Why Does E=mc2?: (And Why Should We Care?) Book

Cox and Forshaw pack Einstein's theories of relativity and much more into 250 pages. They state upfront that their book is intended to be challenging. And it is, despite simplistic analogies and explanations tucked in between some pretty dense material. Their underlying premise is "From the simplest of ideas". Einstein noticed that Maxwell had shown that the speed of light was a constant and from this he constructed the Special Theory of Relativity. Then Einstein thought about the fact that all objects fell at the same rate as Galileo demonstrated. He turned this idea into the General Theory of Relativity.

The first half of the book centers around a derivation of E=MC2. Many complex topics are addressed along the way. The authors employ high school algebra and geometry but their manipulations can be intricate. The derivation is not done historically. They use Pythagoras's theorem to compute the value of time dilation, the difference in time between a stationary observer and one in motion. They note that the observer in motion and stationary observer are interchangeable. Each can perceive the other as the one moving and the one for who time slows. There is no absolute motion as Galileo validated.

Time, size and distance are observer dependent but the solution must be invariant, looking the same to all observers. To achieve this space and time must be combined into a single entity with four dimensions. The authors introduce us to Minkowski space which blends space and time. In spacetime Euclidian geometry won't work. In it Cox and Forshaw use a modified Pythagorean formula that avoids going back in time which would violate the principle of causality, e.g. you can't kill your parents before you were born. To measure distance in spacetime, the constant c, is introduced to calibrate. It is the universal speed limit and the speed of light. Everything moves through spacetime at this speed. If at rest the movement is all through time. If moving through space then time slows proportionately from the point of view of a stationary observer. Thus both moving and stationary observers agree on movement through the combined spacetime and invariance is achieved.

To complete their derivation the authors introduce momentum, the product of mass and velocity. Momentum is a three dimensional vector in our everyday 3D world and four dimensional in the 4D world with the added component of time. The time component of the momentum vector in 4D space is mc, mass times the universal speed limit. Momentum is a conserved quantity as is mass which is equivalent to energy. Mass and energy are different manifestations of a single underlying physical quantity. Energy, mass and momentum form a spacetime object known as the energy-momentum four-vector. From this the authors produce E=MC2. The details are in the book. The foregoing is just intended to give the flavor and flow of the book.

The second half of the book is easier to digest as Cox and Forshaw give a broad overview of assorted physics topics. They describe the vast amount of energy in a tiny amount of mass and how that mass is converted, not just in nuclear reactions but in chemical reactions and other everyday phenomena. They venture into particle physics and quantum mechanics describing the emission and absorption of photons from electrons and subsequent changes in their "orbits". The authors discuss the Higgs boson as the origin of mass, even though this was just a prediction when they wrote the book. They even go back to the Big Bang and the disparity between matter and anti-matter. They then present the equation for the Standard Model, explaining what each term represents. They discuss how the model was put together and the various contributors, Glashow, Weinberg, Salam, Feynman, and Gell-Mann. Finally such a wide ranging review would not be complete without General Relativity to which the last chapter is devoted.

I enjoyed this book. However the presentation was a bit disjointed. The authors write for readers at varying levels bouncing back and forth between simple explanations and more difficult detailed ones. They insert apologies to those for who the material might be too complicated and for those who might get bored. While the math itself was not overly difficult, following it in terms of the concepts it represented was more demanding. Still I applaud the effort to put some accessible math behind concepts that are deep and not intuitive. Regardless of level this is a book for a non-scientist reader with a strong interest in the subject. Cox and Forshaw said the book was meant to be a challenge. It was and that made it worthwhile.