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If the speed changes (as it does when accelerated), the added distance it travels due to the acceleration is equal to the average of the extra speed and the time during which the acceleration has acted. Therefore, the height H of the falling object decreases by an amount equal to the area of the white triangle: one-half times the product of the extra speed v multiplied with the time step t. Because we already had V=gT, this means that an object starting from rest at height zero has fallen to a depth H= −gT2/2 during the time T: the distance fallen increases with the square of the time.

It is quite easy to demonstrate this by means of an idealized ‘Lorentz clock’: two parallel mirrors with a light ray bouncing up and down between them. Every reflection marks a point in space-time (called an event), and an observer may determine the time intervals between successive events. The time between reflections is equal to the distance between the mirrors divided by the speed of light. For example, if the mirrors are 300 metres apart, an observer who is standing next to the clock measures one millionth of a second between events.

Likewise, tides caused by Earth across the Moon lock the rotation of the Moon in such a way that it always points the same side towards Earth. 60 Reflections The main reason why mechanics was a very good candidate for the title ‘Theory of Everything’ is probably that it feels so definitive, not only in its strict and transparent mathematical structure, but also in its workings. If we want to know the future, all we have to do is specify the positions and velocities of all material at some initial time, and then the remainder of eternity can be computed, at least in theory.

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