The weird rules of quantum mechanics lead  to all sorts of bizarre phenomena on tiny   scales— particles teleporting through  walls or being in multiple places at   once or simultaneously existing and not.

But wouldn't it be cool if we could see   some of this magical behavior on at a human  scale.

Well today I'm going to teach you how.

All you need is the second most abundant  element in the universe and absolute cold.

Or if you don't have those, the corpse  of a dead star will do just fine.

Perpetual motion machines are all scams.

But perpetual motion itself is possible.

Sort of.

If you stir a cup of tea you’ll create a  vortex that slows down over time.

But there is a   type of fluid in which the vortex will never  stop—at least theoretically.

Even unstirred,   it will climb the walls all by itself, and  even leak through the microscopic channels   in the otherwise watertight porcelain.

The fluid in question is liquid helium   cooled to near absolute zero when it becomes an  exotic state of matter known as a superfluid.

Superfluidity is the most characteristic  behavior of the bizarre state of matter called   the Bose-Einstein Condensate.

This is a state of  matter in which the weirdness of the quantum world   invades our large-scale reality.

To understand  this, we do need a bit of background—and that   background is our last episode where we talked  about how the behavior of matter depends on how   nature counts its particles—described in the field  of statistical mechanics.

Watching that episode   either right now or right after this episode will  really help your understanding of this phenomenon.

We’ll also be referring to this episode, but  that you can definitely watch afterwards.

First though, let's recap just a little  of what we learned in the last episode.

We saw that we can understand a lot of the  behavior of matter by counting the number   of different ways in which particles can be  divvied up into the available energy states.

Particles will tend to shuffle energy between  each other until they have the most probable   energy distribution.

The shape of that energy  distribution determines the thermodynamics—which   means, how things like temperature,  pressure, volume etc.

relate to each other.

We also learned that there are different types of  particles - bosons and fermions - which shuffle   around their energies differently.

To remind you:  no two fermions can occupy the same quantum state,   which means they can’t have exactly  the same energies.

On the other hand,   any number of bosons can occupy the same state.

In everyday life, this difference doesn’t   matter.

Everything else being equal, a cloud of  bosons and a cloud of fermions behave the same.

But there are circumstances where the  differences become very important.

And   that includes the worlds of the very small—the  quantum world.

But also the world of the very   cold.

There the quantum behaviors of these  different particle types are as clear as day.

In our other previous episode we talked about  the reason for the different behavior of bosons   and fermions—we saw how quantum spin determines  the symmetry of the symmetry wavefunction,   and its this symmetry that determines whether  two particles are allowed to have identical   wavefunctions.

However that episode was on the  mathy side, and also focused on fermions.

For   now I want to try to give you a more intuitive  view - and one that lets us understand the   behavior of bosons, which, afterall, is  what we need to understand superfluids.

In quantum mechanics, we describe particles as  wavefunctions—mathematical objects that encode   the probability that we will observe a  certain position, velocity, whatever,   if we were to try to measure it.

Wavefunctions are  well named, because they’re wavy.

For simplicity,   let’s just look at one component of  a particle’s position wavefunction,   representing its blurry quantum location  in space, which might look like this   wave-packet-a sine wave that tapers off on  either side.

The height of the wavefunction   at any point represents the probability of  the particle actually being in that location.

Now let’s think about two particles moving  together.

At a certain point their wavefunctions   will overlap - and what happens then depends on  the symmetry of the wavefunction.

In this context,   when you have a symmetric wavefunction, then  when they’re in the same quantum state their   peaks and valleys line up perfectly.

A pair of  symmetric wavefunctions can stack, doubling the   height of the peaks and the depth of the valleys.

In the case of an anti-symmetric wavefunction,   if you try to put them in the same quantum state,  the peaks of one will always valley line up with   the valleys of the other, and vice versa.

In  that case, overlapping the wavefunctions causes   the entire thing to cancel itself out, with the  peaks of one negated by the valleys of the other.

The case of the symmetric wavefunction  all of this is straightforward enough to   interpret.

The fact that they can stack  without canceling each other means that   particles of this type—bosons—can be placed in  the same state without breaking any physics.

Fermions, on the other hand, with their  antisymmetric wavefunctions, appear to cancel   each other out.

If the wavefunction encodes their  possible positions in space, then when they cancel   out there’s zero probability of either particle  being anywhere.

That doesn’t mean that pairs of   fermions destroys each other.

That would break  several conservation laws—from conservation of   energy, conservation of charge, even of quantum  information.

A wavefunction can’t just be deleted   from the universe.

So rather than telling us that  fermionic wavefunctions cancel each other out when   the overlap, this canceling effect actually tells  us that fermions can’t ever overlap perfectly.

They can not ever occupy the same state.

In fact if you try to push two of the same   type of fermion into the same state, they will resist with a force so powerful that, for example,   it can help a dead star resist collapsing  into a black hole.

But that’s another story.

This way of describing the difference between  bosons and fermions is extremely heuristic—it’s   heavy on analogy and shouldn’t be interpreted  too literally.

For one thing, the part of the   wavefunction that’s symmetric or antisymmetric  doesn’t look like a simple sine wave—it’s the part   of the wavefunction associated with the rotational  state, not the position state.

It’s connected to   particle spin.

In fact, spin defines whether  a wavefunction is symmetric or antisymmetric.

All particles with values of quantum  spin that are an integer—so 0, 1, 2,   etc.

are symmetric and are bosons.

Those with half-integer spin—½, 3/2,   etc—and antisymmetric fermions.

For a  more nuanced description of all of this,   including a lot more on this spin stuff,  check the episode I mentioned earlier.

But for now, let’s just take one  critical fact from all of this:   bosons, with their integer spins and  symmetric wavefunctions can be stacked,   fermions, with their half-integer spins  and antisymmetric wavefunctions, cannot.

And by the way, all of the elementary matter  particles—everything that makes up physical   stuff—are fermions.

And the inability for them  to perfectly overlap is why physical stuff   is physical in the first place—for example,  atoms have structure because electrons can’t   all fall into the lowest atomic orbital together.

On the other hand, photons and other bosons can   overlap completely and that's what makes lasers  possible—a laser beam consists of many,   many photon wavefunctions that are perfectly  overlapping, or in phase with each other.

So what would it look like if we could turn fe rmions into bosons?

Would it be possible to make   an electron laser?

Could we make atoms that  collapse into super-dense states?

Actually,   we can turn fermions into bosons, and one  possible result is the Bose-Einstein condensate,   and this superfluid thing that I’ve been  teasing at for the past several minutes.

Fermion wavefunctions have half-integer  spin.

Multiple fermion wavefunctions that   are somehow connected to each other have spins  equal to the sum of those spins.

For example,   a proton is made of three quarks, two with +½ and  one with -½, adding those up you get a proton that   also has a spin of a ½ so is a fermion.

But what  if we could connect just two spin-½ particles?

That would give us a to spin of 1 which is  an integer and so it should produce a boson.

Or take the helium-4 atom.

It has two protons,  two neutrons, and two electrons - all spin-½   particles.

In this case, 3 are spin +½ and  3 spin -½, which gives the overall atom a   spin of 0.

That’s an integer, therefore Helium-4  must be a boson.

Its component particles remain   fermions and behave as fermions with respect  to each other within the atom - they have   different internal energy states.

But the entire  helium-4 atom acts like a boson with respect to   its neighboring helium-4 atoms.

That doesn’t mean  they overlap in physical or position space—their   internal fermions would resist that.

But the atoms  as a whole can occupy identical energy states.

We really only see the effect of this at extremely  low temperatures.

So let’s do an experiment and   cool down some helium-4.

At atmospheric pressure  and room temperature the helium is a gas.

At this point it wouldn’t matter what the gas  was—the shape of this distribution would look   the same and only depend on the temperature.

But  as temperature drops, more and more particles   move to lower energies.

At around 5.2 K  the gas condenses into a regular liquid.

But as we cool things down further,  things start to look different.

If this was a gas of fermions, the inability of  particles to occupy the same energy levels would   prevent all particles from falling to the lowest  energy states.

That has its own bizarre effects,   especially at very high pressures,  but we’re talking about bosons here.

For the boson Helium-4 atoms, there’s nothing  stopping all particles entering the lowest   energy state.

When we hit a temperature  of 2.17 K, close to absolute zero,   that’s exactly what happens.

Rather  than having a distribution of energies,   all particles have the same energy—the lowest  possible energy.

In fact they can’t have any   other energy because at this low temperature,  there isn’t enough energy to jump to higher   states.

But they also can’t lose energy -  they already have the least possible energy.

In normal states of matter, when two atoms  get close to each other they repel each other,   exchanging energy.

Typically one loses energy  and one gains it.

But when all the particles   have the same energy then interactions that  require the exchange of energy aren’t possible.

For example, a fluid made of such particles  loses all friction.

Normally, when fluids flow,   currents or streamlines within them that have  different speeds within the fluid drag on each   other—we call that viscous drag.

That drag  is caused by particles at the streamline   boundaries colliding and exchanging energy,  and it causes the flows to slow down.

Such a   fluid has viscosity—the higher the viscosity, the  more drag, and the less easily the fluid flows.

But the streamlines in very cold helium-4 don’t  exchange energy with each other—they slide past   each other without friction, and so the fluid  has zero viscosity.

It is, in fact, a superfluid.

And now finally we get back to stirring  our cup of tea.

Particle interactions with   the walls and with each other cause the  circular currents to slow down and stop.

But if your tea is superfluid helium-4, then  these interactions can’t happen.

Stir the cup   and the vortex should last forever.

In reality,  this would also require the walls of the cup to   be perfectly smooth.

According to this  cool simulation, when superfluid flows   around the microscopic bumps of a container  wall it forms tiny perfectly-flowing vortices   that do actually slow down the overall flow,  but in a different way to a regular fluid.

By the way, saying that all particles  in a superfluid have the same energy is   a bit simplistic.

Energy states can vary  a bit across the fluid due to different   speeds of its streams, different  heights in the gravitational field,   etc.

But the point is that particles near  each other are extremely close to having   the same energy state and so are restricted  in how they can interact with each other.

There are a few other weird superfluid  behaviors.

All fluids will creep up   the walls of their containers a little  bit due to the mild attraction between   the atoms of the fluid and container.

But in  a superfluid, the frictionlessness allows the   fluid to literally flow up the wall, at least once  that wall is coated with enough fluid to itself be   frictionless.

Then when the flow drops over  the other side, it acts like a siphon, and can   drain your container of your precious helium-4.

Superfluids will also flow through microscopic   fissures and pores in a container, causing it to  appear to leak through apparently solid material.

This Houdini-like nature of helium-4 reminds me of  quantum tunneling—how quantum objects can teleport   short distances through solid barriers.

But  this superfluid thing is NOT quantum tunneling,   however it is a true quantum effect, visible  on a macroscopic scale.

All of the behaviors   of superfluids are due to the quantized  nature of the energy levels in the fluid.

Superfluids aren’t just a novelty found in physics  labs.

They are believed to exist for example   inside neutrons stars, where fermionic neutrons  team up to act like bosons, and form these   whirlpools trom the surface of the star to its  core that hold insane amounts of energy.

They last   for a long time because-superfluid-but when they  finally do break they are believed to cause the   neutron starquakes that we see in the glitches of  pulsar signals.

And superfluidity is basically   what electrons are doing inside the otherwise  solid crystal lattices of a superconductor,   as we showed you in our episode on quasiparticles.

In that case, the electrons connect with each   other over large distances to form Cooper pairs,  so that these fermion pairs also act as bosons,   leading to frictionless flow of the electrons.

This manifests as superconductivity.

At a more fundamental level, the fermionic quarks  can join in pairs to become bosons, which allows   them to serve as strong-force-carrying mesons.

The bosonic nature of the Higgs field allow its   particle to form a slightly different kind of  condensate—one which fills the entire universe,   and which is responsible for giving elementary  particles their mass.

Now I feel like we’ve   pointed you to earlier episodes even more than  we usual do in this episode.

But, yeah, we have   one on the Higgs stuff also.

But by now I think  we’ve all realised that, just like with bosons,   there is no limit to the number of overlapping  references to past episodes of Space Time.