Category Archives: physics

Why Does E=mc²? by Brian Cox and Jeff Forshaw

Way back in the mists of ancient time, when I was a college drama student, we all went down to New York City to see Tom Stoppard’s Arcadia. I don’t remember much of it now, but I remember it had to do with math and fractals, time and space, and that when the play was over and we all went outside for a smoke, I had a moment of what could only be called sublime clarity. I stood out there with my cigarette, staring off into the middle distance, and – for just an ever-so-brief time – I understood everything.

Not the play, mind you. Everything. It all made sense. It was nothing I could have put into words or explained in any period of time shorter than a lifetime, but it all worked. It all fit together, and I knew what the universe was and what my place in it was. It’s probably how Fenchurch felt in The Hitchhiker’s Guide right before the Earth was demolished.

And that feeling was wonderful.

It passed, though, because no one can be allowed to hold on to that kind of clarity of understanding. We’d never get anything done. By the time I got on the bus, I was trying to claw my way back to it, understanding but not caring that this was a place you couldn’t find the same way twice. The fine, crystalline perfection of the universe had once again been hidden from my mind, and all that was left was the memory of what it had felt like to know that everything was as it should be.

Reading this book was kind of the opposite of that experience. On every page, I knew that if I would be able to hold on to these ideas just a moment longer, if I could just put the pieces together a little faster, then I would have true understanding of the elegant beauty of creation. But I couldn’t, and I was left with the feeling that it was my own shortcomings that were at fault, rather than those of the authors.

Cox and Forshaw have set a very interesting challenge for themselves in this book. They want to explain one of the most famous equations in human history, and to do it in such a way that the non-scientist reader can understand not only what it means, but where it came from and what its implications are. This is no mean feat, of course, on any front. For all its simplicity, E=mc² contains within it some of the most important and fundamental understandings about how the universe works. To truly understand this equation is to understand time and space, matter and energy, existence in four dimensions and at scales both vast and tiny.

They begin with what looks like a very simple question: where are we? Galileo pondered this question for a while, and came up with an answer that was probably both enlightening and horrifying for his time.

We don’t know.

Oh sure, we can know where we are in relation to something else – between a pair of arbitrarily numbered latitude and longitude lines, for example, or at a position around the star that we orbit. But a moment’s thought reveals that we still need to explain where the reference point is, and that we can only explain that in relation to something else, which can only be positioned by yet another relative measurement. In other words, there is no such things as an absolute location in space. There is no universal “there” there by which we can understand the position of anything.

Man, that must’ve freaked him out.

The next insight is that if there is no absolute place, then there also cannot be any absolute motion. As I type this, I am sitting in my comfy chair. As far as I’m concerned, I’m motionless. But I’m not. To an alien on the moon, I’m moving with the Earth’s rotation, whipping past at a breakneck pace of about 1,600 kilometers per hour. On top of that, the Earth is moving around the sun at over 100,000 km/h. which is in turn dragging the whole solar system around the center of the galaxy at roughly 220 kilometers per second, and the galaxy itself is moving through intergalactic space at over 600 km/s, and space itself is expanding at what can only be Ludicrous Speed.

So questions that seem like they should be simple turn out to be really hard to answer. But what comes next is even worse: if there is no absolute place or motion, then what about time? How can we have an immutable, fixed time if there is no such thing as an immutable, fixed place?

Cox and Forshaw proceed to lead us by the hand through the discoveries and realizations of scientists such as Faraday and Maxwell, with a little bit of Pythagoras and Galileo, before bringing us to Einstein and beyond. Through the use of lightspeed trains, mirror-clocks, and a whole variety of illustrative analogies, they take us step-by-step through the process of moving from our understanding of three-dimensional semi-Euclidean space to a four-dimensional spacetime. They guide us through physics and geometry, on scales both large and small, and show not just what E=mc² means, but how Einstein got to it, and how we’ve proven it so far.

In that sense, this book is a great success. The popular vision of Einstein is that he came up with Relativity because he was bored at work, and that it popped into his head fully formed. But without the work of countless scientists before him, Einstein wouldn’t have had a place to start. E=mc² is built on the foundations of meticulous science, and is supported by a logical structure that is both elegant and simple. What’s more, his theories of relativity have been tested again and again in all kinds of ways, and they have stood up to those tests. And not for lack of trying, mind you – there isn’t a physicist alive who wouldn’t be thrilled to prove Einstein wrong and propose a more accurate version of reality. But so far, it seems to be the best explanation there is.

For all their care and meticulousness, however, the book is still a bit tough to get through. One of the things that got in my way was how they constantly apologized for using math. I understand why they did it – a lot of adults have a hate-fear relationship with math, and especially equations that start using letters. Math still has an element of mystery and wizardry about it, at least if you’re not very proficient in it, and I get that they didn’t want to scare off any math-phobics from their book.

But at the same time, I think I would rather they had said, “Okay, follow along with us – it’s about to get MATHTASTIC!” Well, maybe not those words, but I started to get a little tired of being talked to like a timid child as the book went on. They said over and over that I could skip the math parts if I wanted to, and sure enough that’s what I ended up doing. But I think I would have come out of this book with a much better sense of understanding and accomplishment if Cox and Forshaw had said, “We’re going to do math and you’re going to understand it.” As it is, they talked to me like I was a slightly dim child, and I still didn’t fully understand. So what, then, does that say about me?

That I seriously overthink things, for a start.

In any case, even if I didn’t get the math, and didn’t see where all their conclusions came from – especially when they started going over the Master Equation of particle physics near the end – I at least came away with a better understanding of both the chain of reasoning that led to E=mc² and the ramifications it has on our understanding of the universe. I don’t understand everything this time, at least not yet, but I know more. And that will have to do.

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“Science at its best is driven by inquiring minds afforded the freedom to dream, coupled with the technical ability and discipline to think.”
– Brian Cox & Jeff Forshaw, Why Does E=mc²?