Something called entropy

Even if time does not flow, we can still assign to it a direction,
called an arrow of time. This is an abstract concept which simply
means that we can define an ordering of events. An arrow of
time points from the past towards the future, from earlier events
to later ones. It is a direction in time in which things happen. It
is important here to make the distinction between a flow of time
and a direction of time. Imagine looking at individual frames on a
reel of a movie. We can easily define an arrow of time pointing in
a particular direction along the reel based on which frames were
earlier and which were later. We do this despite the fact we are
looking at still shots of events and there is no movement in the
frames. Each one is a snapshot frozen in time.
Evenwhenit comes to the direction of timewemust be careful.
We must not confuse the real direction of time (if any such thing
exists) with our subjective feeling for the direction of time. Let
me first define what may appear to be an obvious arrow of time,
known as the psychological arrow, which is the direction that we
perceive time to point in; the fact that we remember events in our
past and look ahead to events that have yet to happen in our
future. If your psychological arrow of time were to suddenly flip
over it would appear as though everything around was running
in reverse. Everybody else’s future would be in your past and vice
versa. This is clearly so ridiculous that I will not waste any more
time discussing it and you can stop trying to make sense of it. Is
there indeed a problem with the arrow of time at all? Surely the
fact that we see the past happening before the future is because the
past does happen before the future!
The reason why I ambeing cautious here is that the equations
of physics do not even provide a direction in time. Time could
flow backwards and the laws of physics would stay the same.
You might argue that this is just tough luck for physicists. If
the direction in which time should point is missing from the
equations of physics then they cannot be telling us the whole
story. Just because they cannot discern a direction for time from the mathematics does not mean that there isn’t one in the real world But the problem is more serious than this. Even in the real
world, at the level of atoms, almost all processes are reversible in
time. If, in a subatomic process, two particles, a and b, converge
and collide they will often bounce off each other and separate
again. If you were to watch a film of such a process and then
watched it running in reverse, you would not be able to decide
which way round the process happened. The time-reverse process
still obeys the laws of physics. I should point out that this would
have to be a thought experiment. We could not really do it since
no microscope on Earth is powerful enough to resolve detail down
at the subatomic level.
It often happens that instead of the same two particles
bouncing off each other, two new ones, say c and d, are produced
and fly apart. Again, you would not be able to decide on the
true order of events if you watched a film of this process because
the laws of physics state that the reverse process is also possible.
Particles c and d could have collided to produce particles a and
b. You therefore cannot assign an arrow of time that would state
which way round the process occurred.
This is in sharp contrast with events that happen around us in
everyday life where we have no trouble deciding which direction
time is pointing. For instance, you never see smoke above a
chimney converging on it and getting neatly sucked down inside
it. Similarly, you cannot ‘unstir’ the sugar from a cup of coffee
once it has been dissolved, and you never see a pile of ash in
the fireplace ‘unburn’ to become a log of wood again. What is it
that distinguishes these events from the subatomic ones? How
is it that most of the phenomena we see around us could never
happen backwards? Surely everything is ultimately made up of
atoms and at that level everything is reversible. So at what stage
in going from atoms to chimney smoke, cups of coffee and logs of
wood does a process become irreversible?
On closer examination we see that it is not that the processes
I have described above can never run in reverse, but rather that
they are extremely unlikely to do so. It is entirely within the laws
of physics for dissolved sugar to ‘undissolve’ through stirring and
reconstitute itself into a sugar cube again. But if we ever saw this happening we would suspect some kind of conjuring trick. And
rightly so, for the chances of it happening are so tiny they can be
ignored.
Let us consider a simpler example using a pack of cards. It
is simpler because we are dealing with a much smaller number
of components (fifty two cards) than the number of molecules of
sugar or smoke or wood in the above examples. Begin with a
pack of cards which has been ordered such that the four suits are
separated and the cards in each suit are arranged in ascending
order (two, three, four, . . . , jack, queen, king, ace). By shuffling
the cards a little the order will be ruined. Now we can ask what
happens to the order of the cards upon further shuffling? The
answer is obvious: it is overwhelmingly more likely that the cards
become even more mixed up than it is for them to return to their
original ordered arrangement. This is the same irreversibility as
in the case of a partially dissolved sugar cube which on further
stirring always carries on dissolving.
To give you an idea of the probabilities involved, if you were
to take a completely shuffled pack of cards then the chances of
getting the ordered arrangement you started with through further
shuffling is about as likely as it would be for you to win Britain’s
National Lottery jackpot not once or twice but on nine consecutive
draws!
It is all down to an important law in physics called the second
law of thermodynamics. The subject of thermodynamics involves
the study of heat and its relation with other forms of energy. The
astronomer Arthur Eddington went so far as to claim that the
second law held the supreme position among all the laws of nature.
There are three other laws of thermodynamics which are to do with
how heat and energy can be transformed into each other, but none
is as important as the second law. It has always amused me that
one of the most important laws in the whole of physics cannot even
make it to the number one spot on the list of thermodynamics laws.
The second law of thermodynamics states that things wear
out, cool down, unwind, get old and decay. It explains why the
sugar dissolves in the coffee but never undissolves. It also states
that an ice cube in a glass of water will melt because heat is always transferred fromthe warmer water to the colder ice cube and never
in reverse. To understand the second law a little better I must
introduce you to a quantity called entropy. The second law is a
statement of increasing entropy. In an isolated system, entropy
will either stay the same or increase, but can never decrease.
Entropy is a quantity which is a little difficult to define
precisely so I will do so in two ways:
1. Entropy is a measure of untidiness in a system; how mixed
up things are. The ordered pack of cards described earlier is
said to have low entropy. By shuffling the pack we are ruining
their initial order, and increasing the entropy. When the cards
are completely mixed up the entropy of the pack is said to be at
its highest and further shuffling cannot mix them any more2.
2. Entropy can also be thought of as a measure of a something’s
ability to do work (by which I mean the possibility of
extracting useful energy from it rather than work in the usual
meaning of theword). Afully charged battery has low entropy
which increases as the battery is used. A clockwork toy has
low entropy when wound up which increases as it unwinds.
When it has completely unwound, we can reset its entropy
back to a small value by winding it up again. The second law
is not being violated here because the system (the clockwork
toy) is no longer isolated from its environment (us). The toy’s
entropy is being decreased but we are ‘doing work’ to wind
it up and our entropy is increasing. Overall, the entropy of
toy + us is increasing.
It is a little difficult to provide an example of entropy which
encompasses both of the above definitions: that of increasing
disorder and that of the ability to do work. However, one such
example of the unavoidable increase in entropy is my children’s
bedrooms. Before they get back from school in the afternoon their
rooms are tidy and said to be in a state of low entropy. Once they
are home and playing behind closed doors there is an impressively
rapid rise in entropy. Lego bricks, cars, dolls, teddy bears, plastic tea sets and an assortment of plastic food all get pulled out of their
boxes and strewn randomly across the floor. The only way to get
the rooms back to their initial low entropy state is to ‘apply external
work to the system’ (usually in the form of their mother). It would
be against the laws of physics (or what is known as the second law
of the Al-Khalilis) for the children to enter a high entropy bedroom
and, without any external work (such as verbal threats) to decrease
its entropy.
Another example of increasing entropy is cigarette smoke in
the library canteen at my university (the last refuge for smokers on
campus). When a cigarette is lit in the smoking area entropy is said
to be low since the smoke is neatly confined to a small volume of
the canteen. But thanks to the second law of thermodynamics we
are all soon sharing the fumes. The second law of thermodynamics
states that you never witness smoke that is evenly distributed
around the canteen collect back in the corner again.
We sometimes see examples where it appears as though
entropy is decreasing. For instance, a wristwatch is a highly
ordered and complex system that is produced from a collection
of bits of metal. Surely this is violating the second law. In fact
this is just a more complicated version of the example of the
clockwork toy. The watchmaker has put a certain amount of effort
into making the watch, increasing his own entropy slightly. In
addition, smelting the ores and machining the metals that are
needed have produced a certain amount of waste heat that more
than compensates for the small decrease in entropy due to the
creation of the watch.
If it ever seems like entropy is decreasing we always find
that in fact the system under consideration is not isolated from its
surroundings and that, by zooming out to view a wider picture,
the entropy will always be greater than it was before. We can
view many processes that happen on Earth, from the evolution
of life to the building of highly ordered and complex structures,
as reducing the entropy on the surface of our planet. Everything
from cars to computers to cabbages has lower entropy than the
raw materials it is made up from. Despite this, the second law is
not being flagrantly disregarded. What we are missing is the fact that even the whole Earth cannot be considered as isolated from its
surroundings. We must not forget that almost all life on Earth, and
hence all low entropy structures, is thanks to sunlight. When we
consider the combined Earth + Sun system we see that the overall
entropy is increasing because the radiation that the Sun pours out
into space (only some of which is absorbed by the Earth) means
that its entropy is increasing by much more than the corresponding
decrease on Earth.