In order to make a nice, clear ice cube for your drinks, it’s important to consider quantum fields.
First, boil to release dissolved gasses, then make sure the freezing extends through the cube
from a single surface. If the crystallization process starts from multiple nucleation points
then there’ll be imperfections in the lattice structure where the regions of spreading ice
meet - what we call topological defects. So where do quantum fields come into all of this? Well, it turns out the
universe is a gigantic ice cube, and the imperfect freezing of its quantum fields right after the
Big Bang very likely left vast topological defects stretching across the sky. These are
cosmic strings, and many physicists think that they have to exist, and that we can find them.
Reality has cracks in it. Universe-spanning filaments of ancient Big Bang energy,
formed from topological defects in the quantum fields, aka cosmic strings. They have subatomic
thickness but prodigious mass and they lash through space at a close to the speed of light.
They could be the most bizarre undiscovered entities that probably actually exist. To understand cosmic
strings, and to convince you that they probably do exist, we need to understand phase transitions
in quantum fields - we need to see how a whole universe can freeze like a badly-made ice cube.
Heat up ice and it melts, keep heating the water and it vaporizes, more heat still and that water vapor
ionizes into plasma. But that’s not the final phase transition. Keep heating until you hit
temperatures of the extremely early universe and a phase transition occurs in the quantum fields that
underlie all particles. Just as with water, a field’s inherent temperature massively changes its
behavior. For example, the force-carrying field of the modern universe has a complicated structure.
There are many different ways it can vibrate. These modes manifest as different force-carrying
particles moving in what we think of as separate force fields. This gives us our familiar
electromagnetic, strong and weak nuclear forces. But at very high temperatures,
the complexities of the quantum fields sort of get ironed out, a little like how the complex
crystal structure of ice dissolves when it melts. It seems pretty certain that in the first searing
instant after the big bang, most of the modes of vibration of the quantum fields vanished.
The many force-carrying fields behaved as a single field, generating a single master force.
We know for sure that this is true of the electromagnetic and weak nuclear forces - we’ve
re-merged those in our particle colliders - but it’s almost certainly the case for the
strong nuclear force and the Higgs field also. That’s right, I said Higgs field. We think of the
Higgs field and Higgs boson as giving elementary particles their masses, but we should also think of
the Higgs as a fifth fundamental force, because it arises from the same field structure as the
other non-gravity forces. And it’s the freezing of this field that can give us our cosmic strings.
Now a quantum field is just some numerical property that the fabric of space can have.
The field at any point can oscillate around that value, and those oscillations can have
quantized energy states. These vibrations can move through space, and we see them as particles.
A field’s numerical value is called its field strength and it depends on
the amount of energy in the field, sometimes in complex ways. In the absence of particles,
a field will always drop to the nearest minimum in energy - this is the vacuum state of the field.
In the early universe, the Higgs field had a very simple response to changes in energy,
with a single minimum value, and even this vacuum state still contained a lot of energy.
The shape of this so-called potential curve depends on the temperature. As the universe
expanded and things cooled down, the Higgs field potential developed a bump. The lowest
energy value was no longer a single number - instead new minima appeared around the old value.
Actually, the Higgs field is really characterized by two numbers - a pair of field strengths, and so
the new minimum formed a ring around the old minimum, resembling an item of festive Mexican headwear.
So, quite suddenly the Higgs field everywhere in the universe
found itself sitting at a higher energy than it needed. It was momentarily stable at that point,
just like a ball sitting at the top of a hill. But the slightest quantum jiggle would send the ball,
or the Higgs, rolling down in a random direction. And that’s what happened. Here and there across
the universe, the Higgs field started falling towards the new vacuum state - we call this vacuum
decay. Neighboring points in a field drag on each other, pulling them towards the same value, just
like how the magnetic dipoles in a ferromagnet drag each other into alignment. So, when vacuum
decay started at one point neighboring points were dragged to the same part of the Higgs minimum.
A bubble of this lower vacuum energy was nucleated, and it expanded at the speed
of light. Many bubbles would have started at different places across the universe,
and when the bubbles found each other and merged, the old, high-energy vacuum was completely erased.
Or mostly erased. Just as with ice, topological defects should have formed where these bubbles
met. Our ice cube forms sheets, but our Higgs field formed strings. Remember
that the vacuum decayed in a random direction towards this circular valley.
That means we can ascribe an angle to every point in space defining the relative
value of the two components of the Higgs field. We’ll call that the phase angle.
Across a single expanding region of decaying vacuum, the phase angle would have been similar
because these points were all pulled in the direction of the initial nucleation event. But
independent bubbles may have very different phase angles. When bubbles met, the Higgs phase angle at
the boundary tried to rotate to line up. This led to textures of slowly shifting phase angles across
the universe. But if multiple bubbles join with different phase angles then sometimes the lowest
energy approach to lining up the phase angles is for them to vary smoothly around a loop - a
2-pi rotation of the phase angle around the intersection. And that left a knot somewhere
inside the loop where the fields couldn’t align. The Higgs field at the center of that knot
was forced to take on the Higgs value at the top of the potential hill rather than the valley. It
became a fossil of the ancient, high-energy vacuum that would persists into the modern universe.
This sort of swirly topological defect is called a vortex, and we see 2-D versions everywhere from
cyclones to swirls of hair on your head. But in a 3-D space, like, you know, actual space,
this sort of defect manifests as a cylindrical swirl around a central line.
And that central line is our cosmic string. Other topological defects may be possible.
For example, a zero-dimensional, point-like topological defect would be a magnetic monopoles,
which we talked about recently. There are also ways to produce 2-D defects called domain walls,
but that’s for another time. OK, so we’ve managed to freeze the
quantum fields amidst the first bawlings of the baby universe and woven some cosmic strings.
What do they look like and what do they do? Those phase angles really do prefer to line up, which
means the loops around the defect tighten as much as they can. The filament of high vacuum energy is
squeezed it down to one-ten-trillionth the width of a proton. And yet it still holds an incredible
amount of energy, which gives it the mass of the planet Mars for every 100 meters of length.
And these things are long. They started as long as light can travel between the nucleation event
and the completion of vacuum decay and then the expanding universe stretched them up to the size
of the observable universe. We actually expect multiple nucleation events in each causal horizon,
potentially leading to dozens of cosmic strings in a network across the universe.
Unlike the topological defects in ice, cosmic strings move and vibrate. They are
also under pretty insane tension, so vibrations travel along them at near the speed of light.
This inevitably leads to collisions between segments of strings–either
two distinct strings or two sections of the same string. When this happens either the
two segments pass straight through each other, or they switch partners - they intercommute.
If a straight string collides with itself it can cut out a loop. Then, if the loop intersects with
itself again, it forms two smaller loops, chopping up into smaller and smaller loops. But larger and
larger loops keep forming from the original giant cosmic strings. Over time, the size of the largest
loops increases, while at the same time populating the universe with their chopped-up offspring.
Once intercommutation occurs, a pair of “kinks” is formed in each of the newly formed strings speed
away from each other along the string at near the speed of light. They’re whipped back and forth by
the oscillating string, and the incredible mass in the kinks causes them to radiate
gravitational waves. In this way cosmic strings shed energy, and so they slowly decay away.
Eventually they vanish as the Higgs field smooths itself out across the filament. The smaller the
loop size the quicker they evaporate, so the breaking up of loops accelerates their demise.
OK, that’s what cosmic strings do. Now, how do we find them, assuming they exist? Well let’s start
with these gravitational waves. That radiation should be emitted in beams in the direction of
oscillation of the string, so we might see flashes as these beams pass over our gravitational wave
observatories. These are likely too weak to be seen at our current detectors such as LIGO,
but future detectors such as LISA might be sensitive enough. Then there’s the Pulsar
Timing Array - as we’ve described previously, it detects gravitational waves by looking for
irregularities in the period of the fantastically regular flashes of light from pulsars.
It also has the potential to spot the tell-tale signals from gravitationally radiating kinks in cosmic strings.
The other way to spot cosmic strings also relies on a gravitational effect: gravitational
lensing - which is the warping of background light sources due to the space-time warping effect of gravity.
When a massive object sits between us and a distant light source, it bends all
passing rays of light inwards, so focusing them towards us. We can see multiple images or even a
ring surrounding that lens. A cosmic string would also deflect light towards itself, but that can
only lead to a pair of split images, and that could potential leave a chain of split images across the sky.
No such chain has yet been detected, but upcoming gigantic all-sky surveys
may give us the data that we need to find these. Now if we do find a cosmic string, there’s one
other point of confusion we’d need to settle. Is this a cosmic string, or is it a cosmic
superstring? You’ve probably heard of string theory - we’ve certainly talked about it enough
on this show. It’s perhaps the most established candidate for a theory of everything - a theory
that brings together all physics as we know it. The fundamental building blocks of the theory are
these subatomic 1-dimensional filaments called, fittingly, strings. The strings of string theory
have nothing to do with the cosmic strings that I described. For one thing, they’re ridiculously
tiny instead of universe-sized. However the universe may have found a way to confuse the two.
Many physicists think that in the extremely early universe the so-called inflationary epoch expanded
the subatomic into the cosmic. Some of these string-theoretic strings may have been stretched
to universe-size by that event. Now those are called cosmic superstrings, and annoyingly they behave
like “regular” cosmic strings in many ways - like the gravitational waves and the lensing.
But there are differences. While cosmic strings almost always intercommute when they collide,
cosmic superstrings are far more likely to pass straight through each other,
which reduces the rate of chopping up. They can also form junctions, specifically where two
different types of superstring meet and combine to form a third, connected string which is,
in a sense, a combination of the two. This gives us a potential way to distinguish our
cosmic string-type. If one of these superstring junctions does any gravitational lensing,
it should produce a six-part image, perhaps with a parade of split pairs approaching it.
Observation of such a junction would be the best - dare I say only - evidence to date in
support of string theory. We also expect cosmic superstrings to decay less quickly
because they don’t chop into loops as fast. That means they should result in a stronger
gravitational wave background, and possibly a distinct gravitational wave signature.
Now we haven’t actually found cosmic strings or superstrings … yet. But our searches
have given us bounds on the range of allowed tensions–and therefore energies–of these things.
And we have to keep looking, because it’s very possible that the universe is riddled with veins
of its primordial vacuum. If we can find one who knows what we’ll learn? We may discover truths
about the origins of the universe, or the nature of quantum fields, or the validity of string
theory. Many murky mysteries may become as clear as a well-made ice cube. I mean, what better way
to see its inner workings of the universe than to find a crack in the fabric of spacetime.