THE GENERAL THEORY OF RELATIVITY AND GRAVITATIONAL WAVES

Dr. B. Sathyaprakash ,Dept. of Physics and Astronomy, Cardiff University, on 5 December 2003

 

The year 2005 will be the anniversary of Einstein’s paper on Special Relativity.

Newton assumed that gravitational influence was transmitted instantaneously However, the special theory of relativity places a restriction on the speed at which data can transferred from one place to another, namely, ‘c’ the speed of electromagnetic radiation (e.g. light).

The General Theory of Relativity, which was published 10 years later, was based on the analogy between objects acted on by a ‘force’ of gravity (Newton) and objects in a ‘uniformly accelerating frame of reference’ (Einstein). The ‘Principle of Equivalence’ on which the general theory of relativity is based means that an experimenter in a closed room would not be able to tell whether everything was experiencing a ‘force of gravity’ or whether the room was accelerating upwards.

If a beam of light were shone horizontally across the room, it would hit the other wall slightly lower than the position it would strike if the room were not accelerating upwards – thus the light beam would be seen to be curved. A Newtonian physicist would say that light was curved by the gravitational field but an Einsteinian one would put the curvature down to an accelerating frame of reference.

The special theory of relativity (which deals with non-accelerating frames of reference – i.e. rooms in free fall) showed that time and space are inter-related and that there is no absolute time difference nor spatial separation between two events – it all depends on the point of view of the observer. The different points of view of two observers depends on the relative speed between them. The only thing they would agree on is the space-time interval between the events and this is defined by four-co-ordinates: three of space and one of time.

It follows that the mathematics relates to an unimaginable 4-dimensional ‘space time’. The only way we can think about it without mathematics is to discard one of the four dimensions (e.g. height) and visualise a two-dimensional sheet in which the ‘time dimension’ is represented by a hollow in the vicinity of any mass; the greater the mass, the deeper the hollow. Light still follows the shortest ‘4-dimensional distance’ (a geodesic) in this space. However, if the space is curved, the geodesic will appear to us to be curved. To understand this, stretch a piece of string between two places, say London and Delhi, on a globe and note the places it passes over. The string takes the shortest path between the points (the route an aircraft could take). If you plot the course of the aircraft on a flat map, it will appear to be curved though it is the shortest route.

A classical physicist would say that there is a strong gravitational field near to massive objects like the Sun, whereas a relativist would refer to a frame of high acceleration. Both would observe that the mass of the Sun would cause light to curve. General Relativity explains why, classical physics does not; in fact, as photons are massless, according to classical physics they should continue in a straight line. Sir Arthur Eddington made an expedition to Brazil to use the 1919 eclipse to verify relativistic against classical physics. As predicted by the General Theory of Relativity the apparent spacings of the stars near the Hyades were altered by the Sun’s mass.

The planets orbit the Sun in ellipses and the position of the closest point of each to the Sun, the perihelion, is not fixed – it ‘precesses’. The precession calculated using Newton’s mechanics and that observed differs by 43 arcseconds. Einstein did not know of this but the precession calculated using the general theory of relativity was in agreement with observation.

Movement or compression of mass or the transformation of mass into energy causes ripples in the space-time continuum (i.e. gravitational waves) which travel at the speed of light. However, electrostatic forces, which hold atoms and molecules together, are 1040 times as strong as gravitational forces so it takes a very large mass disturbance to produce gravitational waves.

The escape velocity from the Earth is about 6 km/s. However, if the Earth were compressed into a very small sphere this would increase until it was the speed of light – it would then be a black-hole. Compression of stars into neutron stars or black holes take place during supernova explosions so such events should generate gravitational waves.

A binary pulsar consists of two neutron stars in orbit, one of which is a pulsar. The one discovered in 1974, which earned Hulse and Taylor a Nobel Prize in 1992, consists of two neutron stars, each with a mass of 1.4 times that of the Sun and with an orbital period of 7.5 hours. This means that they are moving with a speed 1/1000th that of light and therefore should be emitting gravitational waves. This loss of energy means that they are speeding up and Einstein’s Special Theory predicts that they will take 100 million years to come together and coalesce. This is in agreement with the observation that their orbital period is increasing by 10 microseconds per year. There might be thousands of such coalescences each year (perhaps a few have occurred during this lecture!), each producing gravitational waves.

Now the General Theory of Relativity is entering the realm of observation.

Gravitational Wave Detectors

By an arrangement of mirrors and beam-splitters (which absorb only one millionth of the incident light), a laser beam is made to travel there and back over identical distances in directions perpendicular to each other. The resulting combination of the returning beams will interfere. The expected change in length for a typical astronomical source is likely to be only 10-22, however, so the path lengths must be very great. There are many detectors being built. The speaker is involved with two of these projects - the British-German GEO600 detector in Hanover and collaborating with the two 4km LIGO detectors in the USA. LISA is a space project proposed by NASA and will observe galaxies anywhere in the Universe.

The sources which they hope to detect include: binary neutron stars, binary black-holes, single asymmetrically rotating neutron stars, X-ray binaries and supernovae, the ripping apart of neutron stars as they plummet into black-holes, collisions between black-holes.

Gravitational waves have no horizons. Electromagnetic radiation must have started 300,000 years after the Big Bang because, before recombination, free electrons made space opaque. Gravitational waves are not affected so they will be observed from the Big Bang itself!

  B. Sathyaprakash