GENERAL RELATIVITY

Eben van Zyl

Every motion is relative to reference frames or systems of co-ordinates. In the Special Theory of Relativity, we deal only with displacement of co-ordinate systems in straight lines from the original system. Einstein worded the General Principal of Relativity as follows:

"All bodies of reference are equivalent for the description of natural phenomena, whatever may be their state of motion."

If the motion of a train carriage is changed into non-uniform motion, e.g., by powerful application of the brakes, the occupant of the carriage will also experience a corresponding jerk of push forwards. The Galileian/Newtonian law will not hold for non-uniform motion of the carriage.

According to Newton an apple falls to the ground and the Moon stays in its orbit because they are attracted to the Earth. This action at a distance, through empty space cannot be explained without the intervention of a pervading medium.

A magnet attracts iron because a magnetic field exists around the magnet and this field acts on iron forming a beautiful pattern of iron filings. With the aid of this field, electro-magnetic phenomena can be theoretically represented more satisfactorily than without it, applying particularly to the transmission of electromagnetic waves.

Gravitation must be regarded in an analogous manner. The Earth ( and other bodies ) must produce a field which gets weaker inversely proportionally to the square of the distance. All bodies are subject to this field, not only iron.

A body moving in a gravitational field experiences acceleration or retardation according to its direction of motion. So too Einstein postulated, that light is propagated curvilinearly in a gravitational field. He calculated from his theory by how much light would be deflected by the Sun, for example. the first opportunity to test this was the total eclipse of 29 May 1919. Photographs showed that stars in the same general direction as the Sun seemed to be deflected outwards from the Sun. This could only happen because the rays of light from the stars were bent by the Sun's strong gravitational field. The average amounts of the deflections of seven stars were:

Not only would light be deflected by the Sun, but the light from distant bodies, lying exactly on the line of sight of massive bodies between them and the Earth, would undergo bending, the massive body acting as a gravitational lens.

The massive body M, a galaxy or group of galaxies, not necessarily visible, situated at a distance of 4 milliard light years, forms two images Q1 and Q2 of the Quasar Q. Einstein also showed that the image of the distant object could be deformed into a ring. Such an Einstein ring has been observed in the case of the Quasar MG 1131 +04 56 in the constellation Leo, as well as in other cases.

The General Theory of Relativity compels us to adopt new ideas about the space-time continuium, which cannot be Euclidean, but is curved in three dimensions and has time as the fourth dimension.

Einstein made use of Gaussian co-ordinates - a system of arbitrary curves. Neither the u-curves, nor the v-curves ever intersect each other. ( vide iron filings around a magnet ).

From this Einstein stated the Principle of Relativity as follows:

"All Gaussian co-ordinate systems are essentially equivalent for the formation of the general laws of nature".

Moving clocks and measuring rods must therefore be affected by a gravitational field, which, together with matter, must satisfy the law of conservation of energy and impulse; energy and matter, being the two fundamental concepts of nature. That matter and energy are equivalent, were shown by Einstein when he derived the equation E = mc² , in which E is the energy in ergs, m the inertial mass in grams and c is the speed of light in centimetres per second. If 4 grams of solar, or stellar, matter are therefore converted into energy, the amount of energy liberated will be 2573 x 10¹⁶ ergs. This is enough energy to completely vaporise, in one second, a dam of ice-cold water 35 metres in diameter and 1 metre deep. ( 0.7% of 4 grams is converted ).

The energy released by the first atomic bomb corresponded exactly to the amount calculated from Einstein's formula.

Hans Bethe and Carl von Weizsäcker proposed in 1938 ( before the first atomic bomb was exploded in 1945 ), that the Sun's energy is derived from the transmutation of hydrogen into helium according to Einstein's formula.

According to Newtonian mechanics, the elliptical orbits of planets maintain their orientations relative to the fixed stars. But the stars are not fixed; nothing is at rest. Therefore Einstein calculated that the planetary orbits must rotate forwards. The amounts are immeasurably small, except in the case of Mercury, where the observed amount of 43'' per century corresponds exactly to the amount Einstein calculated. This was hailed as the first proof of General Relativity.

Einstein also showed that the general theory of relativity demands that the spectral lines of stars must undergo a small amount of redshift on account of the effects of the star's strong gravitational fields which lengthen the wavelengths of the emitted light. When the gravity gets concentrated enough, the gravitational field can get so strong that the escape velocity reaches the velocity of light. In this case, no radiation can escape from the centre of gravity, thus forming a GRAVITATIONAL VORTEX, commonly known as a Black Hole.

Karl Schwarzchild calculated that the radius of the EVENT HORISON in the case of a body of mass equal to the Sun would be only 2 kilometres.

Einstein/Weyl/Lorentz: The Principle of Relativity Einstein: The Theory of Relativity Gibilisco: Understanding Einstein's Theories of Relativity. P G W Davies: Space and Time in the modern Universe A Eddington: The Nature of the Physical World.