The quantum nature of reality may enter in unexpected places.

The legitimacy of this little thought experiment is closely linked to Einstein's deep questions. If the laws of Nature allow one and only one set of the values for the constants of Nature then the freedom we appear to have to consider worlds in which they are different is merely a consequence of our relative ignorance. We think there is freedom to change their values without constraint only because we do not understand the extent to which those values are hardwired into the forms of the laws themselves. On the other hand, if the constants are not uniquely fixed by the one and only possible form for the laws of Nature then there may exist other worlds where they take different values.

The last important lesson we learn from the way that pure numbers like α define the world is what it really means for worlds to be different. The pure number that we call the fine structure constant and denote by α is a combination of the electron charge, e, the speed of light, c and Planck's constant, h. At first we might be tempted to think that a world in which the speed of light was slower would be a different world. But this would be a mistake. If c, h and e were all changed so that the values they have in metric (or any other) units were different when we looked them up in our tables of physical constants, but the value of α remained the same, this new world would be observationally indistinguishable from our world. The only thing that counts in the definition of the world are the values of the dimensionless constants of Nature. If all masses are doubled in value you cannot tell because all the pure numbers defined by the ratios of any pair of masses are unchanged.

THE SUPER-COPERNICAN PRINCIPLE

‘A physicist is a mathematician with a feeling for reality.’

Norman Packard23

The name of the great Polish astronomer, Nicolaus Copernicus, is linked forever with the move to relinquish the presumption that the Earth is at the centre of things. For Copernicus himself it was the assumption, held for thousands of years, that the Earth was at the centre of the solar system that was the focus of attention. Copernicus constructed a picture of the motions of the planets around the Sun in which the Earth was no longer central. In time this heliocentric model proved the superior description of what was seen by astronomers, surpassing the explanatory power of the ancient Earth-centred picture of Ptolemy and his successors.

The impact over the following centuries of Copernicus' leap away from the prejudices of anthropocentrism was felt across the whole spectrum of human investigation. We began to appreciate our place in the Universe was by no means central. Indeed, in many respects, it appeared to be almost peripheral.

The march towards established constants of Nature that were not explicitly anthropocentric, but based upon the discovery and definition of universal attributes of Nature, can be seen as a second Copernican step. The fabric of the Universe and the pivotal structure of her universal laws were now seen to flow from standards and invariants that were truly superhuman and extraterrestrial. The fundamental standard of time in Nature bore no simple relation to the ages of man and woman, no link to the periods of days, months and years that defined our calendars, and was too short to allow any possibility of direct measurement.

There was a third step still to be taken in this extension of the Copernican perspective. It was to show that the laws of Nature displayed a Copernican complexion. This is a much subtler matter and required one of Einstein's greatest insights to carry it out. First, what does it mean?

Einstein argued that the laws of Nature should appear to be the same for all observers in the Universe, no matter where they were or how they were moving. If they were not then there would exist privileged observers for whom the laws of Nature looked simpler than they did for other observers. Such a view would be anti-Copernican; it would give someone (not necessarily us on Earth) a special position in the Universe. At first one might think that having universal constants of Nature based on superhuman physical standards would be enough to ensure that things looked the same to everyone. However, this is far from sufficient. A classic case is provided by Newton's famous laws of motion. Take the first law as an example. It tells us that bodies acted upon by no forces do not accelerate. They remain at rest or move at constant velocity. However, as Newton appreciated very clearly, this famous ‘universal’ law is not really universal. It will only be found to be true by a special class of observers in the Universe – those which are called ‘inertial’ observers.