Thursday, January 21, 2010

Book Review: Why Does E = mc2?

So I spent the majority of the money I got for Christmas on books, because I'm a dork.  One that I was really excited to read was Why Does E = mc2? (and Why Should We Care?) by Brian Cox and Jeff Forshaw.  First, because I've seen Brian Cox on a number of TV specials talking about particle physics, and thought he was a really interesting guy.  And second, because I realized, when I saw the title, that I wanted to know how Einstein came up with his theories of relativity.

I knew a little bit about relativity and Einstein's theory before reading. I understood the basic idea of relativity: that there is no such thing as absolute motion.  For instance, I'm sitting on my couch right now writing a book review for my wildly popular blog, so it appears that I am not moving at all (v = 0).  But that's relative to the Earth.  The Earth (and me along with it) is rotating at 15o per hour (0.5km/sec), and revolving around the Sun at 30 km/sec.  And although from within the solar system, the Sun appears to be stationary, and thus an absolute reference for motion, the solar system is moving at 250 km/sec relative to the center of our Milky Way galaxy.  And the galaxy is also moving relative to the local cluster of galaxies.  All motion has to be measured relative to some other object (hence the name relativity).

I also understood that the equation E = mc2, from Einstein's theory of special relativity, means that mass and energy are essentially interchangable.  The mass of an object is the amount of latent energy within that object.  I also knew that Einstein's theories predicted that the speed of light (c) is constant, regardless of frame of reference, though I had a really hard time understanding how that worked, or how it was even possible.  I also knew very little about how Einstein figured all of this out.

After reading this book, I understand a lot about Einstein's process in discovering this immortal equation.  Cox and Forshaw do an excellent job describing the state of knowledge before Einstein, and how we get from there to knowing that E = mc2.  Each step of the process is explained intuitively, clearly and logically progressing from one idea to the next.  Each chapter reads like a story, without creating false drama or interest with useless tangents and distractions (for the most part, described below).

The explanations include useful analogies and examples, which allowed me to understand concepts that I never had a good grasp of before.  For example, they use the analogy of a motorcycle moving at a constant speed in different directions to explain what how space and time are related into a single medium called spacetime.  We can think of sitting still as moving only in the time dimension (moving completely north in the motorcycle example).  When we begin moving in space, we start to move in a more northeasterly direction, and as we speed up in space, we get closer to moving east.  But since the motorcycle is moving at a constant speed, when we move faster in space, we must also be moving slower in the time direction, meaning time slows down for someone moving fast. I've read a number of books and articles about all of this, and this was the first time I felt like I grokked spacetime.  (That's right, a Stranger in a Strange Land reference!)  All of the threads really started to come together for me while reading the examples used in the book.

That's not to say the book is without problems.  Cox and Forshaw try to simplify the math throughout the book, in order to make it accessible to those of us who aren't physicists or mathematicians.  While the sentiment is good, and I'm sure it made the book more readable for some, I had a hard time understanding some of the proofs they presented with words, rather than math.  It meant that they had to explain their proof with several pages of text, rather than a few compact equations.  This also meant diagrams that should make understanding the concepts easier, were difficult to use because of constantly flipping pages back and forth to refer to them throughout a multi-page explanation. 

Other simplifications require readers to simply trust that some equality holds, or some next step makes sense, without explaining the proof in enough detail to convince me.  If you're willing to take a few things for granted, its easy to follow the logical conclusion, and understand the progression of the proofs.  However, there are a number of cases where I can't know for sure how some of the steps came about, and whether they really reasonably follow.

For example, they show that if spacetime follows the rules of Euclidean geometry, the rules of cause and effect can be violated, which is a big problem.  They use the Pythagorean theorem (a2 + b2 = c2), which holds in Euclidean geometry, to explain how this works, and it was easy to understand and very enlightening.  However, they then make the seemingly random step of changing the plus sign in the Pythagorean theory to a minus sign, resulting in (a2 - b2 = c2), and associating this new equation with Minkowski spacetime, which is a geometry that is different from Euclid's, and as we can guess from its name ends up being the correct geometry for describing how spacetime works.  But they neglect to explain how they came about making this change, or why this equation is relevant to Minkowski spacetime.  If we take this manipulation of Pythagoras for granted, the rest of the discussion shows why this equation does not violate any cause and effects laws, and the discussion is interesting and enlightening once again.

While many of the figures are useful, none of them contain captions that describe what's going on, and usually are referred to in the text three or four pages after the figure is shown, making them very difficult to understand. There is also a chapter near the end of the book, called The Origin of Mass, which seemed like a tangent, not really related to the rest of the book.  It's as though Cox and Forshaw wanted to talk about their own research on the Higgs boson particle, regardless of its relevance to this book.  It was certainly an interesting discussion, it just seemed misplaced.

Although the book certainly isn't perfect, I still highly recommend it to anyone interested in physics, and how the cosmos works at the most fundamental levels.  While there are still some holes in my knowledge about how we know that E = mc2, my understanding of the basic thought process by Einstein and his contemporaries has increased immensely after reading this book.

I think the best thing about this book, is that it clears up many of the misconceptions about how Einstein made his discoveries.  Einstein is often thought of by the general public as someone who sat in a room, thinking to himself, and came up with E = mc2 out of thin air.  Cox and Forshaw show that Einstein relied on previous knowledge in physics, such as the work of Faraday and Maxwell.  He also relied heavily on mathematics (despite the urban legends about his poor math skills) and observations made in the real world.  Einstein is famous for using thought experiments, such as thinking about what it would be like to ride a beam of light.  But these thought experiments are only a small step, which initiated his research, which involed a lot of real work.  I think that this book is a much better example of how real science works for aspiring young scientists, or even just the average person, than the urban legends of an isolated Einstein pulling theories and equations out of nowhere.

Why Does E = mc2? is both widely accessible and mind-expanding; a rare and welcome combination in popular science literature.


  1. v. good review, also I spent my xmas money on books too, it doesn't mean you're a dork, it means you are awesome

  2. Einstein was wrong about e=mc2. See