The video “Thermodynamics and the end of the Universe” explained how according to
the second law of thermodynamics, all life in the Universe will eventually end.
However, after watching, many people have written comments questioning whether
or not the second law of thermodynamics is actually a fundamental law of physics.
For example, the second law of thermodynamics states that this event can never occur.
However, many people have commented that although the
probability of all the balls gathering back together in just one area
of the box is very low, the probability is not zero.
Therefore, some people have argued that the second law of thermodynamics is not
a fundamental physical law due to the fact that it can theoretically be violated.
Other people have argued that the second law of thermodynamics
is not a fundamental physical law for a very different reason.
They commented that even if we had never heard of the second law of thermodynamics,
we would still be able to calculate the future paths of these balls
just by using the other laws of physics, such as Newton’s Laws of motion.
Therefore, they argue that the second law of thermodynamics
is not a fundamental law because it does not say anything new
about the universe that was not already implicit in the other laws of physics.
Unfortunately, it turns out that neither of these arguments are valid.
To the best of our knowledge, the second law of thermodynamics
is a fundamental law of the Universe, and one of the most important ones.
The second law of thermodynamics states that a property that we call
the “entropy of the Universe” always increases.
Entropy is a measure of the number of different ways that a state can occur.
For example, suppose we have five objects and two spheres.
If one of the five objects is in the right sphere,
there are five different ways this can happen.
On the other hand, if we have two objects in the right sphere,
then there are many more ways this can happen.
When there are more ways that something can happen,
we give this a name, and we say that this state has a higher entropy.
A state in which all the objects are in the same sphere has the lowest entropy,
because there is only one way that it can happen.
The more evenly spread out the balls are between the two spheres,
the higher the entropy.
Since the second law of thermodynamics says that
the entropy of the universe always increases, this means that all the balls
will be evenly spread out throughout the two spheres if we wait long enough.
It also means that once the balls do spread out,
they will never again gather together in just one of the spheres,
no matter how long we wait.
But, what about the two criticisms of the second law of thermodynamics?
After all, if which sphere each ball ends up in is just a matter of probability,
isn’t it at least theoretically possible that the balls will eventually
end up all gathering back together inside just one of the two spheres?
Also, if we can predict the future path of each of the balls
using Newton’s Laws of motion, wouldn’t we have been able to
predict that the balls would evenly spread throughout the two spheres,
even if we had never heard of the second law of thermodynamics?
Let us address this second question first.
In order to be able to predict the future path of a particle,
we need to know two things.
One of these is the laws of physics.
The other is the starting conditions.
If we have no knowledge of the starting conditions of the particles,
then knowing the laws of physics will not do us any good.
If each set of starting conditions was equally likely to occur,
then the starting conditions which we would most likely get is one in which
the entropy was already at the maximum possible value to begin with.
The second law of thermodynamics can therefore be viewed as a statement
about the initial conditions of the universe, and about the
initial conditions of every subset of the Universe.
Without the second law of thermodynamics,
we could just as easily live in a Universe where life never existed,
due to the fact that the entropy of the Universe had always been
and will always continue to be at the maximum possible value.
And in fact, that is what would be the most likely scenario
if each set of possible initial conditions was equally likely.
Let us recall that with the exception of the second law of thermodynamics,
all the other laws of physics work the same way both backwards and forwards in time.
That is, if you reverse the direction of the particles,
and then follow the laws of physics, you will get the same outcome in reverse order.
Therefore, if we know a set of initial conditions, we can
use the laws of physics to run a simulation forward in time to predict the future,
or we can use the laws of physics to run a simulation backwards in time
to determine the past.
If every possible set of initial conditions is equally likely
in a physics simulation, there are two types of initial conditions that
would be extremely unlikely to occur.
The first of these two extremely unlikely scenarios is a
random set of initial conditions where, if you run the simulation forward in time,
the entropy would decrease as a result.
The second of these two extremely unlikely scenarios is a
random set of initial conditions where the entropy would decrease
as you run the simulation backwards in time.
The second of these scenarios is equally unlikely to the first.
Yet, this second scenario is precisely the Universe we live in.
Since all the other laws of physics are symmetrical with regards to time,
a Universe in which the entropy constantly increases with time is
no more likely than a Universe in which the entropy constantly decreases with time.
This is why the second law of Thermodynamics
says something very profound about the initial conditions of the Universe,
and this could never be derived from the other known laws of physics.
But, what about the other criticism of the second law of thermodynamics?
What about the fact that the second law of thermodynamics
only deals with probabilities, and that it is therefore still theoretically possible
that the balls will all gather together again in one small area of the box.
Well, according to Quantum Mechanics,
it appears that the behavior of all particles is inherently probabilistic,
even on a subatomic scale.
For example, the electrons orbiting the nucleus of an atom
are described by what we call a wave-function.
The wave function describes the probability of
where we will see the electrons when we look.
As we move far away from the nucleus of the atom,
the probability of finding an electron goes down very rapidly.
However, there is no point in space anywhere in the entire universe
where the probability goes down completely to zero.
Therefore, although it is extremely unlikely, it is theoretically possible that
all the particles in our bodies will suddenly appear on the other side of the Galaxy.
This is in exactly the same way in which although it is extremely unlikely,
it is theoretically possible that all the balls will gather together again
in one small area of the box.
However, these events are so unlikely that we would
most likely never see them occur, even if we waited
several orders of magnitude longer than the present age of the Universe.
This is true both with regards to the quantum probability,
and with regards to the probability of all the balls gathering together again
in one small area of the box.
Also, it is interesting to note that although the second law of thermodynamics
was discovered long before quantum mechanics,
the second law of thermodynamics seems to hold just as true
for quantum mechanical systems as it did for classical systems.
Whereas Quantum Mechanics overturned even our most basic assumptions
of how the universe operated, the second law of the thermodynamics
survived completely intact.
But, one of the negative aspects of the second law of thermodynamics surviving
is that it implies that all life in the Universe will eventually end.
Detailed information about this is available in the video on this channel titled
“Thermodynamics and the End of the Universe.”
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