What a Wonderful World (22 page)

There remains a puzzle, however. The electrons in an atom can occupy any of the permitted quantum waves, known as orbitals. But, in the real world, things have a strong tendency to minimise their energy. For instance, a ball, given a chance, will roll to the foot of a hill to minimise its gravitational energy. So, in an atom with more than one electron, why do they all not roll down the energy hill to the bottom? Why do they not crowd into the lowest-energy orbital, closest to the atom?

If this happened, atoms as we know them would not exist. For one thing, there could be no light. Photons are emitted only when an electron drops from one energy level to another,
shedding
its excess energy in the process. But, if all electrons were in the
same
state, at the
same
energy, there would never be any energy to be shed.

A more serious problem is that it is the
outermost
electrons that determine chemistry – how one type of atom joins up with other types of atoms to make molecules. For instance, some atoms have one outer electron, some two, three, and so on; and some atoms have outer electrons pointing in certain directions and other atoms in other directions, and so on. It is this that creates the huge variety of nature ’s atoms, from hydrogen, the lightest, to uranium, the heaviest. But, if all the electrons in every type of atom piled into the innermost orbital, all atoms would present pretty much the same exterior to the world. Instead of 92
naturally
occurring kinds of atom, there would be only one. There would be no chemistry. No complexity. No us.

Once again, quantum theory rescues the atom – and the
Universe
– from such a stultifyingly dull fate. Recall that quantum ingredients, when combined in different permutations, spawn all sorts of novel and surprising behaviours. For instance, the mix of superpositions, electron spin and the law of conservation of
angular
momentum creates the madness of non-locality, of quantum particles influencing each other instantaneously when separated by impossible distances. Here is another mix: electron spin, the wave nature of electrons, and the fact that electrons are
indistinguishable
. The last is yet another new-under-the-Sun quantum property. Objects in the real world are always distinguishable – two similar cars by a scratch on the paintwork, for instance, or a slight variation in tyre pressure. But electrons are utterly
indistinguishable
. They cannot be marked. If two electrons are switched, there is no way to know that this has happened even in principle.

This mix of quantum ingredients spawns the Pauli Exclusion Principle.
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In a nutshell, this edict says that no two electrons in an atom can share the same orbital. More specifically, no two
electrons
can share the same quantum numbers. A slight twist is that there is a fourth quantum number: spin. Remember, an electron in a magnetic field can either have a spin up or a spin down. So, the Pauli Principle says that no two electrons can share the same
four
quantum numbers.

The Pauli Principle stops electrons all piling on top of each other in the same orbital. It is why there are 92 types of naturally occurring atoms, not one. It is why there is variety in the world and you are here to read these words.

Because of the Pauli Principle, electrons arrange themselves in shells at successively greater distances from a nucleus. The first shell can contain a maximum of 2 electrons; the next 8; the next 18, and so on. Here are some examples … Take an atom with 6 electrons – it has 2 electrons in its inner shell and 4 in its outer shell. One with 12 electrons has 2 in its inner shell, 8 in the next shell and 2 in its outer shell. Immediately, it is clear why some kinds of atom behave similarly. For instance, lithium, sodium and potassium all have 1 electron in their outermost shell and so appear much the same to the outside world.

So there you have the origin of the world’s stability and diversity. The wave-like nature of atoms prevents their electrons spiralling down to the nucleus in the merest split second. And the Pauli Exclusion Principle prevents the electrons piling on top of each other so, instead of just one kind of atom, there is a huge number of types. ‘It is the fact that electrons cannot get on top of each other that makes tables and everything else solid,’ said Feynman.

The Pauli Exclusion Principle applies to all subatomic particles with so-called half-integer spin – that is, ½,
^³
⁄
_²
,
⁵
⁄
_²
units, and so on (quarks, by the way, have spin ½ just like electrons). Such particles, known as fermions, are characterised by their enormous unsociability. Particles with integer spin – that is, 0, 1, 2 units, and so on – on the other hand, are gregarious. They do not obey the Pauli Exclusion Principle. This is why photons, which are bosons, are able to flock together in untold quadrillions to create the phenomenon of laser light.

It seems that there is nothing in the world that cannot be explained by quantum theory. It is the most successful physical theory ever devised. Inventions that exploit the ideas of quantum theory are estimated to account for 30 per cent of the GDP of the United States. Each and every one of us is a product of quantum theory. We live in a quantum world. But, although the quantum world is a magical world, there is little doubt that it is a mind-stretching world. ‘If anybody says he can think about quantum physics without getting giddy’, said Niels Bohr, ‘that only shows he has not understood the first thing about it.’

Infinity is a number bigger than any other. If a body could travel at infinite speed, you would never be able to catch it up. Not only that but, no matter how fast you moved, the body would always appear to you to be infinitely fast, since your speed would
always
be negligible by comparison.

In our Universe, the role of infinite speed, for some reason, is played by the speed of light – 300,000 kilometres per second. No material body can ever catch it up. And no matter how fast you move relative to a source of light, or a source of light moves relative to you, the light will always appear to be travelling at 300,000 kilometres per second.

The remarkable fact that the speed of light – christened
c
by physicists – is doggedly unchanging was revealed by American physicists Albert Michelson and Edward Morley. In 1888, they measured the speed of light when the Earth, in its orbit around the Sun, was flying in the same direction as their light beam; and, six months later, when the Earth was moving in the opposite direction. To their consternation, they found that the speed of their light was the same in both cases. In fact, even had the Earth been orbiting the Sun at the truly enormous speed of half the speed of light, Michelson and Morley would still have measured the speed of light as
c
– not (
c
+½
c
) = 1½
c
; or (
c
-½
c
) =½
c
. What does the peculiar constancy of the speed of light mean? That question was answered by Einstein in his miraculous year of 1905.

The speed of anything is simply the distance it travels in a given time – for example, a car may travel 50 kilometres in an hour. So, for everyone to measure the same speed for a beam of light – no matter how fast they are moving or how fast the source of light is moving – something weird must have to happen to each person’s measurement of distance and time.

We think of one person’s interval of space – say, a metre – as being the same as someone else’s, and one person’s interval of time – say, a minute – as the same as another’s. But this cannot be true if everyone is to measure the same speed for light. If the speed of light is the rock on which the Universe is built, space and time must be like shifting sand.

In fact, as Einstein realised, space
shrinks
and time
slows down
from the point of view of a moving observer. Or, to be more
precise
, if someone is moving relative to you, you see them shrink in their direction of motion and slow down as if they are moving through treacle.
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‘Moving rulers shrink,’ goes the saying, ‘and moving clocks slow.’

Einstein had a more tongue-in-cheek – and, by today’s
standards
, less PC – way of saying it: ‘When a man sits with a pretty girl for an hour, it seems like a minute. But let him sit on a hot stove for a minute – it’s longer than any hour. That’s relativity!’

But what is it like from the point of view of the person flying past you? Well, they see
you
shrink in the direction of
your
motion; they see
you
slow down as if wading through treacle. This is because what you each see depends only on your
relative
motion
– and both of you have the
same
relative motion.

This fact reveals the second foundation stone of Einstein’s theory – in addition to the constancy of the speed of light – and explains why the theory is called relativity. Galileo, four centuries
ago, was the first to realise that all people travelling at constant speed relative to each other see the same thing. Take, for instance, someone who throws a ball, which loops through the air to a friend who catches it. The ball will follow the same trajectory whether the thrower and catcher are on a beach or on a ship ploughing through the sea.

When Galileo maintained that all people travelling at constant speed relative to each other see the same thing, he specifically meant that they see the same laws of motion. Two and a half
centuries
later, Einstein simply extended Galileo’s idea. It is not just the laws of motion that are the same, he claimed, it is
all
the laws of physics, including the laws of optics, which dictate that the speed of light is unvarying.

Think of the person moving past you at constant speed, and their space shrinking and their time slowing. From their point of view, you are moving with respect to them at the same relative speed – you are just moving backwards. So both of you see the same thing. That is the magic of relativity.

An obvious question is: why do we never see the weird effects of relativity – technically, time dilation and Lorentz contraction? Specifically, when someone runs past us on the street, why do we not see them shrink in the direction of their motion and slow down? The answer is that such effects are noticeable only for bodies flying past each other at speeds approaching that of light. But the speed of light is tremendously fast – about a million times faster than a passenger airliner. We do not see the effects of relativity because we live our lives in the cosmic slow lane. Relativity, in a sense, is the discovery of our slowness.

But, if we do not see the effects of relativity, how do we know that time really slows as we approach the speed of light? How
do we know that space really contracts? The evidence is actually coursing through your body at this very instant.

Muons are subatomic particles, created about 12.5 kilometres up in the atmosphere when cosmic rays, high-energy atomic nuclei from supernovae, slam into atoms of the air. Like
subatomic
rain, muons shower down through the atmosphere. But there ’s the rub. A muon disintegrates after a characteristic interval of time.
2
The interval is very short – a mere 1.5
millionths
of a second. By rights, therefore, none should travel more than about 500 metres down through the atmosphere before disintegrating. Certainly, none should reach the ground, 12.5 kilometres below.

But they do.

The reason is that muons are travelling at 99.92 per cent of the speed of light. From your point of view, they live their lives in slow motion. In fact, time passes 25 times slower for them than for you, which means they take 25 times as long as usual to realise it is time to disintegrate. When they do, they have already reached the Earth’s surface.

But, of course, there is another point of view – that of the muon. From its angle, time is passing at its normal rate – after all, a muon is stationary
with respect to itself
, as are you. Instead, it sees
you
shrink in the direction of its motion – or, rather,
your
motion, since, from the point of view of a muon, it is the ground that is approaching at 99.92 per cent of the speed of light. But not only do you shrink, so too does the atmosphere. It shrinks to a mere 1/25th of its normal thickness. Which means the muons have time to get to the surface before they disintegrate.

Whatever way you look at it – from your point of view, where the muon’s time slows down; or from the muon’s point of view,
where the atmosphere shrinks – the muon gets to the ground. It is one more example of the magic of relativity.

But what would it be like if you, like a muon, could travel at close to the speed of light? For one thing, you would learn some profound truths about the world. You might think that relativity tells us that one person’s interval of time is not the same as another’s. It does. But, more specifically, it tells us that one
person
’s interval of time is another person’s interval of time
and
space. In other words, what one person sees as two separate events at the same location – say, two explosions – might appear to someone else as two events at different locations.

You might also think that relativity tells us that one person’s interval of space is not the same as another’s. But, actually, it tells us that one person’s interval of space is another person’s interval of space
and
time. In other words, what one person sees as two events happening simultaneously another person might see as two events happening at different times.
3

But, if at speeds close to that of light, intervals of space morph into intervals of time and vice versa, then surely space and time cannot be fundamental things? Exactly. The
fundamental
entity, which becomes apparent only close to the speed of light, is
space–time
. It turns out that, in a low-speed world, we only ever see shadows of this seamless entity – a space shadow or a time shadow.

Here is an analogy. Imagine a walking stick suspended from its midpoint like a giant compass needle. It is in a square room with windows on two adjacent sides. Oh, and it is gloomy in the
room so you cannot tell you are looking at a walking stick, just an object. You look through one window and you call what you see ‘length’. Then you look through the adjacent window and you call what you see ‘width’. Makes perfect sense. So far, so good.

Now imagine the walls of the room are on a turntable (this is not a simple analogy!). It turns. And you look through the windows again. To your surprise, you see that the length has changed. And so too has the width. It dawns on you that your labels of length and width were not sensible at all. The
fundamental
thing is the object – the suspended walking stick. But you have mistaken mere projections – shadows – of the object for the fundamental thing.

This is the way it is for space and time. The fundamental object is space–time. But we have mistaken mere projections of it – shadows – for the fundamental thing. It is not our fault. Our mistake becomes glaringly obvious only at speeds approaching that of light when space morphs into time, and time into space. Actually, in a deep sense, travelling close to the speed of light is like rotating our viewpoint – just as with the room on a
turntable
– so that we see different space and time projections of space–time.

It was not Einstein who had this insight but his former
mathematics
professor, Herman Minkowski, who famously called his pupil a ‘lazy dog’. On later realising his mistake, Minkowski also recognised the key importance of space–time. ‘From now on,’ he said, ‘space of itself and time of itself will sink into mere shadows and only a kind of union between them will survive.’

The speed of light is uncatchable by any material body. This is pretty amazing. After all, if we were really talking about infinite speed, it would be obvious that, no matter how hard and how long we pushed a body, it would never attain infinite speed. But the speed of light, though huge by human standards, seems
so
much smaller than infinity.

Well, since the speed of light is unattainable – the cosmic speed limit – something must happen as you push a body faster and faster. There must be some kind of resistance to your
pushing
, and the resistance must become infinite close to the speed of light so that no amount of pushing will ever get you there.

One property of a body provides resistance – its mass. In fact, that is how we define mass. A body that resists being pushed a lot, such as a loaded fridge, is said to have a big mass, while a body that resists very little, such as a feather, is said to have a small mass. See where this is going? If, as a body approaches the speed of light, its resistance grows, it must mean that it
gets more massive.

But where is the extra mass coming from? There is a
fundamental
law of physics called the law of conservation of energy that says energy can be changed only from one form into another, and never created nor destroyed. For instance, electrical energy can be changed into heat energy in an electric fire; the chemical energy of your food can be changed into energy of motion in your muscles. But, if you are pushing and pushing the body and the energy you are putting in is not going into energy of motion, it must be going somewhere. Well, the only thing that is changing is the mass of the body. The energy you are putting in must be
increasing its mass. But remember, energy can be transferred only from one type into another.
Mass must therefore be a form of energy.

And, in fact, this is true. Not only did Einstein discover that space and time are mere facets of the same thing, he discovered that energy – energy of motion, sound energy, any energy you imagine – has an equivalent mass.

If you think all this is esoteric, with nothing much to do with you, think again. The quarks that contribute most of your mass are very insubstantial indeed.
4
In fact, they account for only about 1 per cent of your mass. This is explained by something called the Higgs mechanism. You may have heard of the Higgs particle, whose discovery was announced with a huge fanfare at the Large Hadron Collider near Geneva on 4 July 2012.
5
So where does the lion’s share of your mass – the other 99 per cent – come from? The answer is relativity.

The quarks within the protons and neutrons of atoms are whirling around at close to the speed of light. This means they have enormous energy of motion. And this energy of motion, according to Einstein, has mass. It accounts for most of the mass of protons and neutrons – and, therefore, you. Without the effects of relativity, you would weigh less than 1 kilogram.

You may ask: why are the quarks whirling around at speeds approaching that of light? The answer is that they are in the grip of the enormously powerful strong nuclear force. A force field contains energy, which, according to Einstein, has mass.
Ultimately
, then, it is this gluon field that accounts for most of your mass. It does not matter how you look at it. Ultimately,
something
as mundane and everyday as your mass is inexplicable
without
the effects of relativity.