Mass and energy.

  How could it be that we cannot accelerate something to go faster than light? Surely we could kick a ball again and again and again until it travels faster right? No! and the reason is quite interesting.

As something is moving with respect to another object we say that the moving thing has a certain amount of energy by virtue of its motion. Energy is the ability to do some work, and, indeed, a moving thing can be lassoed and made to do some work, like pulling a car (of course in so doing it looses energy and slows down).

Now, when we have the above object moving, it will have a certain amount of energy. Einstein argued, the only way we can insure that it cannot be accelerated indefinitely, is if there is a universal equivalence between mass and energy. The more energy an object has, the heavier it will be. When we speed it up a little bit it becomes a bit heavier, and so it also becomes a bit harder to speed it up further. In fact, the closer we are to the speed of light, the larger the force is needed to accelerate the object; an infinite force is needed to speed up a material object to the speed of light: it never happens!

But there is more to the equivalence of mass and energy, for it also implies that an object of mass m has energy, just by virtue of its existence; the specific relationship is

E = m c² .

This formula plays a basic role in nuclear reactions (and in atom bombs, for that matter): in these processes an atomic nucleus of initial mass M is transformed (either because the environment is tailored to insure this or because is is unstable and disintegrates spontaneously) into another object of smaller mass m. The difference in mass is released as energy in the amount ( M - m ) c².

To give an idea of how powerful this is, suppose we initially have a sheet of paper weighing 6gr, and that at the end we have something weighing half this amount. The energy released is then so big as to turn on a light bulb of 100W for about 86,000 years, or run a hair-drier for about 4000 years.

The energy released through the transformation of mass is also capable of destroying a whole planet (or at `least' all life on it). Einstein was not aware of this application until much later in his life.

The principle E = m c² was used during the Second World War to develop what is now known as atomic weapons (Fig. 6.16). Shortly thereafter it was used to develop the hydrogen bomb. Atomic bombs were used during the Second World War in two Japanese cities, Hiroshima and Nagasaki. Hundreds of thousands of people died. The creation of nuclear weapons was one of the watersheds of the 20-th century, and it marks one of the most dramatic instances in which physics has affected the social structure of the planet. Yet the very same formulas also suggest the possibility of obtaining vast amounts of energy which can be used for constructive purposes. It is a burden of post-second World War physicists to deal with this issue, and to strive for decent and environmentally safe applications of nuclear power.

 

Figure 6.16: An atomic explosion.