Space and Time

The concepts of space and time are so basic for the description of natural phenomena that their modification entails a modification of the whole framework that we use to describe nature.

The most important consequence of this modification is the realization that mass is nothing but a form of energy.

Even an object at rest has energy stored in its mass, and the relation between the two is given by the famous equation E= mc2, c being the speed of light.

This constant c, the speed of light, is of fundamental importance for the theory of relativity. Whenever we describe physical phenomena involving velocities which approach the speed of light, our description has to take relativity theory into account. This applies in particular to electromagnetic phenomena, of which light is just one example and which led Einstein to the formulation of his theory.

In 1915, Einstein proposed his general theory of relativity in which the framework of the special theory is extended to include gravity, i.e. the mutual attraction of all massive bodies.

Whereas the special theory has been confirmed by innumerable experiments, the general theory has not yet been confirmed conclusively. However, it is so far the most accepted, consistent and elegant theory of gravity and is widely used in astrophysics and cosmology for the description of the universe at large.

The force of gravity, according to Einstein’s theory, has the effect of ‘curving’ space and time. This means that ordinary Euclidean geometry is no longer valid in such a curved space, just as the two-dimensional geometry of a plane cannot be applied on the surface of a sphere. On a plane, we can draw, for example, a square by marking off one metre on a straight line, making a right angle and marking off another metre, then making another right angle and marking off another metre, and finally making a third right angle and marking off one metre again, after which we are back at the starting point and the square is completed. On a sphere, however, this procedure does not work because the rules of Euclidean geometry do not hold on curved surfaces. In the same way, we can define a

three-dimensional curved space to be one in which Euclidean geometry is no longer valid. Einstein’s theory, now, says that three-dimensional space is actually curved, and that the curva- ture is caused by the gravitational field of massive bodies

Wherever there is a massive object, e.g. a star or a planet, the space around it is curved and the degree of curvature depends on the mass of the object. And as space can never be separated from time in relativity theory, time as well is affected by the presence of matter, flowing at different rates in different parts of the universe. Einstein’s general theory of relativity thus completely abolishes the concepts of absolute space and time. Not only are all measurements involving space and time relative; the whole structure of space-time depends on the distribution of matter in the universe, and the concept of ‘empty space’ loses its meaning. The mechanistic world view of classical physics was based on the notion of solid bodies moving in empty space. This notion is still valid in the region that has been called the ‘zone of middle dimensions’, that is, in the realm of our daily experience where classical physics continues to be a useful theory. Both concepts-that of empty space and that of solid material bodies-are deeply ingrained in our habits of thought, so it is extremely difficult for us to imagine a physical reality where they do not apply. And yet, this is precisely what modern physics forces us to do when we go beyond the middle dimen- sions. ‘Empty space’ has lost its meaning in astrophysics and cosmology, the sciences of the universe at large, and the concept of solid objects was shattered by atomic physics, the science of the infinitely small.

At the turn of the century, several phenomena connected with the structure of atoms and inexplicable in terms of classical physics were discovered. The first indication that atoms had some structure came from the discovery of X-rays; a new radiation which rapidly found its now well known application in medicine.

X-rays, however, are not the only radiation emitted by atoms. Soon after their discovery, other kinds of radiation were discovered which are emitted by the atoms of so-called radioactive substances. The phenomenon of radioactivity gave definite proof of the composite nature of atoms, showing that the atoms of radioactive substances not only emit various types of radiation, but also transform themselves into atoms of completely different substances.

Besides being objects of intense study, these phenomena were also used, in most ingenious ways, as new tools to probe deeper into matter than had ever been possible before. Thus Max von Laue used X-rays to study the arrangements of atoms in crystals, and Ernest Rutherford realized that the so-called alpha particles emanating from radioactive substances were high-speed projectiles of subatomic size which could be used to explore the interior of the atom. They could be fired at atoms, and from the way they were deflected one could draw conclusions about the atoms’ structure.

When Rutherford bombarded atoms with these alpha particles, he obtained sensational and totally unexpected results. Far from being the hard and solid particles they were believed to be since antiquity, the atoms turned out to consist of vast regions of space in which extremely small particles-the electrons-moved around the nucleus, bound to it by electric forces. It is not easy to get a feeling for the order of magnitude of atoms, so far is it removed from our macroscopic scale.

The diameter of an atom is about one hundred millionth of a centimetre. In order to visualize this diminutive size, imagine an orange blown up to the size of the Earth. The atoms of the orange will then have the size of cherries. Myriads of cherries, tightly packed into a globe of the size of the Earth-that’s a magnified picture of the atoms in an orange.

An atom, therefore, is extremely small compared to macroscopic objects, but it is huge compared to the nucleus in its centre. In our picture of cherry-sized atoms, the nucleus of an atom will be so small that we will not be able to see it. If we blew up the atom to the size of a football, or even to room size, the nucleus would still be too small to be seen by the naked eye.

To see the nucleus, we would have to blow up the atom to the size of the biggest dome in the world, the dome of St Peter’s Cathedral in Rome. In an atom of that size, the nucleus would have the size of a grain of salt! A grain of salt in the middle of the dome of St Peter’s, and specks of dust whirling around it in the vast space of the dome-this is how we can picture the nucleus and electrons of an atom.