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

*Why Does E=mc2?* is one of those questions that educated

non-physicists must have been asking themselves for over a hundred

years, ever since Albert Einstein derived the equation back in 1905.

Now, in this easy-to-read little book from Brian Cox and Jeff Forshaw,

we have the answer. The authors are both professors of physics at

Manchester University, and Brian Cox is also a well-known TV

personality—well known enough to warrant a jacket blurb from Stephen

Fry.

The book begins with the traditional approach to explaining the slowing

of clocks for observers in motion relative to one another, by examining

the geometry of a light beam bouncing up and down in a moving vehicle.

The authors demonstrate just how easy it is to get to Einstein’s time

dilation formula using nothing more than Pythagoras’ Theorem and the

knowledge that the speed of light is capped. But they don’t leave it

there. In the first half of the book they consider two more approaches

that lead us to the same conclusion.

Along the way, they very cleverly introduce all the ideas we will need

to get to the world’s most famous equation, E=mc2. What is more, they

focus on the most puzzling part: the question of what c, the speed of

light, is doing in there. Very early on, they introduce c as a scaling

factor so that we can talk about “distances” in spacetime. Later, by

various means, they explain why c has to be the maximum speed that

anything can travel. It is a small triumph of the book that Cox and

Forshaw make the attempt to show the logical necessity of there being a

universal speed limit, and that their arguments are so presented so

clearly.

Yet, as with any book of this size tackling a subject so enormous, it is

not long before the authors start asking us to take things on trust,

undermining the comprehensibility of their presentation. The first big

one is when they introduce Maxwell’s equations and ask us to believe

they demand that the rate of propagation of an electromagnetic field be

constant for all observers. Then comes the work of mathematician Emmy

Noether and her demonstration that invariance leads to the conservation

of quantities.

These, and many others introduced later, are tough ideas and hard to

swallow. The authors introduce them to provide alternative ways into the

understanding of relativity and that famous equation. It is to their

credit that they do not always hide the complexity nor the long history

of ideas behind relativity, but it would have been better, perhaps, to

have spent a few more pages on some of these notions.

It is also to their credit that they make the case, as Feynman and

others have done before them, that, at some level, the weirdness of the

universe just has to be accepted, and the only test of physical theories

that matters a damn is whether they are supported by actual observation

and experiment.

And there would have been many pages to spare for additional background

and explanation if, near the end, the book had not wandered into obscure

and largely unrelated areas as it tackled a broad-brush description of

the Standard Model in an attempt to explain what mass is. It was

inevitable that some particle physics had to be discussed and that this

would lead to discussions of quantum theory.

After all, the book’s sub-title is *And Why Should We Care?* and

the reasons given largely involve nuclear power, chemistry, and

cosmology—all of which are helped by discussions at a subatomic level.

Perhaps also Brian Cox’s involvement at CERN (he heads a project there

to upgrade the ATLAS and CMS detectors for the Large Hadron Collider)

meant that a discussion of the Higgs particle was inevitable.

Nevertheless, this, and the very brief glimpse of general relativity

right at the end, seemed to detract from the clarity and force of the

earlier exposition.

It is a curious book that tackles several of the most difficult ideas in

modern science in the tone of a friendly, almost patronizing,

high-school teacher, trying to ensure that the slow kids manage to keep

up with the rest of the class. The tone and the endless asides (did you

know that the Sun converts 600 million tonnes of hydrogen into helium

every second?) can become a bit wearing, but Cox and Forshaw have to be

praised for their unwavering insistence that their subject is accessible

to anyone at all who will stay with them and think about it.

In an age when most lay people throw up their hands at the mention of

relativity or quantum theory, when religious creation stories and New

Age mysticism offer a far simpler, less challenging route for the

intellectually overwhelmed, it is hugely important that ordinary people

see that physics is not just for the egg-heads, that it can be

understood, and that there is a grand beauty in what it reveals about

our world. Cox and Forshaw have made an important contribution in this

area, one that will help school science teachers as much as it will

their students.