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The argument about whether or not the universe had a beginning, persisted into the 19th and 20th centuries. It was conducted mainly on the basis of theology and philosophy, with little consideration of observational evidence. The cosmologist, Sir Arthur Eddington, once said, ‘Don’t worry if your theory doesn’t agree with the observations, because they are probably wrong.’ But if your theory disagrees with the Second Law of Thermodynamics, it is in bad trouble. In fact, the theory that the universe has existed forever is in serious difficulty with the Second Law of Thermodynamics. The Second Law, states that disorder always increases with time. In an infinite and everlasting universe, every line of sight would end on the surface of a star. This would mean that the night sky would have been as bright as the surface of the Sun. The only way of avoiding this problem would be if, for some reason, the stars did not shine before a certain time.

In a universe that was essentially static, there would not have been any dynamical reason, why the stars should have suddenly turned on, at some time. The situation was different, however, when it was realised that the universe is not static, but expanding. Galaxies are moving steadily apart from each other. This means that they were closer together in the past. One can plot the separation of two galaxies, as a function of time. If there were no acceleration due to gravity, the graph would be a straight line. It would go down to zero separation, about twenty billion years ago. One would expect gravity, to cause the galaxies to accelerate towards each other. So the time of zero separation, would have been less than twenty billion years ago.

At this time, the Big Bang, all the matter in the universe, would have been on top of itself. The density would have been infinite. It would have been what is called, a singularity. At a singularity, all the laws of physics would have broken down. This means that the state of the universe, after the Big Bang, will not depend on anything that may have happened before, because the deterministic laws that govern the universe will break down in the Big Bang.

Quantum theory can predict how the universe will begin. Quantum theory introduces a new idea, that of imaginary time. Imaginary time may sound like science fiction, and it has been brought into Doctor Who. But nevertheless, it is a genuine scientific concept. One can picture it in the following way. One can think of ordinary, real, time as a horizontal line. On the left, one has the past, and on the right, the future. But there’s another kind of time in the vertical direction. This is called imaginary time, because it is not the kind of time we normally experience. But in a sense, it is just as real, as what we call real time.

The three directions in space, and the one direction of imaginary time, make up what is called a Euclidean space-time. I don’t think anyone can picture a four dimensional curve space. But it is not too difficult to visualise a two dimensional surface, like a saddle, or the surface of a football. It is proposed that space and imaginary time together, are indeed finite in extent, but without boundary. They would be like the surface of the Earth, but with two more dimensions. There wouldn’t be any singularities in the imaginary time direction, at which the laws of physics would break down. The no boundary proposal, predicts that the universe would start at a single point, like the North Pole of the Earth. But this point wouldn’t be a singularity, like the Big Bang. Instead, it would be an ordinary point of space and time, like the North Pole is an ordinary point on the Earth.

Excerpted from CNBC article dated 19 Feb 18, Billionaire Mark Cuban