of Relativity proposed in 1905. General Relativity Theory described the way in which very strong gravitational fields could alter the ‘geometry of spacetime’. It described how massive bodies can literally warp or curve space and time surrounding them. In Einstein’s own words: “Matter tells Spacetime how to curve and Spacetime tells matter how to move.”

Einstein showed that in contrast to electric and magnetic fields, gravitational fields exhibit an important and fundamentally different property. Objects moving solely under the influence of a gravitational field “receive an acceleration which does not in the least depend either on the material or physical state of the body”. It is for this reason that a lump of lead and a feather would fall at the exact same rate in a vacuum. It is this property that Galileo tried to demonstrate at Pisa and Neil Armstrong did demonstrate on the surface of the moon. Einstein went on to state that : “The same quality of a body manifests itself according to circumstances as ‘inertia’ or as ‘weight so the Gravitational mass of a body is equal to its Inertial mass.” This is the famous principle of Equivalence, one of the foundation stones of GR Theory.

According to General Relativity (GR), bodies in motion follow the shortest path, a straight line referred to as a Geodesic. But the geometry required to describe motions in four dimensional spacetime is complex and the familiar Euclidean geometry has to be abandoned in favour of a system using Gaussian co-ordinates which can be applied to a continuum of four or more dimensions where straight lines become deformed by the curvature of space. General Relativity may therefore be regarded as: a theory of gravitation which deviates from the Newtonian version only where gravitational fields are very intense.

The test of a good theory is in the experimental confirmation of the predictions which it makes. One of the first tests of curved Spacetime concerned the motions of orbiting bodies in a strong gravitational field. This was first demonstrated by accurate measurements of the advancing perihelion of Mercury, measured at about 43 seconds of arc/century, almost exactly the figure derived from GR theory.

The fact that strong gravitational fields can bend light was first demonstrated during the total eclipse of the sun in 1919. The positions of stars close to the sun’s limb were measured and shown to have been deflected by the sun’s gravitational field almost precisely as Einstein had predicted. (For a ray of light passing the sun at a distance n sun-radii from its centre, the angle of deflection A should amount to: A = 1.7 arc secs/n ) Half of this deflection is produced by the Newtonian field of attraction by the sun and the other half by the ‘curvature of space’ caused by the sun.

Today, of course we can observe many instances of the effect of strong gravitational fields deflecting light in deep space. The phenomenon known as ‘gravitational lensing’ occurs when very strong gravitational fields, surrounding distant clusters of galaxies for example, bend the light from more distant objects to a focus, acting in the manner of a lens.

Another prediction from relativity theory concerns the effects of strong gravitational fields on the radiations from massive bodies such as stars, causing red shifting of the spectral lines.

In attempting to escape the star’s gravitational field, the radiations loose energy. The frequency therefore decreases and the wavelength is increased. This is the so called ‘Einstein Shift’ expressed mathematically as:

dK/K = Gm/c²r

Einstein’s general theory of Relativity also predicted gravitational waves, ripples in spacetime which travel at the speed of light. The waves should be produced by cataclysmal events such as stars exploding as supernovae, merging galaxies or massive binary stars and should affect all matter, but they are very weak waves and consequently very difficult to detect. So far our best evidence for the existence of gravitational waves is indirect and is derived from the observations of a binary pulsar. Delicate observations show that its orbital period is decreasing with time by about 75 microseconds per year. This value is exactly that predicted by (GR) as a result of the emission of gravitational waves. However, this is just one observation and so far all other methods of detecting gravitational waves have failed to confirm their existence.

The theory of General Relativity also predicted the existence of ‘Singularities’ or ‘Black Holes’ - regions with intense gravitational fields, so intense that even light is unable to escape. Although we have no direct evidence of the existence of Black Holes, there are now numerous contenders for the title and their existence is now more or less generally accepted.

Although we cannot say that Relativity Theory has been definitely proven, it has so far stood up well to all the tests applied to it and at present it’s the best theory of gravitation that we have to work with.

Gravity is a property of matter, but what actually is it about matter that endows it with the power to attract? Matter is composed of atoms and atoms are built from fundamental particles. Einstein’s general theory of relativity (GR) predicts the existence of gravitational waves but we appear to live in a quantum universe, a universe constructed from and dependant upon the interactions of fundamental particles and ruled by the laws of Quantum Mechanics. So is there a fundamental particle responsible for that property of matter known as gravity? And how is gravity propagated and does it travel at the speed of light? Recent experiments suggest that it does.

Light sometimes behaves as if propagated by waves, and at other times by particles - Photons. Does gravity have a quantum equivalent of the photon? Some scientists have suggested that it does - the Graviton. The Graviton has been predicted as having zero charge, zero rest mass and a spin of 2 but as yet this particle is purely hypothetical - it has not so far been detected.

Einstein spent the latter part of his life attempting to unify his theory of General Relativity and gravitation with the laws describing electromagnetism and failed. His efforts were not helped by the fact that he found the whole concept of Quantum Mechanics and its reliance on chance and probability, abhorrent. It proved to be totally at variance with his deep rooted religious beliefs, exemplified by his famous retort to Neils Bohr: “God does not play dice!” The work continues and scientists are still struggling to incorporate a quantum theory for gravity into a single ‘Grand Unified Theory’ (G.U.T.) - the so called T.O.E - Theory Of Everything, so far without much success.

Now, of course, we have a ‘new’ force to contend with - Dark Energy. Certain observations have indicated that the expansion of the Universe is accelerating with time, which is counter intuitive to our understanding of the basic theories of Relativity and gravitation. Dark Energy appears to be a repulsive force, a force acting against gravity. It is interesting to reflect that Einstein, who was also unhappy about the whole idea of an expanding universe, incorporated a constant into his field equations to hold the Universe static. His ‘Cosmological Constant’ - a force acting against gravity, was according to him, ‘his biggest blunder’. Dark Energy, on the other hand is a force acting against gravity that is accelerating the expansion of the Universe. Understanding this force and its interaction with gravitation is going to take a little more than the contemplation of a falling apple!

Over 300 years have passed since Newton laid the foundations for our understanding of the universal force of gravity and a century has now passed since Einstein first proposed his Special Theory of Relativity but we still lack any significant understanding of the weak force that holds the Universe together and even less concerning the ‘new’ force- Dark Energy, that may one day rip it apart!

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