[MUSIC PLAYING]
 The most successful
theory in physics
combines the weirdness
of quantum mechanics
with, well, the weirdness
of special relativity,
to give quantum field theory.
This theory tells
us that particles
can be created and destroyed
during interactions.
Even so, every observer agrees
on whether a particle exists
or not, right?
Yeah, about that.
[MUSIC PLAYING]
Both theories of relativity,
special and general,
tell us that many things
are observer dependent.
Different observers might
disagree about speeds, lengths,
or times, but the
laws of physics
should be the same for everyone.
And for two observers with
very different, but constant
speeds--
inertial observers, the vacuum
itself should appear the same.
But relativity can throw
some weirder things
into the mix, specifically
the idea of a horizon.
For example, the event
horizon of a black hole,
out of which no
information can travel
or the cosmological horizon that
limits the observable universe.
And a strange type of
apparent event horizon
even appears when we accelerate.
Generally speaking, a horizon
is a boundary in space time
from beyond which no
influence can pass.
It limits an observer's
causal connection
to a part of the universe.
As weird as the space
times with horizons may be,
the statement from before holds.
The fundamental laws
of physics shouldn't
change if we go
near a black hole
or if we start accelerating, but
enforcing this isn't automatic,
and something has to give.
As it turns out, what gives
is the nature of the vacuum,
and in fact, the notion
of what a particle is
becomes observer dependent.
In coming episodes, we will be
delving into Hawking radiation
and the Unruh effect, both
of which are very similar
and are results of this
observer dependent vacuum.
There are a couple of
compelling, but inaccurate
explanations of Hawking
radiation around,
and here at Space Time, we
want to be as simple as we can,
but no simpler.
So we're going to
take this episode
to lay the final
stepping stone we
need to examine these effects
in detail and accurately.
To get at this idea of observer
dependent particles and vacua,
we're going to need some
quantum field theory,
and we're going to need to draw
heavily on this recent episode.
In QFT, we think about
each particle type
as having its own
quantum field that exists
at all locations in space.
If the field vibrates with
a single quantum of energy,
we see a particle.
That oscillation
can be distributed
over some region of
space, representing
the possible positions
of the particle.
The properties of
the particles are
encoded in the
properties of the fields.
The laws of physics,
as we know them,
are the rules defining
how particles interact.
For the laws of physics
to be consistent,
the fundamental
properties of these fields
must be the same
for all observers.
Imagine I fire a
pair of photons,
which annihilate to produce
an electron, positron pair.
All observers, be they
floating in empty space
or accelerating or
orbiting a black hole,
should agree on the basic
result of that interaction-- two
photons in, one electron,
one positron out.
That means everyone has to
agree on the fundamental nature
of the quantum fields that
describe these particles
and the way they interact.
There's no conflict for constant
speed inertial observers.
In fact, quantum field theory is
what we call Lorentz invariant.
Special relativity is built in.
So the equations describing the
interaction transform cleanly
between inertial reference
frames in a way that
leaves the laws of physics
and the nature of the vacuum
intact.
But when an observer
who sees a horizon
tries to write down
these equations,
in order to preserve
the laws of physics,
they find they have to redefine
the nature of the vacuum,
itself.
To see how this happens,
we need to think
about how particles,
interactions, and vacuums are
described in quantum
field theory.
Imagine the simplest
type of quantum field.
It's comprised of
oscillators at all locations.
A bit like a bed
of springs, they're
all attached to each other.
Or even better, an infinite,
extremely flexible drum skin.
Now imagine an oscillation in
any one of these locations.
A particle perfectly
localized in space--
a single spring or a single
point on the drum skin.
That oscillator can increase
in energy in discrete chunks--
in quanta.
And we interpret each
quantum of energy
as representing a
single particle.
Now every point in this
field, this drum skin
is connected to
neighboring points.
The equations we write to
describe the oscillations
are coupled to each other.
This coupling allows
the oscillation--
the particle to
evolve through space.
But it also makes it
devilishly difficult
to solve those equations because
the individual oscillations
in space can't be
solved independently.
But there's a neat trick
to get around this.
As we saw in our recent
episode on Fourier transforms,
it's possible to describe any
vibration or wave in two ways.
Sound waves can be described
in terms of variation over time
or variation over frequency.
Quantum wave functions
and quantum fields
can be described in
terms of variation
with position or
variations with momentum.
So instead of writing the
field as having a value
at every possible
position in space,
we can write it
as having a value
for every possible momentum.
We switch between them
with a Fourier transform.
So let's take our
spatial quantum field--
our drum skin, with its
single, localized particle,
and transform to momentum space.
That momentum field also
has infinite oscillators,
but now each one represents
a different possible momentum
for the particle.
Bizarrely, in momentum
space, that single, perfectly
localized position
oscillation can also
be described as an infinite
number of unlocalized momentum
oscillations.
Now, each one of
these momentum modes
exists at all spatial
points in the universe.
If we add these momentum
oscillations together
with the right weightings,
they cancel out
everywhere except at
the spatial location
of the original particle.
The superposition of infinite
universe size momentum
oscillators-- momentum
particles can represent
a single spatial oscillator.
One particle at one
point in the universe.
Let's go back to the slightly
less abstract infinite
drum skin.
Now it starts out
with no oscillations,
analogous to the vacuum state
in quantum field theory.
If we were to make an excitation
at a particular spot--
make a particle, we hit
that spot with a drumstick
and set the oscillation going.
Most of the amplitude
will be where we hit it,
but really, the vibration will
extend everywhere on the drum.
We could, in principle,
make the same oscillation
by simultaneously hitting
the drum everywhere
with an infinite drumstick,
adding global vibrations
with different frequencies
that cancel out everywhere
except that one spot.
But why exchange a
single spatial equation
for infinite equations
in momentum space?
Well, because they actually make
the mathematics much easier.
Those momentum oscillations
have two important qualities.
They behave like simple
harmonic oscillators,
so their value over time
is like a simple sine wave.
But even more importantly,
they are uncoupled.
The field at each momentum
spot oscillates independently
from its neighboring momenta.
Dealing with uncoupled equations
allows you to add and subtract
oscillations without affecting
the neighboring momenta.
However, changing
the momentum modes
does affect the superposition--
the sum of all oscillations,
for example, by creating
or destroying particles.
OK, so a single particle can be
described as many oscillations
in momentum space.
Those oscillations
can be reconfigured
with our infinite drumstick
to add new particles
or remove old ones, for
example, to describe a particle
interaction like those
two photons annihilating
into an electron, positron pair.
There's a nice mechanism
in quantum field
theory for doing this.
It's called the field
operator, and it
is our infinite drumstick.
It's comprised of a creation and
an annihilation operator that
can raise or lower the number
of particles, one at a time,
by changing the number of
particles or oscillations
in each momentum mode.
Here, the field operator
represents the field properties
or the laws of physics.
This is the thing that needs
to be the same for everyone.
But there's no such
restriction for the creation
and annihilation
operators it's made of,
and it's these operators
that define the vacuum.
As discussed in a
previous episode,
we can think of the vacuum as
a sea of virtual particles.
In momentum space,
we can think of it
as a superposition of
infinitely many momentum modes.
Infinite spatially undefined
particles with defined momenta,
and these just happen to
cancel each other out,
leaving 0 particles or a vacuum.
OK, so what happens
when we add a horizon
to our infinite quantum field?
What if, say, there's
an edge to the drum skin
or we cut a hole in the middle?
Now our skin responds very
differently to the drumstick.
For example, we no longer have
access to part of the skin,
and oscillations can
reflect from the boundary.
If we want to make the
same particle as before,
we need to strike
the remaining part
of the skin in a
very different way,
with different
forces at each point.
Well, the same is
true of the universe.
If we introduce
an event horizon,
then we lose access to
some momentum modes,
while other modes
behave very differently.
That means we have to
reconfigure our old field
operator, our infinite
drumstick, in order
to create and annihilate
the same particles
as we had in an infinite,
horizonless universe.
We need to rejig the field
operator for the laws
of physics to be consistent.
Now if you'll forgive
a little QFT jargon,
the new annihilation
operator needs
to be a mix of the old
annihilation operator
and the old creation operator.
Now when you use the
new, rejigged field
operator to describe the
vacuum, some momentum modes
that once canceled out
no longer cancel out.
What was once a vacuum
now has particles.
So you can be that
horizon's drum skin
to produce oscillations that are
consistent with the infinite,
un-horizoned skin.
But doing so leaves
additional oscillations.
What does that look like?
It looks like heat.
The vacuum acquires a
non-zero temperature.
It appears to be bathed
in thermal particles--
particles that don't
exist for an observer
who doesn't see that horizon.
In some cases, changing the
boundaries of space time
actually reduces the number
of particles, for example,
in the Casimir effect.
Now we've already
seen how this effect
reduces the energy of the vacuum
between conducting plates.
In upcoming
episodes, we'll apply
these ideas to
finally understand
Unruh and Hawking radiation.
So this year, keep your
eye on the horizon--
the event horizon and
the strange things
it does to the quantum
contents of space time.
As always, thanks a million to
all of our Patreon supporters.
It's hard to be sure of anything
in this relative universe,
whether it's the
existence of a particle
or funds for a YouTube show.
But your regular support gives
us some wonderful surety,
and an extra huge thank
you to Anton Lifshits,
whose support at
the big bang level
is really helping to keep the
annihilation operators at bay.
Last week, we talked about
the sounds that stars make--
the wonderful worlds of
helio and asteroseismology.
You guys had some
really good questions.
Loki and Alex ask
whether seismic activity
in neutron stars
can be used to probe
their interior properties.
Well, actually, yes.
Neutron stars certainly seem
to experience star quakes--
massive releases of energy, as
the star's ion crust cracks.
These are observed
as X-ray flares.
Extremely large quakes can
set the entire star ringing,
which is observable in its
effect on the extremely regular
flashes of its pulsar jet.
Actually, this is really a
whole episode worth of awesome,
so I won't go on right now.
Several of you asked
where the sounds
of stars we played at the end
of the last episode came from.
Well, first, I want to
apologize for not linking these
immediately.
They were a last minute,
happy discovery the day
before release, and we
dropped the ball in our rush.
Now these are from
asteroseismology simulations
made by Manuel
Perez de Lima Lopez.
The frequency spectra
for resonant oscillations
of several stars were
shifted to a range audible
to human hearing.
The results are
eerie and amazing.
Link in the description.
No Justice, No Peace wonders
whether stars may actually
be speaking, considering
Penrose's quantum brain
hypothesis, which states that
any sufficiently complex system
creates consciousness.
Well, let me first
say that I really like
this idea for a sci-fi book.
But my first objection would
be regarding Penrose's idea
that neurons perform a sort
of quantum computation,
and that this is the
source of consciousness.
There's so little evidence that
this either happens or is even
needed to explain
consciousness that it's
hard to take it seriously.
It feels like it's in the family
of, we don't understand it,
so it must be quantum mechanics.
Obviously, Roger Penrose is a
genius, so there's more to it
than that.
But geniuses say a lot of stuff,
and not all of it's right.
Second, stars aren't complex in
the sense that Penrose means.
Complexity implies
intricate structure,
like a neural network.
Things that are capable
of organizing information.
Stellar interiors are
more simple and chaotic
than they are complex
and structured.
All that said, I love the idea
of stars twinkling meaningfully
at each other from
across the galaxy.
