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It may be the most sacrosanct principle in all of science – something you learned in elementary
school - the idea that overall energy is always conserved, that Energy can never be created
nor destroyed. It can only change form. So for example, when a car is in motion,
but comes to a stop, the kinetic energy of its motion is converted to frictional
heat from the brakes. No energy is lost, it is just converted from one form to another.
Similarly, a swinging pendulum converts it gravitational potential energy when at its maximum
height to kinetic energy at its lowest height. If there were no friction from the fulcrum or air,
the pendulum could theoretically swing back and forth forever. But even with friction,
overall energy is still conserved when you take the heat from friction into account.
What if I were to tell you that although the conservation of energy for all practical
purposes and applications on earth is conserved, on the scale of the universe,
this is not the case. Energy is not conserved in the universe as a whole.
What? How can this be? Stay tuned because I’m going to explain that, coming up right now…
Conservation of energy is a conservation law that states that in an isolated system,
overall energy remains the same over time. There is sometimes some confusion about isolated
system vs closed system. In thermodynamics, an isolated system is one in which no energy or
matter enters or leaves. A well insulated thermos would approximate an isolated system, but there
is no perfect isolated system we know of. A closed system is one in which no matter
enters or leaves, but energy can. A covered pot, or cup of tea would approximate a closed system.
So in an isolated system, that is a system in which no matter or energy enters or leaves,
overall energy remains the same. Energy only changes form
We see examples of this every day. When you are driving and you slam the brakes to stop,
what happens to the kinetic energy of your car? Well, it is converted to heat by the friction from
the brakes. You don’t feel this heat because this is not an isolated system. The heat is dissipated
to the atmosphere. But if you could somehow put your car brake, road and atmosphere in a box,
and measure the heat, you would find that the kinetic energy of the car has
nearly perfectly transformed into heat energy. The same holds true for any isolated system,
and would apply to other phenomena such as the pendulum I talked about earlier.
So, the question we want to ask is whether this holds true for the universe as a whole.
Can we consider the entire universe a well-defined isolated system? Since the universe is everything,
shouldn’t it be the ultimate isolated system? It turns out that the answer not
straightforward. Let’s examine why. If we want to include the whole universe,
we have to include everything from the very small to the very large. Let’s
start with the very small. The behavior at the microscale is described by quantum mechanics,
which is the physics of the smallest scale objects from the subatomic to the atomic and beyond.
At the quantum level, the concept of energy conservation is explicitly
defined. This is illustrated in arguably the most important equation in quantum mechanics,
the Schrodinger equation. This equation is all about energy. It shows that total energy
is equal to kinetic energy plus potential energy. Energy is conserved according to this equation.
This is just one example, but we can invoke other equations as well, in order to show that energy
is explicitly conserved in quantum mechanics. So there is no problem at micro scales. Now
let’s look at the largest scales. The best tool we have to describe
objects at the largest scales such as the earth, sun and galaxies is Einstein’s theory
of general relativity. The core of this theory is represented by Einstein’s field equations,
which in its simplified form, looks like this: I’ve discussed this in several videos in the past,
but let me do a quick recap. The left side describes the curvature of spacetime,
the right side represents the matter and energy contained in spacetime.
What this equation shows is that matter and energy affects the curvature of spacetime. This
curvature is what we perceive as gravity. And the curvature of spacetime affects matter and energy.
The simplest way to summarize this equation is as the famous physicist John Wheeler put it,
“Matter tells spacetime how to curve, and spacetime tells matter how to move.”
The matter and energy is contained in this term on the right side of the equation “t
sub mu nu” – this is known as the stress energy tensor, also called the energy-momentum tensor.
We need to take a closer look at this because this is where energy is defined in General Relativity.
And General Relativity reveals that the derivative of the energy-momentum tensor is zero.
To be more precise, the term on the left is called the covariant derivative,
but for simplification pertaining to what we are discussing, you can think of it as the
derivative. So the simplified way to think of this equation is that the change in energy and
momentum remains zero. This is called the principle of energy momentum conservation.
Note that this equation is not saying that energy stays the same, only that
the combination of energy AND momentum remains the same. In other words only the
combined energy and momentum is conserved. What General relativity tells us is that if
spacetime were standing still, that is, if it were flat and not changing, then energy
would be constant. But if spacetime is curving and changing, then the momentum is changing,
and thus the energy is changing as well. So, astonishingly, it tells us that at
large scales, energy is really not conserved in the universe.
We can point to several observations that confirm this.
The first is the observed expansion of the universe. The first empirical evidence of
this was gathered In 1929 by Edwin Hubble. Then, in the late 1990s scientists discovered
that the universe is not only expanding, but that this expansion is accelerating.
This acceleration is called Dark Energy. The problem with expanding spacetime is
that empty space has energy. If the volume of this space is increasing then energy is
increasing. We know that the energy density of spacetime doesn’t change, but energy density is
energy over volume. If the volume increases, then energy also increases. This phenomenon appears to
indicate that energy is not being conserved. Another consequence of an expanding spacetime
is the observed redshift. The light from distant galaxies is redshifted. As the universe expands,
the wavelength of light also expands. And as we learned from Max Planck:
E equals h nu, where h is Planck’s constant and nu is the frequency, which we can rewrite as the
speed of light divided by wavelength, lambda. Thus, we see that if the wavelength is longer,
the energy is lower. So the photons have
lower energy by the time they reach us. This appears to violate conservation of energy.
Where did this loss of energy go? Well, the energy of the photon is observer dependent. From our
perspective, the photon loses its energy to the expanding spacetime between its origin and us.
Now I know some of you are going to ask, since we know that dark energy is increasing, could
it be that the energy that light waves lose turns into dark energy, thus conserving energy overall?
Well, the problem with that idea is that even if you take all the observed light of the
universe into account, it would not account for the amount of dark energy in the universe.
Dark energy is almost 70% of the energy of the universe, whereas all the matter and light that we
can observe is only about 5%. The lost energy of light would be miniscule portion of all the energy
needed too counterbalance increasing dark energy. The expansion of the universe presents a major
issue with treating the universe as an isolated system. We don’t even know what the size of the
universe really is, so we can’t define what the isolated system would be. We only know the
observable universe, which is about 94 billion light years in diameter. There is a so called
cosmic event horizon which is the end of this observable universe. The galaxies at the edge of
this cosmic event horizon are moving away from us such that the light beyond it will never reach us.
I was watching a video on Magellan TV, today’s sponsor, which showed how it’s
possible that the universe beyond the visible universe could be infinite. And if that’s true,
then the universe would definitely NOT be an isolated system, since we could not put any
boundary around it. In this case we would have to conclude that the universe likely does not
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Now, even if the universe is not infinite, it is probably still the
case that it is much much larger than the 94 billion year diameter that we observe.
So we don’t know what the isolated system in which energy may or may not be conserved consists of.
Should the isolated system be just the observable universe? If so,
what about the galaxies that are moving out of the observable universe. What about their energy?
If we consider just the observable universe as a isolated system, then we are clearly losing
matter and due to E=mc², we are also clearly losing energy from our system
when galaxies leave our observable universe! Now I must point out that some experts believe
that overall energy is conserved in an expanding universe because, they argue, you have to include
the energy of the gravitational field along with the energy of the matter and radiation. In other
words, as distances between objects increase, the increasing gravitational potential between them
can be thought of as a kind of negative energy. How the heck is this considered negative energy?
Legendary physicist Stephen Hawking explained it this way: when you pull two object apart,
you need to expend energy to overcome the gravity that pulls them together;
since it takes positive energy to separate them, gravity must be negative energy. And
this increasing negative energy perfectly cancels increasing dark energy, some argue.
This is not an incorrect way to think of it. The problem is that unlike dark energy,
which has a constant energy density, there is nothing like a constant gravitational density
in the universe. The curvature of spacetime is not defined at every point in space, but is
defined locally by whatever matter and energy may be present. So calculating whether the notion of
negative gravitational energy counterbalancing dark energy cannot practically be done.
But the main point against this notion is that since General Relativity plainly points out that
energy on its own is not conserved, we may be better off just letting go of the idea of energy
conservation at the scales of the universe, even though it is nearly perfectly valid at the human
scales in which we operate. So, practically speaking, our energy conservation equations
are valid. They only begin to show cracks when we start looking at very large scales. So we should
not be throwing out our thermodynamics books quite yet. I’ll see you in the next video my friend.