A Brief History Of Time

Time was completely separate from and independent of space.

If one carried out experiments with moving bodies on the train, all Newton’s laws would still hold. For instance, playing Ping-Pong on the train, one would find that the ball obeyed Newton’s laws just like a ball on a table by the track. So there is no way to tell whether it is the train or the earth that is moving.

Newton’s law of gravity says that the gravitational attraction of a star is exactly one quarter that of a similar star at half the distance. This law predicts the orbits of the earth, the moon, and the planets with great accuracy.

In such a scheme it is reasonable to suppose that we might progress ever closer toward the laws that govern our universe. Yet if there really is a complete unified theory, it would also presumably determine our actions. And so the theory itself would determine the outcome of our search for it! And why should it determine that we come to the right conclusions from the evidence? Might it not equally well determine that we draw the wrong conclusion.? Or no conclusion at all?

Einstein’s general theory of relativity predicted a slightly different motion from Newton’s theory. The fact that Einstein’s predictions matched what was seen, while Newton’s did not, was one of the crucial confirmations of the new theory. However, we still use Newton’s theory for all practical purposes because the difference between its predictions and those of general relativity is very small in the situations that we normally deal with. (Newton’s theory also has the great advantage that it is much simpler to work with than Einstein’s!)

Any physical theory is always provisional, in the sense that it is only a hypothesis: you can never prove it. No matter how many times the results of experiments agree with some theory, you can never be sure that the next time the result will not contradict the theory. On the other hand, you can disprove a theory by finding even a single observation that disagrees with the predictions of the theory.

I shall take the simpleminded view that a theory is just a model of the universe, or a restricted part of it, and a set of rules that relate quantities in the model to observations that we make. It exists only in our minds and does not have any other reality (whatever that might mean).

difficulty is that in an infinite static universe nearly every line of sight would end on the surface of a star. Thus one would expect that the whole sky would be as bright as the sun, even at night.

if, on the other hand, there were an infinite number of stars, distributed more or less uniformly over infinite space, this would not happen, because there would not be any central point for them to fall to. This argument is an instance of the pitfalls that you can encounter in talking about infinity. In an infinite universe, every point can be regarded as the center, because every point has an infinite number of stars on each side of it.

The story that Newton was inspired by an apple hitting his head is almost certainly apocryphal. All Newton himself ever said was that the idea of gravity came to him as he sat “in a contemplative mood” and “was occasioned by the fall of an apple.”