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What drives natural phenomena? Why do atoms form molecules? Why does oxygen combine with
hydrogen to form water? Why does a boulder on top of a mountain fall to the bottom? Why does
a pencil on its tip always fall to the table? Perhaps the most fundamental principle
of the universe is that things always tend towards their lowest energy state. Atoms
combine because sometimes two atoms such as hydrogen are a lower energy state when they
are bonded together. A boulder at the bottom of a mountain is in a lower energy state than at the
top of a mountain. This is the way nature works? But why is nature driven this way?
Well this has to do with another concept in physics, and that is the idea of entropy.
Entropy is always increasing. A simple way to think of entropy is disorder. In fact,
the entire universe is on an inexorable path to higher and higher disorder.
But what’s driving this disorder? What is the underlying cause of
higher entropy? What does entropy have to do with a pencil falling to the table?
We are going to get at the bottom of this, so stick around because that’s coming up right now.
The second law of thermodynamics states that the total entropy of a closed system always
increases over time, or remains constant in reversible processes. But what is entropy?
The way entropy is typically described is disorder. Higher entropy means higher disorder.
Well, this is a very simplified way to think of it. This description doesn’t really give
us many insights. Why should the universe favor disorder over order? The answer is not obvious.
Instead of trying to understand the definition of entropy, let’s step back and think about why
it was conceptualized in the first place. Think about what drives natural phenomena.
Why do things happen? Why do certain atoms combine to form molecules. Why do certain
chemical reactions take place and others don’t. Why does heat flow from one place to another.
Whenever something happens, some kind of change has to occur. Properties like speed,
mass or temperature change. Physics defines the rules that allows us to predict these changes.
Some of the rules are that overall energy does not change, overall momentum does not change. These
are conservation of energy and momentum laws. But if something can change from say configuration
A to configuration B, then why shouldn’t the reverse also be allowed from B to A?
When a ball rolls down a hill from a certain height, it should be able to roll back up to
the same height. If energy is conserved, then all its potential energy when it is on top of
the hill is converted to kinetic energy at the bottom. And this kinetic energy should
completely convert back to potential energy, back to the height that the ball originally
started from. But this is not what happens. Some energy is always lost in this process to friction,
air resistance and so on. Most natural phenomena are not reversible. They are irreversible.
We can scramble an egg, but we can’t unscramble it, Why?
Conservation laws can’t answer the question why there is a preferred direction to any particular
change. Things move in a particular direction as time moves forward. What distinguishes
time moving forward from time moving backward. Well, it’s not as mysterious as it might sound.
It all has to do with probability. Let’s do a very simple example. Let’s hold
a pencil upright on a table. If we let go, it will fall and lie horizontally. Why did this happen?
When it was held up, it had a high potential energy. Just before it hit the table,
most of that potential energy had been converted to kinetic energy – the energy of its motion.
When it hit the table, that kinetic energy was transferred to the table and air in the
form of heat and sound. Energy is conserved. Buy why did this transfer of energy happen?
Why doesn’t the reverse happen? Say the pencil was lying flat on the table, why doesn’t the energy
of the air and heat configure itself in such a way that it results in the pencil standing
up. Energy would be conserved in that case too. You might say well, things just tend to go to
their lowest energy state. Well, it’s true that the pencil went from a high energy state to a
lower energy state. But the table and air went from a lower energy state to a higher energy
state. No change in overall energy occurred. So we can’t really say that this happened because
everything wants to go to a lower energy state, because if that were the case, then
why did the table and air go to a higher energy state. Something else has to be happening here.
What’s really happening is that although energy is conserved, the type of energy has changed.
Useful energy has converted to less useful energy. In thermodynamics, the term "energy" refers to the
ability of a system to do work. When a system is at a high energy state, it has more energy
available to do work. When the pencil was standing on its tip, it had more potential energy, that is,
it had more ability to do work. After it hit the table, it had less energy available to do work.
The energy that transferred to the table and air in the form of heat and sound is less useful.
Similarly, when we say that systems tend to go to their lower energy state,
what we really mean is that they are converting their energy from more useful to less useful.
This is the case for example when two hydrogen atoms combine with oxygen to form water. This
reaction releases energy into its surroundings. The energy of the system that is the oxygen and
hydrogen atoms, has gone from higher ability to do work to a lower ability to do work.
The same thing can be applied to a boulder falling from the top of a mountain to the bottom.
The boulder when at the top has potential energy due to its position, which allows it to do work,
falling down the mountain. As it falls, it loses potential energy and gains kinetic energy, but the
total energy of the system remains constant. After it has fallen, it’s energy will have
converted to heat and sound. Energy is conserved because overall energy is the
same, but it has less ability to do work. The real question we want to answer is why
do some systems tend to transfer their energy to other systems?
To answer this question, let’s go back to the example of the pencil standing on its tip. And
let considering the number of possible ways that the total energy can be divided up between the
pencil and the environment, that is the table and air. This is where probability comes in.
When the pencil is standing up, there is pretty much just a single way you could arrange the
potential energy of the atoms that comprise the pencil. And there are very few ways that you
can put that energy towards the kinetic energy of the pencil. Once the pencil has transferred this
kinetic energy to the movement of atoms on the table and air in the form of heat and sound, there
is an innumerably large number of ways that you could divide up that energy among all the atoms
in the surrounding air and table. For example, all the energy could be concentrated on a single atom,
or you could divide it equally between all of the trillions upon trillions of atoms of the table, or
any other distribution of energy amongst trillions upon trillions of atoms in the surroundings.
So the point here is that while there are just a few ways that energy can go towards the motion
of the pencil, there is a mind-bogglingly large number of ways in which that energy
could be distributed to the motions and vibrations of atoms in the surroundings.
If we assume that the any possible distribution of energy is equally likely, then the case with
a mind-bogglingly large number of possibilities is much more likely to occur. In fact, it will occur
virtually all the time, and the case with just a few possibilities, basically would never occur. So
in the end, energy has transferred from the pencil to the environment because it is vastly more
probable, than the reverse which is so improbable that it would essentially never occur, or at least
not within the lifetime of the universe. This idea of the probability of something
occurring in one direction vs another, when modeled mathematically, results in
the concept of entropy. Entropy is the logarithm of the number of ways a system can be arranged.
The greater the number of ways a system can be arranged, the higher its entropy.
So when we say that a system has a tendency to go to lower energy, what we are really talking
about is that the total energy of a system will be divided up in such a way that maximizes the
number of ways the system can be arranged. So in the case of the pencil, it always
falls to the table because that results in the total energy of system dividing itself
up to maximize the number ways it can be arranged. So the law of entropy, that is, the law that says,
entropy always increases, might be better written as “there is a high probability
that entropy always increases”. It’s not governed by physics, but by probabilities.
Entropy when rigorously considered is not really about randomness or disorder,
but it’s about the number of ways in which you can arrange something, and the probability
of that arrangement randomly occurring. Now let’s go a step further and consider
how this can apply to the entire universe. The universe is expanding. Yesterday it was
smaller in size that it is today. This means there were fewer number of ways in which all the stuff
inside could be arranged. Today since our universe is larger, there is more room and so more numbers
of ways to arrange the stuff inside it. So it’s at a higher entropy today than it was yesterday. It is likely
that the universe growing larger is more probable than it growing smaller, but again not impossible.
Going all the way back to the beginning of the universe, at the moment of the Big Bang,
the universe would have been the smallest size, implying that it was in its lowest entropy state.
And this entropy has been increasing ever since. And this increasing entropy might actually be
giving a meaningful definition to the flow of time in our universe. One way to think of time
is as things changing. Things are always changing. Even if you are not moving and
simply staring at a still object like a wall, things are still changing. Your brain is active,
it has chemical and electrical processes that are occurring. Atoms of the wall are still moving,
vibrating to some degree. And since things are always changing in the higher entropy direction,
we can distinguish higher entropy with the forward movement of time. If there were no change,
then perhaps there would be no time. And if this connection of time and
entropy is valid, then time could also be a statistical phenomenon. In other words time
is much more likely to be moving forward, than not moving at all, or moving backward.
If statistics and probability are really at the heart of the way the universe works, then you may
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