Gravity today: Einstein’s special and general theories of relativity

1.11 Gravity today: Einstein’s special and general theories of relativity

In 1905, as mentioned in Section 1.6.6, Albert Einstein published his paper on the Special Theory of Relativity. One consequence of this theory was that nothing could travel through space faster than the speed of light. This extended beyond material things: information and the effects of force fi elds were included too. Einstein realised that this was not compatible with Newton’s Law of Gravitation which implied ‘instantaneous action at a distance’.

I have italicized the word ‘through’. It is possible for the expansion of space to carry objects apart faster than the speed of light – indeed we believe that this happened during a period called ‘infl ation’ close to the origin of the universe. Imagine making a currant bun: currants are packed tightly into the dough which is then placed into an oven. When cooked, one hopes that the dough will have expanded, increasing the separation of the currants. They have not moved through the dough, but have been carried apart by the expansion of the dough.

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Perhaps a thought experiment will help to make the incompatibility of Newton’s theory with special relativity clear. Suppose that the Sun could suddenly cease to exist. Under Newton’s gravity, where the effect of a change in mass would be instantly felt throughout the universe, the Earth would immediately fl y off at a tangent. Einstein realised that this could not be the case. Not only would we not

be aware of the demise of the Sun for 8.31 min – the time that light takes to travel from the Sun to the Earth – but the Earth must continue to feel the gravitational effects of the Sun for just the same time, and would only fl y off at a tangent at the moment we ceased to see the Sun. This assumes, of course, that whatever carries the information about the gravitational fi eld of the Sun will also propagate at the speed of light.

Consequently, something has to propagate through space to carry the information about a change in gravity fi eld. Einstein thus postulated the exis- tence of gravitational waves that carry such information. As we will see in a later chapter, the existence of such gravitational waves has already been shown indirectly and it is likely that, before long, direct evidence of their existence will

be gained. This concept came out of Einstein’s 1915 paper on ‘The General Theory of Relativity’. (Please note: it is not, as is often stated, ‘The Theory of General Relativ- ity’ although in shorthand it is often referred to correctly as ‘General Relativity’.) In essence, this is a relativistic theory of gravity in which gravity is a concept that we infer to explain what we observe. General relativity regards that the motion of objects through space not in a straight line is due, not to a force applied to it as in Newtonian gravity, but is its natural path in space which has been ‘curved’ due to the presence of mass. (To be precise, we should use the term space–time rather than space, but this is an introductory text!)

In Einstein’s view, in the absence of mass, space is fl at. This term (which the author does not like as it implies that space is two-dimensional) actually means that within ‘fl at space’ Euclidean geometry holds true. That is, if one lays out a large triangle in any orientation in space, the inscribed angles will add up to 180°.

A second property of ‘fl at space’ is that two initially parallel laser beams separated by some distance will remain parallel. If, now, mass is introduced into fl at space, the space around it becomes curved and light or matter will follow curved, rather than straight trajectories. An anal- ogy can help. Imagine a stretched horizontal fl at rubber sheet. Ball bearings will roll across it in straight lines. If a lead ball is now laid on the sheet it will cause a depression (Figure 1.20) and, if ball bearings now come close to the depression, they will follow curved lines. In Einstein’s view, the orbital motion of the Earth around the Sun is simply the natural motion of a body through curved space – the force we perceive is actually just a consequence of curved space–time.

Astronomy, an Observational Science

Figure 1.20 A rubber sheet analogy of the distortion of space–time by mass.

Let us consider a further ‘thought experiment’. Imagine that the northern hemisphere of a large planet had a totally frictionless surface. The inhabit- ants have an unshakeable belief that the surface of their planet is flat. Two explorers set off simultaneously on sledges from two points, 10 km apart, on the equator. They travel on parallel paths pointing true north with identical initial velocities. As there is no friction, they will continue at the same speed and would expect to remain 10 km apart. They will thus be somewhat sur- prised (and possibly hurt) when they collide at the North Pole! They might try and explain how this could have happened without giving up their belief that the surface of their planet is flat. The only way that they could do this would be to postulate a force – that they might call gravity – that attracted them towards each other.

In the same way, gravity is a force that we infer to explain what happens in a curved three-dimensional space if we assume that space is fl at, not curved.

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