HOW DID EINSTEIN DO IT?

Everybody knows Einstein's equation E = mc², in which E stands for energy in ergs. The erg is the energy or work done when a force of 1 dyne moves a mass of 1 gram through 1 centimetre, in 1 second. m is the amount of mass in grams and c is the speed of light in centimetres per second. The speed of light is 300 000 kilometres per second. In 1 km there are 100 000 centimetres. Therefore the speed of light in centimetres per second works out to 300 000 00 000 or 3 x 10¹⁰, a truly colossal figure.

But how did Einstein derive the formula? That is the question.

Suppose we have a space shuttle in orbit around the Earth. It is in "free fall" and there are no forces acting inside the shuttle. Suppose we introduce a wooden or metal cylinder (Einstein used a book) having a mass M. Since there are no forces acting inside the shuttle the cylinder will float freely (Fig 1) and it will be at rest with reference to the frame of reference, the shuttle. If we place a flashlight a short distance from the cylinder, on each side of the cylinder, we could send horizontally moving flashes of light to the cylinder. The speed of the horizontal flashes of light will be equal to c, shown by the arrows. Each flash of light could then supply an amount of energy to the cylinder equal to so that the total energy received by received by the cylinder would be _.

Now let us assume that the frame of reference moves down with velocity v (Fig 2).

The cylinder will then seem to be moving upwards with velocity v and its momentum will be equal to Mv. The horizontal flashes of light will then seem to move with an upward slant (angle a), with velocity c because the velocity of light in all directions is the same. Because of the slanting rays the actual velocity will be equal to v ÷ c and the energy received by the cylinder will be namely . This energy gets added to the momentum Mv of the cylinder, which then has an energy of Mv + .

Let this equal M'v

Thus M'v = M V +

Now divide throughout by v.

Therefore M' = M + or M' - M = .

M' -M is the amount of increase of mass of the cylinder due to the light flashes which it has received. Call this m.

Therefore m = or E = m c².

This is the equivalence between mass and energy and it shows that matter and energy are interchangeable -- the one can be converted into the other. This derivation appeared in Einstein's theory of relativity in 1915, long before physicists had unravelled the structure of the atom. The first atomic bomb (July 1945) showed that the amount of energy set free from the matter which was annihilated in the bomb is exactly equal to the result of Einstein's equation. When protons are fused in the nucleus of the Sun into helium atoms only 1/140, or 0,07% of the matter is annihilated. If all the matter could be annihilated 140 times as much energy would be set free. By the conversion of hydrogen into helium the Sun loses 4 million tons of mass per second. It has been doing this for at least 5 milliard years and will be able to go on doing so for another 5 milliard years before any change can be noticed.

Jan Eben van Zyl