Number of words: 728

That a time scale characteristic of the universe at large exists was first suggested by the discoveries of Hubble in the early twenties. There are two parts to Hubble’s discoveries. The first part relates to what may be considered as the fundamental units or constituents of the universe. It emerged unequivocally from Hubble’s studies that the fundamental units are the galaxies of which our own Milky Way system is not an untypical one. Galaxies occur in a wide variety of shapes and forms. The majority exhibit extraordinary organization and pattern.

To fix ideas, let me say that a galaxy contains some ten thousand million or more stars; its dimension can be measured in thousands of light years: our own galaxy has a radius of 30,000 light years. Further, the distance between galaxies is about 50 to 100 times their dimensions .

The second part to Hubble’s discovery is that beyond the immediate neighbourhood of our own Milky Way system, the galaxies appear to be receding from us with a velocity increasing linearly with the distance. In other words, all the galaxies appear to be running away from us as though, as Eddington once said, ‘we were the plague spot of the universe. Hubble’s law that galaxies recede from us with a velocity proportional to the distance was deduced from an examination of their spectra.

Now suppose that we take Hubble’s law literally. Then it follows that a galaxy which is twice as far as another will be receding with a velocity twice that of the nearer one. Accordingly, if we could extrapolate backwards, both galaxies would have been on top of us at a past epoch. More generally, we may conclude that if Hubble’s relation is a strict mathematical one, all the galaxies constituting the astronomical universe  schould have been together at a common point at a past calculable epoch. Whether or not we are willing to extrapolate Hubble’s law backward in this literal fashion, it is clear that the past epoch calculated in the manner I have indicated does provide a scale of time in which the universe must have changed substantially. Current analysis of the observations suggests that the scale of time so deduced is about seventy thousand rephrased as follows: Have the laws of Nature been constant over periods million years.

With the time scale established, the questions I stated earlier can be was the universe like seventy thousand million years ago? These questions cannot be answered without some underlying theory. While there are as long as say thirty or forty thousand million years? And, what indeed several competing theories that are presently being considered, I shall base my remarks on the framework provided by Einstein’s general theory of relativity. This theory appears to me the most reasonable.

This is clearly not the occasion to digress at this point and describe the content of the theory of relativity. Suffice it to say that it is a natural generalization of Newton’s theory and a more comprehensive one. On Einstein’s theory, applied to the astronomical universe in the large, it follows, that at each instant the universe can be described by a scale of distance which we may call the radius of the universe. At a given epoch it measures the furthest distance from which a light signal can reach us. This radius varies with the time. Its currently estimated value is ten thousand million light years. But the most important consequence that follows from the theory is that this radius of the universe was zero at a certain calculable past epoch some seventy thousand million years ago. In other words, the conclusion arrived at by a naive extrapolation backwards of Hubble’s law, interpreted literally, is indeed a valid one. That the theory predicts such a singular origin for the universe is surprising but it has been established rigorously, with great generality, by a young English mathematician, Roger Penrose. And hnally, it is an exact consequence of the theory that the ratio of the wavelengths of an identified line in the light of a distant galaxy to the wavelength of the same source as measured here and now, is the   same as the ratio of the radius of the universe now and as it was whe the light was emitted by the galaxy. 

Excerpted from page 80-81of  S. Chandrasekhar ‘Man of Science ’ by A.P.J. Abdul Kalam