Inertial observers are those who are not accelerating or rotating relative to an imaginary cosmic background stage of space defined by the most distant stars.24These observers therefore violate the Copernican imperative. They see a Universe whose laws are especially simple. To see why this is so, imagine that you are located inside a spaceship out of whose windows you can observe the unchanging distant stars. Now suppose that the rocket boosters are fired so as to make the spaceship rotate. If you look out of the windows you will see the stars rotating (in the opposite sense) across the expanse of space. These stars will therefore appear to be accelerating25 even though they are not being acted upon by any forces. Newton's law will not be seen to hold for this rotating, non-inertial, observer. By working a little harder the rotating observer can find the law that governs what he sees from his rotating vantage point but it is more complicated than the law seen by inertial observers. This undemocratic situation, that allowed some observers to see simpler laws of Nature than others, struck Einstein as a clear sign that there was something imperfect about the way Newton chose to express his laws of Nature. They could not be truly universal laws of Nature if they only held for special observers.

Einstein enunciated what he called the Principle of Covariance: that laws of Nature should be expressed in a form that will look the same for all observers, no matter where they are located and no matter how they are moving. When it came to implementing this Principle Einstein was very fortunate. During the latter part of the nineteenth century, pure mathematicians in Germany and Italy had been extremely busy developing a detailed understanding of all the possible geometries that could exist on curved surfaces. In doing that they had developed a mathematical language which automatically had the property that every equation possessed a form that remained the same if the coordinates describing it were changed in any way at all. This language was called the tensor calculus. Such changes of co-ordinates amount to asking what type of equation would be seen by someone moving in a different way. One of Einstein's oldest friends was a mathematician called Marcel Grossman who was well informed about all these new mathematical developments. He showed Einstein this new mathematics of tensors and gradually Einstein realised that it was exactly what he needed to give a precise expression to his Principle of Covariance. So long as he expressed his laws of Nature as tensor equations they would automatically possess the same form for all observers.

This step by Einstein completes a dramatic movement in the physicist's conception of Nature that has been completed in the twentieth century. It is marked by a steady march away from there being any preferred view of the world, whether it be a human view, an Earth-based view, or a view based upon human standards. It has been brought about in stages. First, the Copernican revolution in astronomy gave rise to the view that our position in the Universe and the vantage point that we occupy in space and time is not specially privileged. Next, we have seen the creation of units of measurement and constants of Nature which are not reflections of human dimensions or the local astronomical motions of the Earth and the Sun. Instead, they are founded upon universal constants of Nature that transcend the human dimension. Last, we have seen how Einstein recognised that the laws of Nature themselves must be formulated in a way that ensures that any observer in the Universe, no matter where they are or how they are moving, should find the same laws to hold.

These steps have depersonalised physics and astronomy in the sense that they attempt to classify and understand the things in the Universe with reference only to principles that hold for any observer anywhere. If we have identified those constants and laws correctly then they provide us with the only basis we know upon which to begin a dialogue with extraterrestrial intelligences other than ourselves. They are the ultimate shared experience for everyone who inhabits our Universe.

chapter four
Further, Deeper,
Fewer: The Quest
for a Theory of
Everything

‘Physicists are trained to investigate a problem before arriving at a decision. Lawyers, advertisers and others are trained to do exactly the opposite: to seek data to confirm a determination that has already been made.’

Robert Crease1

NUMBERS YOU CAN COUNT ON

‘An equation for me has no meaning unless it expresses a thought of God.’

Srinivasa Ramanujan2

Long ago, it became increasingly evident to our ancestors that Nature displayed both predictable and unpredictable events. The unpredictable aspects of things were dangerous and fearful. Perhaps they were punishments rained down by the gods to show their displeasure at human behaviour. They were also remarkable; as a result, ancient chronicles have a lot to say about plague, disaster and pestilence.