What a Wonderful World (21 page)

Because of interference, the fact that a quantum object such as an electron can be in two places at once
has consequences
. Here is an example. Imagine two bowling balls that are rolled together
so they collide and ricochet off each other. If this happens over and over again, the balls will be seen to scatter in a range of
different
directions. Imagine a giant clock face. The balls will go to every number on the clock face.

Now imagine two quantum particles – say, electrons – which collide and scatter in a similar manner. If this happens thousands upon thousands of times, the electrons will also scatter in a range of different directions. But something very odd will soon become apparent. Some directions will be favoured by the electrons. And others will be studiously avoided. In other words, there will be numbers on the clock face where the electrons
never go.

The explanation is that there are directions in which the electron waves reinforce each other and directions in which they cancel each other out. The latter are the directions in which no electrons are seen.

This interference phenomenon was demonstrated in 1927 by Clinton Davisson and Lester Germer in the US and by George Thomson in Scotland. The physicists bounced electrons off the flat surface of a crystal and noticed that there were directions in which the electrons
never
bounced. The crystal consisted of layers of atoms like a loaf of sliced bread stood on end. Some electrons bounced off the top layer; some off the layer below; some off the layer below that, and so on. And the quantum waves of all these electrons
interfered
with each other. Only in the directions where all the waves reinforced did the experimenters observe electrons.

By showing that electrons can interfere with each other,
proving
that electrons are indeed waves, Davisson, Germer and Thomson won the Nobel Prize for Physics. The irony is that, while Thomson received the Nobel for showing that the electron
is not a particle, his father, ‘J. J.’ Thomson, had received the Nobel for showing that
it is
.
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There can be no better illustration of the paradox at the heart of quantum theory.

What all this shows is that, even though it is not possible to see a single quantum particle go in several directions at once, interference means there are consequences. The quantum waves corresponding to the electron going in all possible directions interfere with each other, reinforcing in some directions and
cancelling
each other out in other directions. That is why there are directions that electrons never go. That is why there is quantum weirdness.
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Currently, there is a race on in the world to exploit
superpositions
– the ability of atoms and the rest to do many things at once – to do
many calculations at once
. People are trying to build a quantum computer, which promises to outperform massively even the most powerful conventional computer with certain types of calculations. The reason for saying ‘certain types of
calculations
’ is that they must have a single answer. Recall that it is
impossible
to observe a quantum particle doing many things at once, merely the
consequence
of it doing many things at once. Similarly, it is impossible to access all the countless individual strands of a quantum computation, only the consequence – that is the single answer made from all the threads woven together.

Building a quantum computer is extremely difficult because, if the quantum building blocks of such a computer interact with their surroundings in any way, the multi-tasking power of the computer is irrevocably lost. So a quantum computer must be
totally isolated in a vacuum chamber so that no air atoms strike it or photons of light. And this is hard.

It is not that the ability of the quantum particles to do many things at once is fragile. It is simply that it is very difficult for a large number of atoms – such as air atoms – to maintain a
superposition
. If the quantum particle impresses its superposed state on a lot of atoms, the impression is quickly lost, a bit like one voice being drowned out in a crowd of chanting football supporters.

This explains why atoms display quantum weirdness but, when large numbers of atoms come together to make everyday objects, those objects do not display quantum weirdness. For instance, you never see a table in two places at once or someone walking through two doors at the same time. We never see quantum behaviour in the everyday world because we never see individual atoms or photons. We see only large numbers. You do not observe the world; you observe yourself. In other words, your brain never observes a photon; it observes the amplified effect of that photon impressed on hundreds of thousands of atoms in your retina. And that impression loses the quantumness of the original photon. This is why, bizarrely, we live in a
quantum
world that
does not look quantum.

Much quantum weirdness is a consequence of superpositions and interference. But there are other quantum ingredients also. And, when they are combined in different permutations, they spawn all sorts of novel and surprising behaviours. ‘Magic without magic’, as it has been called. Take quantum spin. This is a
property, like quantum unpredictability, that has no analogue in everyday life. Basically, a quantum particle behaves as if it is spinning like a tiny top, even though it is not. Physicists say it has
intrinsic
spin, or angular momentum.

An electron has the smallest possible quantity of spin, which for historical reasons is called spin ½
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rather than spin 1, which would be the sensible thing to call it.
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Now a spinning charge acts like a tiny magnet.
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This means that it acts like a compass needle when in a magnetic field, aligning itself either pointing along the field (up) or against it (down). If there are two electrons, one possibility is that electron 1 is spin up and electron 2 spin down; another possibility is that 1 is down and 2 is up. Now here is the important thing. In the quantum world superpositions are
possible
. So the two electrons can be up–down and down–up
at the same time
. A bit like you being simultaneously dead
and
alive.

So much for ingredient 1 – superposition. Ingredient 2 is the law of conservation of angular momentum. Basically, this says that the total spin of the two electrons can never change. Since the two electrons in the above example begin pointing in opposite directions, they must
always
point in opposite directions.
Ingredient
3 is simply quantum unpredictability. If we observe an
electron
, whether it turns out to be spin up or down is fundamentally unpredictable like a quantum coin toss. There is a 50 per cent chance of it being up and a 50 per cent chance of it being down.

If all this is getting complicated, here is the situation where the three ingredients come together to create something
extraordinary
. We start with the pair of electrons that is in a
superposition
of up–down and down–up, and send one a long way away. When we have done this, we look at the stay-at-home
electron
. Perhaps we find that its spin is up. If so, instantaneously, its
partner, far away, must flip down since the two spins must
always point in opposite directions
. Perhaps we find that its spin is down. Instantaneously, its partner must flip up.

What is so surprising about this is that, even if the far-away electron was on the other side of the Universe, it would still have to react
instantaneously
to its partner being found to be up or down. To Einstein this ‘spooky’ action at a distance, apparently in violation of the cosmic speed limit set by light, was so
ridiculous
that it
proved
quantum theory was flawed.
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But, not for the first time, Einstein was wrong. Non-locality was triumphantly demonstrated in a laboratory in Paris by French physicist Alain Aspect in 1982.

It is worth pointing out that separating the two electrons is not like separating a pair of gloves. Clearly, if the stay-at-home glove is found to be the left one, the distant one will be a right one. That is because one glove was a left-hand one and the other a
right-hand
one
at the outset.
But the two electrons were neither up nor down at the outset. Their state was undetermined. The stay-
at-home
electron assumed its state
only when it was observed
. And that state was
random
. This is why non-locality does not violate Einstein’s special theory of relativity. If up and down were like the dots and dashes of Morse code, all that could ever be sent would be a random sequence of dots and dashes because the state of the stay-at-home electron and its far-away cousin would always be selected randomly. The dots and dashes could not be controlled. Special relativity, it turns out, limits only the speed of a
meaningful signal
. Nature does not care about unusable garbage. It is welcome to fly about the Universe at any speed it likes. Nobody knows how this happens. Non-locality is arguably the deepest mystery of quantum theory.

But quantum theory’s greatest achievement is in explaining atoms. ‘Atoms are completely impossible from the classical point of view,’ said Richard Feynman. According to Maxwell’s theory of electromagnetism, an accelerated charge – one that changes its speed or direction or both – radiates into space
electromagnetic
waves.
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An electron orbiting an atomic nucleus is
continually
changing its direction. It should therefore broadcast like a tiny TV transmitter and rapidly lose energy. Calculations in fact show it should spiral into the nucleus in less than a
hundred-millionth
of a second. Atoms, as Feynman observed, have no right to exist.

Quantum theory comes to the rescue because quantum theory recognises that an electron has a wave nature. And it turns out that the smaller the mass of a particle the bigger its quantum wave.
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Because you are so big, your wavelength is ridiculously tiny. This is why you exhibit no obvious wave behaviour. This is why you do not bend around corners or pass by on both sides of a lamp post. But the electron is the smallest particle in nature. It is precisely because it has the biggest quantum wave that it
exhibits
so much quantum weirdness. And its wave nature explains the existence of atoms. A wave is a fundamentally spread-out thing. It simply cannot be squashed into a nucleus.
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So atoms do not shrink down to oblivion in a hundred-millionth of a second. Instead, they can exist essentially for ever.

In fact, the electron wave needs so much room that it explains another puzzling feature of atoms: why an electron orbits so far from its nucleus. An atom is 99.9999999999999 per cent
nothingness
.
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You are 99.9999999999999 per cent nothingness.
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Atoms are empty – or so big compared with their nuclei – simply because an electron wave needs lots of elbow room.

But electron waves have a lot more to tell us about atoms. In fact, they explain
everything
about atoms.

There is not just one kind of electron wave that can exist inside an atom. There are many. A more wiggly, more violent wave has more energy than a more sluggish one. It therefore corresponds to an electron that is capable of defying the pull of the nucleus and orbiting further away. But there is a restriction on what kinds of electron wave are possible. All must fit neatly inside the atom. Think of waves with one hump inside the atom. Or two. Or three. And so on. They
fit
. But waves with 1½ humps or 2.687 humps do not fit. This leads to a crucial distinction between an atom and the Solar System. Although in principle a planet can orbit at any distance from the Sun, an electron in an atom is most probably found only at
certain special
distances
from the nucleus, corresponding only to
certain energies
.
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Immediately, this explains why atoms give out light of only certain energies, or wavelengths (the higher the energy, the shorter the wavelength). When an electron in an atom drops from a high-energy orbit to a low-energy orbit, it sheds its excess energy as light. The energy of this photon is equal to the
difference
in energy of the two states.

There is a twist. Isn’t there always? An atom is a
three-dimensional
object. This means that an electron probability wave might be peaked not only at certain
distances
from the nucleus but also in certain
orientations
. Think of a globe. It takes two
numbers to specify any location on the Earth. Similarly, it takes two numbers to specify an electron wave with a particular
orientation
in space. Add this to the number necessary to specify the distance of an electron from a nucleus and that makes a total of three quantum numbers.

The twist is therefore that an atom gives out light when it drops from
any
high-energy orbit to a low-energy orbit. And those orbits might differ not just in the distance of an electron from the nucleus but in the
orientation
of its orbit. Incidentally, the orientation of the electron wave – at least that of the
outermost
electrons – explains chemistry. An atom can join with another atom via its outermost electrons, which can be thought of as living on its exterior surface. And the locations on this surface where an atom can stick, or bond, with another atom are simply the locations at which the electron wave is biggest – that is, where electrons are most likely to be found.