Why Does E=mc2? by Brian Cox and Jeff Forshaw
Did you know that you’re travelling at the speed of light? Not just you: your book, your chair, the room around you, your home. In fact, everything is moving at the speed of light.
Don’t feel it? Don’t worry, no one else did either until Albert Einstein redefined the substance of reality at the start of the 20th century. Neither Galileo, Michael Faraday, James Clerk Maxwell or Isaac Newton knew about the speed of light thing, despite laying the foundations for the insights that the Austrian patent-clerk-turned-physicist would eventually have.
Let me clarify. We are all moving at a speed “c” that happens to correspond with the speed of light as it moves through a vacuum in normal space. Except that our movement is through a 4D co-ordinate system called spacetime. Unlike 3D space, which allows you to measure the position of an object, spacetime allows you to measure events (where and when). Even if you are sitting still in 3D space (not moving in any direction), you will nevertheless be moving in 4D spacetime (in other words, no movement in the three space dimensions but moving in the “time” direction).
Spacetime is a key component in the step-by-step journey that physicists Brian Cox and Jeff Forshaw take in getting to the bottom of the most famous equation in science, Einstein’s E=mc2, which says that mass and energy are the same thing, and you can convert from one to the other using a constant, “c2”, a number whose value is equal to the square of the speed of light.
Knowing that mass and energy are equivalent has given us, for better or worse, the mushroom cloud and nuclear power stations, but none of these applications were on Einstein’s mind as he explored the fabric of space and time. His formulation of what became known as special relativity tore apart the classical view of the clockwork universe that Newton and his colleagues had developed in the 18th and 19th centuries.
Einstein started with a conundrum, the niggling problem that the ideas of Galileo and Maxwell seemed to be at odds.
Galileo had shown how there was no such thing as absolute motion, that you can only define movement relative to something else. You might feel like you are sitting still right now but that is only true relative to the Earth; relative to the black hole at the centre of our galaxy, we are all moving at hundreds of thousands of miles an hour.
By the end of the 19th century, Maxwell had tied together decades of work on electricity and magnetism by, among others, Humphrey Davy and Michael Faraday, to produce his masterful equations on electromagnetism. These showed that light was a wave in the electromagnetic field, much as ripples on a pond are waves in water or sound is a wave in the air. He also showed that these waves of light moved at a constant speed, “c”, through empty space and that speed remained the same no matter who was watching. Whether you are sitting still or moving at hundreds of miles an hour towards the source of the light, Maxwell’s equations say that the light you see will only ever move at “c” relative to you.
Einstein was curious about why Galileo’s ideas of relative motion seemed to break down in Maxwell’s equations. He incessantly picked at this hanging thread and, in the process, unravelled the whole tapestry the physicists of the enlightenment had put together.
With special relativity, he showed that Maxwell’s number, “c”, was a constant of nature, the fastest speed at which anything could go and, coincidentally, the speed of light too. In Einstein’s view of the universe, “c” was the only thing that stayed the same in all reference frames and, to accommodate that, he showed how time and space themselves were stretchy concepts. No longer was there a fixed backdrop upon which the universe did its work: the familiar ideas of position in space, time and speed were all malleable depending on who is watching what and how fast they are moving relative to each other.
Cox and Forshaw use this background to rattle through concepts that sound more science-fiction than everyday: how time slows down and length contracts the closer you move to the speed of light or why one twin can age more slowly than the other if he goes on a super-fast round trip.
You need the idea of spacetime to explain why, even as you seem to sit still in space, you are still moving at “c” in the time dimension. Think of your normal movements in everyday 3D space and everyday time as the shadow of a more universal movement in 4D spacetime. To make the equations of special relativity work, you need to measure your motion in spacetime, rather than everyday space and time.
Einstein came up with his seemingly baffling ideas as a series of thought experiments, and the fact that they were later proved by experiment is thanks to his skills as a mathematician. Another popular science book might have spared readers the gory details of what Einstein was up to, given that his ideas and results were in themselves so engrossing. But Cox and Forshaw do as much as they can to undermine the old publishing canard that equations in books don’t sell.
Most of the steps they take to reaching Einstein’s famous equation are accompanied by some mathematics. It’s not easy going in parts but then, if you really want to know what Einstein was up to and really want to know why what he did changed physics, you can’t expect it to be easy. Metaphors and lay explanations will only get you so far with special relativity, you have to see the maths to really understand what’s going on.
If anything, the authors are too apologetic about the maths they include, constantly assuring readers that there is a purpose to the strings of symbols, that there is a key insight at the end of the abstractions. For anyone afraid of technicalities, Cox and Forshaw lead the reader by the hand through the complexity, adding in rest stops of wit and real-world examples. Even the hardest bits feel like being taken on an army assault course by the two friendliest drill sergeants in the world. You may have to read some bits twice but, boy, will you feel better for it once the insights become clear.
In the process of exposing the science, the authors do a good job of showing how the hard end of research works: abandon all assumptions and re-build everything from scratch. It’s frustrating, it’s terrifying and it’s slow. Sometimes it is hugely confusing and counter-intuitive. But patience and persistence in the face of dearly held beliefs is exactly why scientists have made such a remarkable fist of understanding (and shaping) our modern world. It’s well worth your while to gulp down any fears of maths and glimpse some of that remarkable achievement in action.