Why Does E=mc²? (And Why Should We Care?) - Brian Cox, Jeffrey R. Forshaw (2009)


Our aim in this book is to describe Einstein’s theory of space and time in the simplest way we can while at the same time revealing its profound beauty. Ultimately, this will allow us to arrive at his famous equation E = mc2 using mathematics no more complicated than Pythagoras’ theorem. And don’t worry if you can’t remember Pythagoras, because we will describe that as well. Equally important, we want every reader who finishes this little book to see how modern physicists think about nature and build theories that become profoundly useful and ultimately change our lives. By building a model of space and time, Einstein paved the way for an understanding of how stars shine, uncovered the deep reason why electric motors and generators work, and ultimately laid the foundation on which all of modern physics rests. This book is also intended to be provocative and challenging. The physics itself is not at issue: Einstein’s theories are very well established and backed up by a great deal of experimental evidence, as we shall discover as the book unfolds. In due course, it is very important to emphasize, Einstein may be forced to give way to an even more accurate picture of nature. In science, there are no universal truths, just views of the world that have yet to be shown to be false. All we can say for certain is that, for now, Einstein’s theory works. Instead, the provocation lies in the way the science challenges us to think about the world around us. Scientist or not, each of us has intuition and we all infer things about the world from our everyday experiences. If we subject our observations to the cold and precise light of the scientific method, however, we often discover that nature confounds our intuition. As this book unfolds, we will discover that when things whiz about at high speeds, common-sense notions regarding space and time are dashed and replaced by something entirely new, unexpected, and elegant. The lesson is a salutary and humbling one, and it leaves many scientists with a sense of awe: The universe is much richer than our everyday experiences would have us believe. Perhaps most wonderful of all is the fact that the new physics, for all its richness, is filled with a breathtaking mathematical elegance.

Difficult as it may sometimes seem, science at its heart is not a complicated discipline. One might venture to say that it is an attempt at removing our innate prejudices in order to observe the world as objectively as possible. It may be more or less successful in that goal but few can doubt its success in teaching us how the universe “works.” The really difficult thing is to learn not to trust what we might like to think of as common sense. By teaching us to accept nature for what it is, and not for what our prejudice may suggest that it should be, the scientific method has delivered the modern technological world. In short, it works.

In the first half of the book we will derive the equation E = mc2. By “derive,” we mean that we will show how Einstein reached the conclusion that energy is equal to mass multiplied by the speed of light squared, which is what the equation says.

Think about this for a moment and it seems like a very odd thing. Perhaps the most familiar kind of energy is the energy of motion; if someone throws a cricket ball at your face, then it hurts when it hits you. A physicist would say that this is because the cricket ball was given energy by the thrower, and this energy is transferred to your face when your face stops the ball. Mass is a measure of how much stuff an object contains. A cricket ball is more massive than a table-tennis ball, but less massive than a planet. What E = mc2 says is that energy andmass are interchangeable much like dollars and euros are interchangeable, and that the speed of light squared is the exchange rate. How on earth could Einstein have reached this conclusion, and how could the speed of light find its way into an equation about the relationship between energy and mass? We do not assume any prior scientific knowledge and we avoid mathematics as much as possible. Nevertheless, we do aim to offer the reader a genuine explanation (and not merely a description) of the science. In that regard especially, we hope to offer something new.

In the latter parts of the book, we will see how E = mc2 underpins our understanding of the workings of the universe. Why do stars shine? Why is nuclear power so much more efficient than coal or oil? What is mass? This question will lead us into the world of modern particle physics, the Large Hadron Collider at CERN in Geneva, and the hunt for the Higgs particle that may lead to an explanation for the very origin of mass. The book finishes with Einstein’s remarkable discovery that the structure of space and time is ultimately responsible for the force of gravity and the strange idea that the earth is falling “in a straight line” around the sun.