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Take a look in the mirror, the left side of your body is almost identical to your right
side.
In nature, we find the same thing in plants and flowers.
This is called symmetry.
We can not only see it around us, but more fundamentally, symmetries seem to be written
within the blueprint of the universe.
For example, symmetries in quantum mechanics result in 3 of the fundamental forces of nature.
They lead to the electromagnetic, weak and strong forces, as I showed in a prior video.
However, as important as symmetries are, there is something that is at least as equally profound.
And that is the fact that certain symmetries can be broken.
And without these broken symmetries we would not have the universe that you and I are familiar
with, and there be no life as we know it.
I’m going to show you how no mass would exist in the universe without breaking symmetries.
But how can symmetries be fundamental if they can be broken.
What are broken symmetries anyway?
And what would the universe be like, if we didn’t have broken symmetries?
That’s coming up right now…
Let’s take a look at what symmetry is.
A simple example is a mirror image.
Symmetry, in physics, is when the properties of particles don’t change after being subjected
to transformations or “operations.”
The simplest example is the fact that the laws of physics are the same whether you are
here, or in China – this is space translation symmetry.
Or the laws of physics are the same today as they were 100 years ago.
This is time translation symmetry.
Symmetries like this show us that mother nature has some simple rules it uses to build the
universe.
But it also sometimes breaks certain of these rules.
Consider the following graph which depicts an energy potential in physics.
We have two minima as shown on the left and right side, and a maximum in the middle.
If we put a mirror vertically along the center, the mirror images are identical.
In other words, the right side is equal to the left site.
Again, this is similar to how humans are also symmetrical along the central vertical axis,
at least externally ignoring minor asymmetries.
Imagine we have this potential.
Now if I asked you to place a ball such that you don’t break this symmetry,
where would you put it?
Well, you would only have one choice.
You would put it in the middle, at the maximum, because this way the mirror images would each
contain half the ball, such that combining the halves of the graph would lead to a complete
round ball and the full graph.
What if instead, we put the ball in one of the minima, let’s say on the left side.
We again place a mirror in the middle.
Now the mirror image of the left side, does not represent what the graph really looks
like.
The symmetry no longer exists.
The symmetry is broken if we put the ball there.
Likewise, it would also be broken if we put the ball on the right side.
This is not just a random example, this is a visual representation of how the Higgs mechanism
works to impart mass to fundamental particles.
Certain fundamental particles break symmetry by not being in the center, by being in the
non-zero potential of the Higgs field.
I made a video on this here, if you want to find out more.
But why does the universe appear to obey certain fundamental symmetries, only to sometimes
break them?
Why is it inconsistent?
Well, we don’t have a satisfactory answer to this question, other than to say that the
universe wouldn’t work the way we observe it to work without symmetry breaking.
Unfortunately, why questions are rarely if ever answered in physics.
We can explain how things work very well, but not why.
Symmetry breaking must occur in order to explain any mass in the universe, which is clearly
what we observe.
Why do I say mass can only be explained by symmetry breaking?
The problem of mass is fundamental to the standard model’s construction.
At its core it has 3 symmetries called U1, SU2 and SU3.
Each symmetry is associated with a fundamental force of nature, namely the Electromagnetic,
weak force, and strong force respectively.
In other words, these symmetries result in three of the four fundamental forces.
These form the basis of the universe we live in.
Without them, there would be no nuclei, no atoms, no chemistry, no structures of any
kind, and certainly no life as we know it.
And these forces, in turn, are mediated by force-carrying particles, namely the photons
in electromagnetism, the W and Z bosons in the weak force, and gluons in the strong force.
Now here is the issue.
These particles must all be massless according the equations of the standard model.
This is a demand from the symmetry of the equations.
They give you massless bosons not massive bosons.
This also includes the Higgs boson; it must also be massless according to the equations.
Furthermore, since all matter particles called fermions also get their mass from the Higgs
field, fermions would also be massless.
This is clearly not the case, because fermions do have mass.
And in the case of bosons, the theory describing the weak force can only work if the W and
Z particles have mass.
Why?
This has to do with the fact that the weak force has a very limited range.
If W and Z bosons were massless, they would work like electromagnetism with unlimited
range. But that's not how they work.
So how do masses of the fundamental particles come about?
They come about due to the Higgs mechanism which is a result from symmetry breaking.
What do I mean?
Briefly, modern quantum theory shows that all particles are excitations in fields that
permeate the entire universe.
The vacuum expectation value of these fields is zero.
Expectation value is the average of all possible measurement outcomes weighted by their probabilities.
Zero would be the expected value for all these quantum fields.
This is a difficult concept to understand, so let me explain this another way.
The Higgs field is a little different than every other field.
The difference is that the lowest energy state of all the other fields is zero.
This means that even though they are modulating and changing, meaning that particle and antiparticles
are quickly coming in and out of existence forming and annihilating all the time, all
the energy used to create these virtual particles which are then annihilated
adds up to a net energy value of zero.
The universe registers this as an overall zero energy state for these fields.
But the Higgs field is different . It’s non zero, even in empty space.
It is in fact 246 giga-electron volts or GeV.
To give you a meaningful comparison, the energy or mass of a proton is only about 1 GeV.
Going back to our Mexican hat potential, the X-axis represents the expectation value.
The Y axis is potential energy.
The ball represents the Higgs field.
When the theory is written in a symmetric state like where the ball is in the center,
again the ball represents the Higgs field, the expectation value of the Higgs Field in
this state is zero.
Everything is massless at this point.
This was the case in the early universe when the energy and temperatures were much higher.
But at lower temperatures, the energy potential of the Higgs field changed.
That is, the ball dropped to a lower energy point.
This is where we are today.
The Higgs field has an even lower energy point where the expectation value is non-zero.
This breaks symmetry.
This means our Higgs field becomes massive at this lower energy state.
What this means is that any fundamental particle that interacts with the Higgs field at this
non-zero potential gains a rest mass.
All the mass associated with the particles of the standard model is due to the fact that
they interact with the Higgs field.
Particles that don’t interact with the Higgs field remain massless, like the massless photon.
This is the so-called Higgs mechanism, and is the way in which certain symmetries of
the standard model are broken spontaneously to impart mass to fundamental particles.
But I stated that ALL mass is due to symmetry breaking, not just the mass of fundamental
particles.
How is that explained?
The Higgs field does not explain most of the mass in the universe.
The mass of protons and neutrons, which is almost the entire mass of atoms, comes mainly
from the binding energy that keeps quarks glued together inside protons and neutrons,
as well as the biding energy that keeps protons glued to other protons and neutrons in the
nucleus.
Put another way, it comes from gluon interactions associated with the strong force.
If you added up the mass of all the fundamental particles that make up atoms, it would only
amount to about 1 percent of their mass.
99% of the mass comes from biding energy due to the strong force.
So now the question is, what kind of symmetry breaking explains this binding energy?
It turns out that other than the gauge symmetries, or force symmetries, which give us the three
fundamental forces, there are also other symmetries in the Standard model.
For example, there is chiral symmetry.
We can think of this as the symmetry of a mirror image.
A chiral symmetric theory treats left handed and right handed particles the same.
For example in such a theory, if we swapped a left handed particle in any reaction, with
a right handed particle, nothing would change.
But the standard model is a chiral theory, meaning that it does not treat left and right-handed
particles the same.
For example, the weak force only acts on left handed, not on right handed particles.
In addition, as far as we know, only left handed neutrinos
exist.
Right handed neutrinos have never been detected.
Consider a left-handed up quark.
It has a mass of around 2.3 MeV.
Now consider the anti-particle of this quark.
Since it’s an antiparticle, it will be right handed.
When these two quarks are bound together, this combination is called a meson.
If left and right chirality were treated equally, this meson would annihilate with a net energy
of roughly zero.
In other words, the combination of a quark/anti-quark pair would result in zero mass.
However, if chiral symmetry is broken, they are not treated equally, and the net energy
is NOT zero.
In fact something remarkable happens to the mass when these two particles are bound together
by gluons.
The total mass is not 0, and it’s not 4.6MeV if you were adding the individual masses of
the quarks together, but a whopping 135 to 140 MeV.
Where did this increase in mass come from?
It comes about due to chiral symmetry breaking.
As the quarks become confined by the strong force via the exchange of gluons, chiral symmetry
breaks.
The gluons form a kind of cloud around the quarks.
This confines the quarks, breaks chiral symmetry, and generates the binding energy that is measured
as mass of the meson.
The same phenomenon occurs in protons and neutrons.
So for example, in a proton, if you add the individual masses of the three constituent
quarks, it adds up to only 9.4MeV.
But the actual measured mass of a Proton is, 938MeV, a difference of nearly 100x.
The additional mass is due to chiral symmetry breaking from the gluon cloud interactions.
This is the origin of 99% of the visible mass in the universe.
The other 1% is due to the mass of fundamental particles from the Higgs boson.
We can visualize the symmetry breaking of quarks in a similar way as the symmetry breaking
of the Higgs field.
At a high energy state, such as the one that existed in the early universe, the expectation
value for the quark/anti-quark pair was zero.
This is a state where chiral symmetry existed.
But as the universe cooled to the energies of today, this symmetry was broken, and today
the result is that quark/anti-quark pairs have a non-zero mass due to the gluon clouds
around quarks.
Now I want to point out that this is the cutting edge best explanation we have today of how
mass comes about, but you should know that this is an active area of research where the
details are still being worked out.
So, we are going to learn a lot more in the coming years.
But for now, if you want to learn a lot more about the settled science that we do know,
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