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to demystify the speed of light. Because the speed of light appears in E = mc2, it often seems as if light itself is important in the structure of the universe. But in the spacetime way of looking at things, light is not so special. In a subtle way, democracy is restored in the sense that everything hurtles through spacetime at the same speed, c, including you, planet Earth, the sun, and the distant galaxies. Light just happens to use up all of its spacetime speed quota on motion through space, and in so doing travels at the cosmic speed limit: The apparent special-ness of light is an artifact of our human tendency to think of time and space as different things. There is in fact a reason why light is forced to use up its quota in this way, and this is intimately related to our goal of understanding E = mc2. So, without further ado, let us continue on our quest.

E = mc2 is an equation. As we have been at some pains to emphasize, to a physicist equations are a very convenient and powerful shorthand for expressing relationships between objects. In the case of E = mc2 the “objects” are energy (E), mass (m), and the speed of light (c). More generally, the objects living inside an equation could represent real material things, such as waves or electrons, or they could represent more abstract notions—such things as energy, mass, and distances in spacetime. As we have seen previously in this book, physicists are very demanding of their fundamental equations, for they insist that everyone in the universe should agree upon them. This is quite a demand—and at some time in the future we might discover that it is not possible to hold on to this ideal. Such a turn of events would be quite shocking for any modern physicist, since the idea has proved astonishingly fruitful since the birth of modern science in the seventeenth century.

As good scientists, however, we must always acknowledge that nature has no qualms about shocking us, and reality is what it is. For now, all we can say is that the dream remains intact. We explored this ideal of universal agreement earlier in the book and expressed it very simply: The laws of physics should be expressed using invariant quantities. All of the fundamental equations of physics that we know today achieve this by being written in such a way that they express relationships between objects in spacetime. What exactly does that mean? What is an object that lives in spacetime? Well, anything that exists presumably exists in spacetime, and so when we come to write down an equation—for example, one that describes how an object interacts with its environment—then we should find a way to express this mathematically using invariant quantities. Only then will everyone in the universe agree.

A good example might be to consider the length of a piece of string. Based on what we have learned, we can see that although the piece of string is a meaningful object, we should avoid writing down an equation that deals only with its length in space. Rather, we should be more ambitious and talk about its length in spacetime, for that is the spacetime way. Of course, for earthbound physicists it might be convenient to use equations that express relationships between lengths in space and other such things—certainly engineers find that way of going about things very useful. The correct way to view an equation that uses only lengths in space or the time measured by a clock is that it is a valid approximation if we are dealing with objects that move very slowly relative to the cosmic speed limit, which is usually (but not always) true for everyday engineering problems. An example we have already met where this is not true is a particle accelerator, where subatomic particles whiz around in circles at very close to the speed of light, and live longer as a result. If the effects of Einstein’s theory are not taken into account, particle accelerators simply stop working properly. Fundamental physics is all about the quest for fundamental equations, and that means working only with mathematical representations of objects