Forces of Nature

by Brian Cox

Science is delighted frustration. It is about asking questions, to which the answers may be unavailable – now, or perhaps ever. It is about noticing regularities, asserting that these regularities must have natural explanations and searching for those explanations.

A tremendous economy of description is one of the defining and most surprising features of modern science; it is not a priori obvious that a small collection of fundamental laws should be capable of describing the limitless complexity of objects that populate our universe, and yet this is what we have discovered over the last few centuries. Perhaps a universe regular enough to permit the existence of natural objects as complex as the human brain must be governed by a simple set of laws, but since we do not yet understand the origin of the laws, we do not know.

Physics is about precision of thought, which is aided and evidenced by precision of language.

Allow me a single paragraph of postgraduate-level physics. I want to take this liberty for two reasons. The first is that there is great joy to be had in understanding a complex idea, and in doing so glimpsing the underlying simplicity and beauty of Nature. The biologist Edward O. Wilson coined the term ‘Ionian Enchantment’ for this feeling, named after Thales of Miletus, credited by Aristotle as laying the foundations for the physical sciences in 600 BC on the Greek island of Ionia. The feeling is one of elation when something about nature is understood, and seen to be elegant. The second reason is to revisit and enhance an idea we’ve been developing. Science is all about making careful observations and trying to explain what you see. That might be the hexagonal structure of a beehive, the jagged symmetry of a snowflake, or the details of how electrons bounce off protons. Careful observations lead to Ionian Enchantment.

Truly deep concepts often sound like utter pedantry. This is one of the few similarities between physics and philosophy.

Many of the things we take for granted in our lives, from the behaviour of storm systems to the ebb and flow of the tides, are the result of the fact that we are spinning, and therefore not in an inertial frame of reference, even though we don’t feel it.

As we’ve already mentioned, there isn’t a ‘special’ inertial reference frame; all inertial reference frames are as good as each other. If you’re in an inertial reference frame, you are allowed to say that you are standing still, and there is absolutely no measurement you can make that will tell you otherwise. It is because we are approximately sitting in an inertial reference frame on the surface of the Earth that we don’t feel as if we are moving from moment to moment. Einstein elevated the requirement that all inertial frames are equivalent to a fundamental principle. This means that identical experiments carried out in different inertial frames will always lead to the same results. To put it another way, the laws of Nature do not change as we switch our point of view between inertial reference frames; if they did, we could tell the difference between the reference frames! I don’t want to give the game away early in the chapter, but this ultimate democracy between inertial frames turns out to be such a severe constraint on the laws of Nature that Newton’s laws and the laws of electricity and magnetism cannot both be right. This may not sound too serious, but we will see in Chapter Four that the laws of electricity and magnetism are one of the great pillars of physics alongside Newton’s laws. They describe so many things we take for granted in our everyday lives; the action of electrical generators and motors, the formation of a rainbow, the action of lenses, the optical ...

In his essay ‘Some Thoughts on the Common Toad’, George Orwell reflects on the simple and available delight of noticing things like the passage of the seasons, and that is really what this book is about: ‘The point is that the pleasures of spring are available to everyone and cost nothing’, he writes. ‘How many a time have I stood watching the toads mating, or a pair of hares having a boxing match in the young corn, and thought of all the important persons who would stop me enjoying this if they could. But luckily they can’t. Humans wouldn’t be here without the Moon; at the very least, evolution would have taken a different path, and it is a major understatement to say that the road to humanity was convoluted. ‘The atom bombs are piling up in the factories, the police are prowling through the cities, the lies are streaming from the loudspeakers, but the Earth is still going around the Sun, and neither the dictators nor the bureaucrats, deeply as they disapprove of the process, are able to prevent it.’

Einstein discovered his Theory of Special Relativity by elevating the idea that all inertial reference frames are equivalent to a great principle; an axiom; a fundamental property of our universe. It was his guiding light.

Einstein was the first to take a very important and, at first sight, rather odd fact seriously. Unlike Newton’s laws, the laws of electricity and magnetism are not invariant under Galilean Transformations. They do not look the same in all inertial frames of reference if you change all the speeds in the way you do for Newton’s laws to account for the shift in perspective.

Maxwell’s equations are correct. The statement that the speed of light is a constant in all inertial frames of reference is on the same footing as the principle of inertia. It is because it is.

Einstein’s brilliance – let us call it genius – was to take Maxwell’s equations at face value and insist that when we hop between inertial frames of reference we keep the speed of light the same. We are not allowed to add velocities in the way that we have been doing; it is simply wrong. The Galilean Transformations are wrong, and therefore Newton’s laws, which possess the symmetry represented by the Galilean Transformations, are also wrong.

Einstein rebuilt physics from the ground up by insisting on two axioms, which are known as Einstein’s postulates. The first is one with which we are very familiar indeed. The laws of physics are the same in all inertial frames of reference. The second postulate is the one that comes from taking Maxwell’s equations at face value: The speed of light in a vacuum is the same in all inertial frames of reference.

Here, we want to explore a very particular consequence of Einstein’s two postulates: the idea that space and time are not what they seem.

We’ve discovered that space and time are not as they seem, if we accept that the speed of light must remain constant for all observers. There is no such thing as absolute space, because observers moving at different speeds relative to each other disagree on the distance between events. The comfortable picture of the Universe as a big box, where every star, planet and galaxy has a well-defined place, cannot be right, because the distances between the stars, planets and galaxies cannot be defined in a unique way. Similarly, there is no such thing as absolute time, because it is not possible to define the time between events in a unique way.

Einstein found a way out. He discovered that, whilst the distance in space between two events and the difference in time between two events each change, there is a quantity that does not change if we switch perspective between inertial frames: the distance in space and time, taken together in a very special way. If we call the distance between Monet’s easel and door Δx and the time difference between the dab of red paint and the click of the lock Δt, then the ‘distance’ Δs2 = c2Δt2 - Δx2 does not change. Both the aviator and Monet agree on Δs, even though they disagree on Δt and Δx. The quantity Δs is known as the distance in spacetime between the two events.

In an undergraduate lecture course on physics, we would now proceed to consider how energy and momentum are treated in special relativity and show that this special speed can be interpreted as the speed of massless particles. Coincidently, as far as we know, photons happen to be massless and therefore travel at the special speed c – and this is why we call it the speed of light.

Two centuries later, with the whole of modern medical science, evolutionary biology and genetics to draw upon, we are still unable to reach an accommodation between our desire to discover a reason for our creation and the scientific consensus that no such reason exists beyond the inevitable action of the laws of nature on a young, active planet. The most interesting questions are those that demand a resolution between apparently irreconcilable positions.

Living things work in the same way from a thermodynamic perspective. They can become more ordered as long as they pay their debt by exporting disorder in the form of heat into the Universe. You are exporting disorder now as you read this book. You are hastening the demise of everything that exists, bringing forward by your very existence the arrival of the time known as the heat death, when all stars have died, all black holes have evaporated away and the entirety of creation is a uniform bath of photons incapable of storing a single bit of information about the glorious adolescence of our wonderful Universe. You are doing this by burning food in oxygen from the air. This is an exothermic reaction, generating plenty of heat for export and more than compensating for the temporary low entropy configuration of your wasteful, highly ordered body.

Serendipity always was and always will be absolutely central to discovery, because the natural world is so intricately interconnected and functions according to a small set of fundamental laws, as far as we know. There are so many ways to discover deep and ultimately useful things that it is futile to imagine that we can predict which investigation of which tiny corner of the natural world will bear undreamt-of fruit.