OK kids, let’s talk about states of matter.

You know your states of matter don’t you?

We have solids, liquids and gasses, and plasmas, quark-gluon plasmas, nuclear matter, bose-einstein condensates, neutronium, time crystals, and sand.

Come to think of it, maybe I don’t know my states of matter.

Or what a state of matter even is.

Let’s see if we can figure it out together.

You know what a state of matter is.

There's solids, there's liquids, there's gases - different states that the same element or molecule could occupy based on the strength of their chemical bonds.

The strong bonds in a solid keep the material rigid, but heat it up and those bonds break and we’re left with weaker bonds that allow the particles to slip and slide around each other while nonetheless generally sticking together, leaving us with a liquid.

Heat it further and the weak bonds break, allowing particles to fly freely around the room - and voila, a gas.

Some of you may have also learned what happens if we keep heating things up.

Electrons are knocked free from atoms, breaking all molecular bonds in the process and creating a Plasma.

So cool, states of matter are just the different, well, states that atoms can be in.

But wait, the quarks inside protons and neutrons are “matter”.

What is the state of matter of those?

Does it depend on the state of matter of the atoms they’re part of?

And what about materials like sand or glass, which may have different properties to their component parts.

And then there are all those pop-sci media claims of “new state of matter discovered” - time crystals being a recent example.

Are they for real?

To answer these questions, we better figure out what a state of matter really is.

If you were to base your reasoning on the states of matter you learned in school - solid, liquid, and gas, and plasma for those who stayed in school too long - a simple pattern is apparent.

Change in temperature results in change in state, or in a phase.

Phase shifts occur at temperatures specific to the material, for example ice melts into water when temperature rises above the 273 Kelvin mark; then evaporates into a gas a hundred Kelvin higher, and ionizes into a plasma at several thousand Kelvin.

Of course it’s a bit more complicated than this.

Transition temperatures depend on the material, but they also depend on pressure.

For example, water boils and freezes at a lower temperature on a mountain top where the air pressure is low.

Instead of a 1-dimensional relationship between phase and temperature, think of a 2-dimensional relationship with both temperature and pressure.

We call this a phase diagram.

It shows us that things are much more complicated than solid, liquid, gas.

For one thing, there are secret hidden states of matter.

For example, at temperatures and pressures above the critical point, the line between gas and liquid blurs and we have a supercritical fluid which shares properties of both.

The two numbers related on the phase diagram - temperature and pressure - are statistical properties of a large collection of particles.

A single water molecule doesn’t really have a temperature, it has a velocity - but the average energy of motion of all water molecules is its temperature.

A state of matter defines how these various average properties relate to each other.

It defines what we call the equation of state.

For example in an ideal gas, pressure is proportional to temperature and inversely proportional to density.

Different states of matter have different equations of state.

In general the field of physics that studies the relationships between the statistical properties of different states of matter is called thermodynamics.

But a state of matter determines and is determined by much more than the thermodynamic properties, subjective qualities, like, say, “wetness" of water - is an emergent property of that state of matter; one not possessed by the component H20 molecules.

And it’s typically the non-thermodynamic properties that formally distinguish one state from another.

For example solids are rigid having effectively infinite viscosity; liquids are viscous and are incompressible; gasses are compressible and diffuse evenly to fill any size container.

In general, we call some collection of stuff a state of matter if it has sufficiently unique set of emergent behaviors - like the extremely low electrical resistance of a superconductor, or the near absence of viscosity in a superfluid.

OK, so a state of matter is an emergent behavior due to the interactions between components under particular conditions.

Does that mean we can make different states of matter from things other than atoms?

It does.

Let’s start our search for some new states of matter by exploring in the direction we started.

What happens if we increase the temperature of a plasma?

A plasma still consists of composite particles: the electrons are elementary, but the atomic nuclei are little bundles of nucleons - protons and neutrons.

Even in a hydrogen plasma, the lone protons are bundles of quarks.

Just as we tore apart the atom when we made our plasma, if we crank temperature up high enough we can destroy nucleons.

Although we’re going to need it fairly hot - around 7 trillion Kelvin, due to the extremely high binding energies of nucleons.

This is the Hagedorn temperature, and when we reach it quarks are stripped from nucleons to produce a quark-gluon plasma.

This is our next state of matter.

You might wonder if this stuff is even more plasma-like that plasma - with the particles more free to zip around the room.

But actually, the interactions between the gluons and quarks remain significant and so a quark-gluon plasma behaves more like a liquid.

We routinely make this stuff in our particle accelerators, but the quantity is tiny - the result of smashing two nucleons together.

However in the very early universe everything was a quark-gluon plasma, and that may also be true in the cores of massive neutron stars.

So if a quark-gluon plasma is liquid-like, does that mean it can freeze?

It can, and its frozen form is a nucleon.

More general, a hadron, so protons and neutrons but also various exotic combinations of quarks.

A hadron is fairly literally a crystal of quark-gluon plasma - it’s the stuff in its “solid” form.

That’s right, you are made of quark snow.

In fact the whole process of creating quark-gluon plasma is like smashing snowballs in the middle of the arctic, hoping to produce a few droplets of water, which freeze again almost instantly.

The stuff of quarks is generically called quark matter or QCD matter - for quantum chromodynamics - the physics of quark and gluon interactions.

To fully convince you that quark matter has its own states of matter, behold its phase diagram.

Here it's temperature versus baryonic potential instead of pressure, which is basically how much energy quarks can absorb or emit.

Our quark-gluon plasma is actually the analogy of gas in atomic matter, even if it’s behavior is more liquid.

Our hadrons are our “solids”.

If you want to see what it’s like to move to right on this diagram, just burrow into a neutron star.

First the individual quark “crystals” merge together into a fluid of neutrons that we call neutronium, and then the neutrons dissolve and we end up with really bizarre forms of liquid-like quark matter.

The states of matter we’re most familiar with can be explained as particles interacting under classical forces.

But once you bring quantum mechanics into the picture, many strange states of matter become possible.

For example, in degenerate matter like neutronium or Bose-Einstein condensates, all quantum states are occupied, leading to some surprising and useful emergent properties, like superconductivity and superfluidity.

Time crystals are the latest and perhaps weirdest quantum state of matter.

These are configurations of entangled particles that oscillate between states even when they have no energy.

In regular thermodynamics, the lowest energy corresponds to absolute zero temperature, which in turn means zero motion of particles.

The lowest energy state of a time crystal involves real motion, which makes them thermodynamically different than other states of matter - so they qualify as a state of matter of their own.

So it sounds like states of matter really are … exactly that - states of matter, rather than states of atoms.

Subatomic particles can have their own states of matter.

And it turns out that two completely different states of matter can exist simultaneously at different scales.

For example, liquid water contains many little nuggets of frozen “solid” nuclear material.

Different states of matter can be sort of nested within each other.

If that’s true for the subatomic states within the atomic states, what about states formed by components larger than atoms and molecules?

For example sand?

Each grain of sand is a solid, but when you make air flow through sand you can change how those grains of sand interact with each other, and the sand will start acting like a liquid.

When this happens, objects that are light enough will float from the bottom to the surface, something that would never ever happen with a solid.

And yet, the grains of sand never stopped being solid and the air never stopped being a gas.

Here’s something we don’t usually think of as particles: human beings, but they can behave in ways eerily close to states of matter.

In a fairly diffuse crowd, people will walk around steering to miss each other with no trouble.

The crowd behaves in some ways like a gas.

But if you increase the people-density to around 5 per square meter or more, a phase transition occurs.

It starts behaving like a liquid.

The frequent interactions between people cause liquid-like phenomena like currents and waves as individuals lose their autonomy of motion.

This is known as a crowd crush, and it can be very dangerous Fortunately, physicists can come to the rescue here.

Using what we know about gases and liquids - about thermodynamics - it’s possible to spot an impending crowd crush and avoid it by changing the “thermodynamic properties” of the crowd.

Namely, lower the density when you see it’s approaching a phase transition.

And it doesn’t stop with people.

Astrophysicists routinely model the galaxies as a sort of fluid of stars, where the interactions are not electromagnetic, but gravitational.

So, galaxies are fluids of stars which themselves are made of plasmas of hydrogen made of frozen nuggets of quark matter.

So if sand and crowds and galaxies exhibit behaviors that resemble states of matter are these really actual states of matter?

Not technically, but that’s really just a matter of convention.

The fact is, the concept of "states of matter" can help us to understand many kinds of interactions, even between macroscopic “particles”.

Max Tegmark from MIT has proposed that consciousness itself can be understood as a state of matter.

Just like the characteristic properties of a regular state of matter, the conscious mind is an emergent property of a type of information system.

The analogs of temperature, pressure, etc.

are informational parameters like memory, computation, and informational integration; the right combination of which lead to specific emergent properties like self awareness.

Thinking of the mind as a state of matter allows us to use the tools of our material sciences - for example quantum mechanics and condensed matter physics - to help us understand why we see the world the way we do.

Or at least, so claims Max Tegmark.

The definition of state of matter is somewhat slippery; its clear enough when we talk about the common states, but gets a bit blurry on the boundaries or in exotic cases.

Despite this, concept is incredibly useful for helping us understand the behavior of physical systems - from the instant after the big bang to the behavior of crowds, and perhaps to the nature of the conscious mind.

Just think of our universe as nested layers of states of matter, from the smallest to the largest scales of space time.