The Big Questions: Physics (17 page)

However, the radiation is also a danger. If it is too intense, mutations in DNA can lead to sterility, cancer – even, possibly, extinction for some species. The fact that this radiation hasn’t wiped out life on Earth is largely due to the fact that our magnetic field deflects most of the solar wind. So what would happen if it failed?

We know that our magnetic field came into existence at least 3.2 billion years ago. The earliest known life forms were in existence 3.5 billion years ago. The implication seems obvious: life has evolved in a magnetic field, and may require it. The moon and Mars both had magnetic fields around 4 billion years ago, but neither body has one now – nor do they harbour life, as far as we know.

Physicists’ best guess about the reason for that is that their small size meant they cooled quickly, losing the heat necessary to keep a liquid core churning. Earth’s larger size maintains the heat in its core, while its tectonic plates cool the mantle relative to the core. That temperature difference keeps the convection currents strong, stirring the iron-rich molten rock and maintaining our field.

And here is another connection to life: Earth’s field maintains our atmosphere. The magnetic field’s deflection of the
solar wind means that the atmosphere is not buffeted by the solar wind’s particles. Maps of Mars’s little remaining ionosphere show that it is thickest where Martian rocks have maintained their magnetism. It seems that, if you lose your magnetic field, the atmosphere goes with it. So, Earth’s magnetosphere does not just protect us from radiation. It also allows our atmosphere to form and develop, giving us oxygen to breathe. Are we about to lose the very air we breathe?

The answer is almost certainly not. The reversal is most likely happening, but all our experiments and observations seem to indicate that any magnetic reversal will take a few thousand years, at the very least. During this process the Earth’s field will weaken, and become massively more complex, but it will remain strong enough to hold on to our atmosphere. It may not be a disaster in other ways, either.

The humans living on Earth at that time will almost certainly be at risk of receiving much more solar radiation. But no one yet knows whether that will really prove a problem. It is possible there could be mass extinction because of DNA damage, but there are so many other factors in play over those kinds of timescales that anything is possible. The last reversal didn’t wipe out our ancestors, and by then we might have developed the technology to create our own artificial radiation shield. Earth’s natural shield might well be failing, but this time we are ready, willing and able to face the consequences.

The equation that underpins the universe

Go on, think of an equation. Given all those years of education, whether you enjoyed or endured them, you might think that an equation you learned at school would come to mind. But it doesn’t. Instead, this one, which you probably learned by accident, pops into your head.

It is the most famous equation in the world. It appeared on the cover of
Time
magazine in 1946, and has since become part of our culture, inspiring artists and musicians, writers and film-makers. It litters the globe: you’ll find it on the logo of a Japanese graphics company, a public relations company in rural England and a Toronto hair salon. Why? Because this equation summarizes how the modern world took its form.

Though the equation, written down by Einstein in 1905, was forty years old before the world saw what it could do, we shuddered at the discovery. On the cover of
Time
, it is written into a mushroom cloud looming over a fire-struck Pacific atoll.
E = mc
²
is the equation behind the atomic bomb. It ended the Second World War, and ushered in the age of nuclear power and nuclear threat. With it came the Cold War and, for the first time, the spectre of total destruction for the human race. Even now, with the Cold War over, the possibility that the wrong person may learn how to convert a tiny mass into an enormous amount of energy hangs heavy over us.

The happier truth, though, is that
E = mc
²
is so much more powerful than a bomb. It is the very root of our life, our continued existence and perhaps our future too. It describes the fundamental nature of reality, revealing just how deep the illusion of the familiar notion of matter goes. If there is only one equation in your head, at least it is the right one.

So where did this equation come from? To be strictly accurate, not, at first, from Einstein. In the paper suggesting this relation between mass and energy, Einstein didn’t actually write down
E = mc
²
. He wrote down
L = mv
²
, where L is the ‘living’ energy, m is mass, and v is velocity. It was seven years later, in 1912, that he began to routinely use
E
for energy, and
c
for
celeritas
, the Latin for ‘swiftness’ and a universally acknowledged symbol for the speed of light. Even ignoring the switch of symbols, Einstein didn’t pluck the equation out of the air. The seeds of
E = mc
²
were sown in laws of physics that were first formulated in the 17th century, then debated for almost two centuries.

The word ‘energy’ has a long history, but we have only recently begun to use it in connection with what we mean by energy today. The
Encyclopaedia Britannica
of 1842, for example, defined energy as ‘a term of Greek origin, signifying the power, virtue, or efficacy of a thing’. That Greek origin, which lies with Aristotle, is actually somewhat closer to the mark. Aristotle defined energy as the source of every thing’s being and function. ‘Energeia’, he said, was what allowed something to do its job.

In Isaac Newton’s day, though, energy was still poorly defined. The concept was there: things that moved – an arrow fired from a bow, for example – had energy. When that arrow landed, however, the energy seemed to be lost. The same happened if two
people collided in the street, knocking each other to the floor. Their energies, according to Newton, cancelled each other out. Before the collision there was energy; after, there was none.

Fortunately for us – according to Newton, at least – God was there. Newton felt that God, as a living and immanent deity, must be at work somewhere in the universe. One of the deity’s vital roles, Newton suggested, was to top up the cosmic energy reserves. God was there to wind up the clockwork universe and keep the planets moving through the heavens, but he also applied himself to everyday situations – to colliding peasants, for example.

‘He had not, it seems, sufficient foresight to make it a perpetual motion.’

GOTTFRIED LEIBNIZ

It was not a view shared by Newton’s great rival, the atheist Gottfried Leibniz. In an acerbic comment on Newton’s view, Leibniz said he found it hard to understand that God Almighty would have to wind up his own watch from time to time. ‘He had not, it seems, sufficient foresight to make it a perpetual motion,’ Leibniz wrote in a 1715 letter to the philosopher Samuel Clarke. Newton and Leibniz were already rivals over the authorship of the mathematical tool known as calculus, which had enabled Newton to calculate the orbital motions of the planets. This conflict over energy, too, could be boiled down to another mathematical issue.

Newton had formulated the energy of a moving body as
mv
, the product of its mass
m
and velocity
v
. Leibniz, on the other hand, thought it to be
mv
²
, the product of the mass and the square of its velocity. The difference had a profound effect. In Newton’s formulation, two identical bodies moving in the opposite direction with the same velocity would have energies
mv
and –
mv
. If they collided, the resulting energy would be zero. Leibniz’s squaring of the velocity meant that the ‘negative’ direction made no difference, because a negative quantity always squares to a positive number. In Leibniz’s formulation, the energy was not lost from the universe.

For a number of years, the question was simply a matter of ideology. If you were English-speaking, you liked Newton’s work and ideas, you thought of energy as
mv
. If you spoke German, you sided with Leibniz, and squared the velocity. This jingoism was overcome through a Dutch and French collaboration. Willem’s Gravesande, a Dutch scientist, had been dropping weights into soft clay from various heights. The depth of the hole the weights made was, presumably, proportional to the energy, which in turn must be proportional to the height from which they were dropped and the speed on impact. The only way the sums worked was if energy was indeed proportional to the square of the velocity. ’s Gravesande didn’t see this for himself. It was a French noblewoman called Emilie du Châtelet who put all the pieces of the puzzle together in the first half of the 18th century and declared Leibniz the winner. The energy due to motion – living, or kinetic energy – was proportional to the square of the velocity.
E
depends on a velocity squared.

Though ’s Gravesende and (in particular) du Châtelet had made great strides forward in illuminating the relationship between a body’s motion and its energy, they still had no idea what happened to all the energy once the motion had stopped. Did it disappear? The answer to that question only came after the discovery of a principle called ‘conservation’.

The first experimental hints at a general principle of conservation came in the late 18th century. In an astonishingly careful set of experiments, carried out just a few years before he was guillotined at the behest of the Paris revolutionaries, the French scientist Antoine Lavoisier monitored how a variety of materials changed with burning, rusting, or some other natural process of change. He found their mass was always conserved in some manner.

Each of the experiments was carried out in a closed container, and the substance under investigation (together with any air or water in the chamber) was weighed before and after the experiment. Within the limits of his experiment, the total mass of
material in the chamber remained constant. Even something as violent as combustion, which altered the physical form of a material so radically, still did not push materials out of existence. The mass measurements told Lavoisier it remained there in the experimental chamber; altered in form but still there nonetheless. Things didn’t simply disappear from the universe, but they could be transformed between different forms.

That probably comes as no surprise to you. Thanks to a couple of centuries of experiments such as Lavoisier’s, we have come to accept that the universe is, effectively, a ‘closed’ system, containing a finite amount of ‘stuff’ that can be transformed from one state into another. And the most fundamental transformable – but always conserved – quantity is energy.

After taking thousands of years to get to grips with the concept of energy, it still took almost the whole of the 19th century for scientists to work out that energy is always conserved in nature. With hindsight, it seems a little odd that this revelation was so slow in coming. It had long been known that kinetic energy could be converted to heat. Those who bored the barrels of cannons, for example, knew that the process generated vast amounts of heat. But it was only with the invention of thermodynamics, the branch of science that relates temperature and heat to the motion of atoms and molecules (see
Why is There No Such Thing as a Free Lunch?
), that we discovered exactly how that worked.