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than a model. If a way of thinking about the world confers a survival advantage, then that way of thinking will become ubiquitous. The scientific correctness of it is irrelevant. The important thing is that, because we chose to accept the results of experiments conducted on Faraday’s mottled benchtop and the explanations codified by Maxwell, we have acted like scientists and rejected the comfortable model of space and time that allowed our ancestors to survive and prosper on the ancient plains of Africa. This model has been embedded and reinforced deep within our psyche by our experiences over many millions of years, and discarding it may well be disorientating. That dizzying feeling of confusion, if (hopefully) followed by an epiphany of clarity, is the joy of science. If the reader is feeling the former, we hope to deliver the latter by the end of the book.

This is not a history book. Our aim is to describe space and time in the most enlightening way we can, and it is our view that the historical road to relativity does not necessarily provide the best path to enlightenment. From a modern perspective, over a century after Einstein’s revolution, we have learned that there is a deeper and more satisfying way to think about space and time. Rather than dig any deeper into the old-fashioned textbook view, we are going to start again from a blank canvas. In so doing we will come to understand what Minkowski meant when he said that space and time must be merged together into a single entity. Once we have developed a more elegant picture, we will be well placed to achieve our principal goal—we shall be able to derive E = mc2.

Here is the starting point. Einstein’s theories can be constructed almost entirely using the language of geometry. That is, you don’t need much algebra, just pictures and concepts. At the heart of the matter, there lie only three concepts: invariance, causality, and distance. Unless you are a physicist, two of these will probably be unfamiliar words, and the third familiar but, as we shall see, subtle.

Invariance is a concept that lies at the core of modern physics. Glance up from this book now and look out at the world. Now turn around and look in the opposite direction. Your room will look different from different vantage points, of course, but the laws of nature are the same. It doesn’t matter whether you are pointing north, south, east, or west, gravity still has the same strength and still keeps your feet on the ground. Your TV still works when you spin it around, and your car still starts whether you’ve left it in London, Los Angeles, or Tokyo. These are all examples of invariance in nature. When put like this, invariance seems like little more than a statement of the obvious. But imposing the requirement of invariance on our scientific theories proves to be an astonishingly fruitful thing to do. We have just described two different forms of invariance. The requirement that the laws of nature will not change if we spin around and determine them while facing different directions is called rotational invariance. The requirement that the laws will not change if we move from place to place is called translational invariance. These seemingly trivial requirements turned out to be astonishingly powerful in the hands of Emmy Noether, whom Albert Einstein described as the most important woman in the history of mathematics. In 1918 Noether published a theorem that revealed a deep connection between invariance and the conservation of particular physical quantities. We will have more to say about conservation laws in physics later on, but for now let us just state the deep result Noether discovered. For the specific example of looking at the world in different directions, if the laws of nature remain unchanged irrespective of the direction in which we are facing, then there exists a quantity that is conserved. In this case, the conserved quantity is called angular momentum. For the case of translational invariance, the quantity is called momentum. Why should this be important? Let’s pull an interesting