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Ash viewers. In physics there is one ultimate goal, and
that is to describe the world we are in. The hope is that one day we will find some underlying
theory that connects all the little pieces into a grand puzzle, forming a theory of everything
- the ultimate theory describing the world we find ourselves in.
So far, the closest we have gotten to this is the standard model of particle physics.
This is like the periodic table of elements for fundamental particles. And the equations
behind this theory are the most accurate we have ever had in physics. It’s pretty good,
but there are a lot of missing pieces, things that the theory just doesn’t account for
like dark matter, dark energy and a quantum theory of gravity, as well as several other
issues. But there is a theoretical idea that many
people think could get us closer to a theory of everything, and could fill several gaps
in the standard model. This theory is called supersymmetry, which
is the idea that matter particles and force carrying particles are connected through a
new kind of symmetry. Although there is no experimental confirmation of this symmetry,
and a perfect supersymmetry almost certainly doesn't exist, it is still important because in physics,
symmetries can be broken. And a broken supersymmetry
could still explain a lot. Supersymmetry is important because if it’s
true, it could solve several problems in our current understanding of the universe. Namely,
it could explain the hierarchy problem with the Higgs boson – why it has a such a low
mass, it could unite 3 of the fundamental forces - the strong force with the electroweak
force, and it could provide a perfect candidate for the elusive dark matter particle.
What is supersymmetry? Why is this idea important? And how would it allow us to better understand
the nature of the universe. That’s coming up right now.
Let’s first understand what symmetry means in physics.
A symmetry exists if you can make a change and that change makes no difference. The physics
governing the laws of the universe seem to be based on symmetries.
For example, physicists have identified several fundamental symmetries in nature. Three of
the more important symmetries are: charge, parity and time.
Charge symmetry means that if you flip the charges of all the particles involved in an
interaction to their opposite charge, you'll get the same interaction. Parity is the idea
that if you look at the mirror image of an interaction, you get the same result. And
time symmetry is the observation that if you run an interaction backward in time, it looks
the same. Together, they are called CPT for charge, parity, and time.
Physical interactions obey most of these individual symmetries most of the time, but not all the
time. There are violations sometimes. But physicists have never observed a violation
of all three symmetries, that is CPT symmetry, at the same time. This means that if you take
every single interaction observed in nature, flip the charges, take the mirror image, and
run it backward in time, those interactions behave exactly the same.
Why are symmetries important in our desire to find a theory of everything?
Because if we find that the universe respects certain symmetries, then this will lead to
new rules that the universe obeys. And this would limit the number of ways that
the universe could be organized. It would lead to new predictions, that would
better point us in the direction of the more likely theory of everything.
Supersymmetry, or SUSY for short, is a symmetry between matter particles and force particles.
In the standard model, the matter particles are the Fermions on the left side, and force
carrying particles are the Bosons on the right side. The key difference between these two types
of particles is spin. All matter particles in the standard model have a spin of ½. Whereas
all Bosons in the standard model have a spin of 0 or 1.
What is spin? Spin doesn’t mean that the quantum object is spinning like a planet.
It is a term related to the way particles are deflected through a magnetic field. They
act like a spinning magnet, but that is not what is actually physically happening
at the quantum level.
The rule fermions obey is that no two of them can be completely identical. They can’t
be in the same spot at the same time with the same spin.
This is what the Pauli Exclusion Principle is all about. And this is the reason that
only two electrons, with opposite spins, can ever be in the same orbital in atoms, but
never more than two, because then at least two of them would be identical.
This rule does not apply to bosons, as many identical bosons can be at the same place
at the same time. The supersymmetric partners of the Fermions
would be bosons, and so they could also be found with others in the same place and time.
Fermions are what makes up the matter in the universe.
Bosons are what carry the forces between matter particles. These two classes of particles
are quite different, so why does anyone think that they could be treated identically.
If you look at the standard model, it seems a bit arbitrary that there should be many
more matter particles than force carrying particles.
Does the universe favor matter over the forces that allow interactions?
Since the standard model is littered with symmetries, like time, parity, charge, and
others, to many physicists, it seems that a fundamental symmetry between fermions and
bosons should also exist. Supersymmetry is the term used to describe
the symmetry between matter and the governing forces.
There are different flavors and modifications on supersymmetry theories, but the essential
concept is fairly simple. We take the mirror image of the standard model. By this I mean
that every particle has a mirror particle, or a supersymmetric counterpart.
Each mirror particle is of the opposite type, so each fermion has a supersymmetric counterpart
that is a boson. Likewise, all mirror particles of the bosons
would be fermions. And with this simple idea of supersymmetry, we can bring a balance to
the model such that we have the same number of fermions as bosons.
Matter is equal to the forces. The naming convention for the supersymmetric
counterparts of the fermions is that we add an “s” in front of the names of the quarks
and leptons, so the mirror particles of the fermions, which are now bosons, are called
squarks and sleptons. For example, the mirror particle of the top
quark is the stop squark boson. The mirror particle for the electron is the
selectron boson and so on. Likewise, the mirror particles of the bosons,
which are fermions gets a suffix “ino”. For example, the Higgs boson mirror particle
is the Higgsino fermion, and the gluon counterpart is the gluino fermion, similarly photino,
wino and zino. You might ask what is the point of all this?
Is it really important that there are an equal number of bosons and fermions? Do we really need
such a symmetry? Well, we cannot be sure of that. But there are some reasons why such
a theory could be desirable. It would help us understand the universe better,
if it is correct. In the early days of the standard model going
back to the 80s, physicists had begun to notice some issues with the model already. In general,
there are 3 main reason why supersymmetry is a good idea.
1) It would solve the low mass problem of the Higgs boson.
2) It would unify 3 fundamental forces: electromagnetism, the strong and the weak force.
3) It provides a solution to dark matter. The first problem in simple terms is that
the mass of the Higgs boson appears unnatural, or at least very finely tuned.
The Higgs has a mass of 125 GeV. Theoretically, this seems improbable.
Why? This is related to how quantum corrections affect the mass of the Higgs boson. In a simplified
way, we can write the mass of the Higgs boson as follows:
There is a measured mass, which is what we can measure in experiments like at
the LHC (Large hadron Collider). M_corrections is the corrections to the mass
calculated based on the equations of the standard model.
And M_naught is a tuned parameter called the bare mass. The standard model doesn’t tell
us what this value should be. We know the measured mass from experiments
at the LHC. The problem is that when calculate the m_corrections
using the equations of the standard model, this turns out be a very larger number, many
orders of magnitude higher than the measured mass. In fact, based on this, m naught would need
to be almost equal to the calculated m_corrections but with opposite sign, which is 1.2x10^19 GeV,
to arrive at the measured mass 125 GeV. In other words, this m_naught parameter would
need to be so high that it almost exactly cancels out the enormous quantum corrections
calculated by theory, such that the Higgs measured mass is only 125 GeV. This high value
of M_naught seems so unnatural that it hints at finetuning, or at least an unlikely coincidence.
This is where supersymmetry can help better explain the measured mass of the Higgs.
Extra bosons from supersymmetry, like the stop squark or some other supersymmetric
bosons, could cancel these extremely large quantum corrections
because bosons contribute opposite to the Higgs mass compared to the fermions. This
equation highlights this fact: In this case the extra particles from supersymmetry
can solve the Hierarchy problem, because there would no longer be these enormous quantum
corrections. In the absence of these corrections, it would
make sense that the Higgs is a fairly light particle just as we have measured it.
Next, there is the question of the unification of forces. The standard model accounts for
the electromagnetic, strong, and weak force, but not gravity and that is another issue
with the Standard model. Physicists believe that at some fundamental
level all forces are united, and that there is some theory that unifies the forces and
explains physics in a unified way. We have good reason to believe that this could be
possible, because history has shown us that forces seem to unite at some higher level.
For example, James Clerk Maxwell unified electricity and magnetism which were once thought to be
two completely different forces, with his equations of electromagnetism.
We have since gone further because in the 20th century physicists showed with the electroweak
theory, that electromagnetism and the weak force are also united at a deeper level.
So it makes sense that the other forces might also be related in some deeper way forming
a more fundamental unified theory of forces leading to a theory of everything.
Each force of the standard model has some coupling constant that reflects the strength
of the force. These couplings constants are not actually constant because they change
at higher temperatures. Physicists expect that the coupling constants
should unite at some very higher temperature where the forces unite, thus at some point
the different coupling constants of the different forces should become equal.
In the standard model, this doesn’t initially seem to be the case.
But adding the extra particles from supersymmetry could change how the couplings change at higher
temperatures such that they might unify at some point. This is because the temperature
dependence of the coupling depends on the number of particles of the theory.
Now finally there is issue of dark matter. A problem that has haunted physicists for almost
a century and we still haven’t resolved it.
Dark matter, if found could explain fundamental astronomical observations such as why our
galaxy stays together even though the stars in the outer edges are moving much too fast
according to Newton’s laws of gravitation. They should fly apart, unless there is more
matter than we can see. It’s called dark matter because we can’t see it, and if it
exists it would form a halo around most galaxies. Calculations show that there is at least five
times as much dark matter as ordinary matter that we can see.
An undetected supersymmetric particle could provide a perfect candidate for this dark
matter particle. It has to be a stable, electrically neutral, and massive.
The lightest supersymmetric particle would be stable, and very massive. We don’t know
which particle because we don’t know which one is the lightest.
Why would supersymmetric particles be very massive? Because if they were light particles,
we would have detected them in particle accelerators by now, given the energies we can produce.
Since we haven’t detected them, scientists believe that they must have more energy (or
mass) than can be produced at our most advanced particle accelerator, like the LHC – perhaps
1000X or more than the mass of the proton. So, if the dark matter particles are very
heavy, then you don’t necessarily need that many particles relative to the number of standard
model particles to have 5 times more dark matter mass in the universe.
This thus supports the idea that a relatively small number of supersymmetric particles could
make up the dark matter density in the universe. You might say, I thought symmetry meant that
you change one property, but everything else stays that same,
like antimatter is exactly the same as matter but with opposite charge.
So shouldn’t supersymmetric particles be just like ordinary particles, but just with
different spins corresponding to fermions and bosons?
Well, in physics symmetries exist, but they can also be broken. This is true for the electroweak
force. The force particles involved in electromagnetism
and the weak force are photons, W and Z bosons.They were theorized to all be massless, meaning their bare mass was zero.
But the symmetry associated with those particles is broken by the Higgs field. That’s why
the Higgs field was theorized to exist. The idea is that “superness” could be
a conserved quantity, like charge or energy. Superpartners would then not be able to decay
to the ordinary fundamental particles of the standard model that we see. So they would
be stable. So why haven’t we handed out the Noble Prize
for supersymmetry already? Well, because it’s only a theory and we haven’t discovered
a single supersymmetric particle. But there could be two good reasons why we
haven’t detected them. The first reason as I stated already could be because the particles
are simply so heavy, that we cannot produce them in our best accelerators.
The second reason is that if they are indeed dark matter particles then they must be WIMPS,
or weakly interacting massive particles. So we could have produced these, but simply not
detected them because their interactions are so weak or rare.
The math and concept are quite clever, and the theory could explain some important aspects
of physics. As time passes though, it seems less and less likely to be correct,
but all hope is not lost, because all we have to do is detect one of them, and that would
bring us much closer to a theory of everything. A theory of everything and the supersymmetry
are very complex subjects. So don’t fret if you found yourself a little lost as I was
explaining these ideas. What I’ve found is that an understanding of the fundamentals
of science is crucial to understanding the most complex ideas.
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