Big Bang. Simon Singh

are two-dimensional representations of four-dimensional spacetime, ignoring time and one space dimension. Diagram (a) shows a flat, smooth, undisturbed grid, representing empty space. If a planet were to pass through this space, then it would follow a straight line.

      Diagram (b) shows space warped by an object such as the Sun. The depth of the depression depends on the mass of the Sun.

      Diagram (c) shows a planet orbiting the depression caused by the Sun. The planet causes its own little depression in space, but it is too small to be represented in this diagram because the planet is relatively light.

      In practice, any attempt to model a complicated system on a trampoline soon breaks down, because the friction of the trampoline fabric disturbs the natural movement of the objects. Nevertheless, Einstein was arguing that exactly these sorts of trampoline effects were really happening in the fabric of spacetime. According to Einstein, whenever physicists and astronomers witnessed phenomena involving the force of gravitational attraction, they were actually seeing objects reacting to the curvature of spacetime. For example, Newton would have said that an apple fell to Earth because there was a mutual force of gravitational attraction, but Einstein now felt that he had a deeper understanding of what was driving this attraction: the apple fell to Earth because it was falling into the deep hollow in spacetime caused by the mass of the Earth.

      The presence of objects in spacetime gives rise to a two-way relationship. The shape of spacetime influences the motion of objects, and at the same time those very objects determine the shape of spacetime. In other words, the dimples in spacetime that guide the Sun and the planets are caused by those selfsame Sun and planets. John Wheeler, one of the leading general relativists of the twentieth century, summed up the theory with the dictum ‘Matter tells space how to bend; space tells matter how to move.’ Although Wheeler sacrificed accuracy for snappiness (‘space’ should have been ‘spacetime’), this is still a neat summary of Einstein’s theory.

      This notion of flexible spacetime may sound crazy, but Einstein was convinced that it was right. According to his own set of aesthetic criteria, the link between flexible spacetime and gravity had to be true, or as Einstein put it: ‘When I am judging a theory, I ask myself whether, if I were God, I would have arranged the world in such a way.’ However, if Einstein was to convince the rest of the world that he was right, he had to develop a formula that encapsulated his theory. His greatest challenge was to transform the rather vague notion of spacetime and gravity described above into a formal theory of general relativity, set in a rigorous mathematical framework.