[GENTLE MUSIC] Are you worried
about black holes? Consider this. Every time you accelerate, put
your foot on the gas, quicken your step, get
out of your chair, you generate an event
horizon behind you. The more you accelerate away
from it, the closer it gets. Don't worry. It can never catch up to
you, but the Unruh radiation it generates sure can. [ELECTRONIC MUSIC] Around the same time
that Stephen Hawking was demonstrating the
existence of the black hole radiation that would bear his
name, three other researchers-- Stephen Fulling, Paul
Davies, and William Unruh-- were looking at an effect
that now seems eerily similar. They were independently
studying how the nature of quantum fields
appears to change depending on whether or not an
observer is accelerating. They found that the
simple act of acceleration cuts off your causal access
to a region of the universe. It creates a type
of event horizon. As we saw in our episode
on horizon radiation, the presence of horizons
distorts the quantum vacuum in a way that can
create particles. This is the Fulling-Davies-Unruh
effect, or sometimes just the Unruh effect. It tells us that accelerating
observers find themselves in a warm bath of particles. To understand this, we don't
need general relativity with its space-time
curvature and conflicts with quantum mechanics. We just need a little
special relativity and a space-time diagram. We've talked about these before,
but here's a quick rehash. A space-time diagram has two
axes, time and, well, space, with time on the vertical axis. We can show an object's
path through space and time using world lines
on the diagram. For an object with a constant
velocity, an inertial object, these world lines are
just straight lines, and the slope gives
their velocity. A particle not moving at all
has a vertical world line. Einstein taught us that
an object without mass, like a photon, can only
travel at the speed of light and no slower. On the space-time
diagram, this is a line with a 45-degree
angle from the vertical axis. This angle isn't
anything special. It's just determined by
the unit of space and time that we choose. Objects with mass can never
reach the speed of light, so the world line
of a massive object, which includes any observer,
has to be less than 45 degrees from the vertical. Extending light ray world lines
backwards from our observer defines what we call
the past light cone, the region of space-time that
can have a causal influence on the observer. That's because photons fired
from anywhere in the past light cone can reach our observer
either at the current point or at some point in
their past world line. As our observer moves
forward in time, as long as they don't
travel faster than light, their past light cone
should eventually contain the entire universe. Well, that's if you ignore
the expansion of the universe, and this makes sense. If you wait long enough, photons
from anywhere in the universe can catch up to you. At least you'd think so, right? But, actually, there is
a sublight speed world line that can outpace light
or at least keep ahead of it. That's the world line of
an observer undergoing constant acceleration. Acceleration means
change in speed, so an accelerating
world line is curved. The slope changes. Here's an example. Imagine my friend is traveling
towards me initially at close to the speed of light. For some reason, they
change their mind. I don't know. They suddenly remember
there's something better on. They fire their rockets and
begin a constant acceleration in the opposite direction. To begin with, that just slows
down their approach speed. Just before they reach
my space-time location, that constant acceleration
brings them to a halt, and they start moving back
in the opposite direction. They then accelerate back up
to close to the speed of light and keep accelerating. OK. Whatever. I didn't want to
hang out anyway. That constant acceleration world
line traces out a hyperbola, and it has a very
interesting property. If I fire a photon at the
point of closest approach, say to send a
message, that photon can never catch up to my
friend as long as they stay on that hyperbolic trajectory. The photon will always
be inching closer. It'll become
asymptotically close, but it will never overtake. Now, this is only
true as long as they continue to accelerate away. Slow down or stop, and
my message can catch up. In reality, eternal
constant acceleration would take infinite energy. So after draining all of
the energy in the universe, they'd finally have
to stop accelerating, and my message
would overtake them. But until that happens, they
stay just ahead of my photon. They also stay
ahead of any photon emitted from this
diagonal line or any point on the other side of it. This means that any
events happening to the left of
that diagonal line will never affect the
accelerating observer, which sounds pretty horizon-like. In fact, the active
acceleration does create a type of event horizon
called a Rindler horizon. It's named after the
coordinate system we use to describe a
constantly accelerating observer in special
relativity, Rindler coordinates, devised by
Austrian physicist Wolfgang Rindler who, by the way,
also invented the term event horizon. The Rindler horizon
flows at a fixed distance behind a constantly
accelerating observer. Let's call them Rindler
observers from now on. The distance of
a Rindler horizon is inversely proportional
to acceleration. The larger the acceleration,
the closer the horizon. All parts of the universe
beyond that horizon are out of causal connection
with the Rindler observer as long as they
continue to accelerate. But here's the weird thing. Even momentary acceleration
generates a Rindler horizon. You don't need to pinky swear
that you'll keep accelerating. It's like the projected
future acceleration gives you a Rindler horizon
in the present. And just as with
Hawking radiation, that horizon cuts
off your access to certain fundamental frequency
modes of the quantum vacuum. The derivation requires a switch
between inertial or Minkowski and Rindler space via
the beloved Bogoliubov transformations, which are also
used in the Hawking derivation. And here they also lead to a
mixing of positive and negative frequency modes in
the accelerating frame of reference, which leads
to the creation of particles in that accelerating frame. Those particles should have
the same type of spectrum as Hawking radiation,
a thermal spectrum. The vacuum should appear warm
with a temperature proportional to the acceleration. This is the Unruh effect. Now, there's a big difference
between the Unruh and Hawking effects. In the case of
Hawking radiation, an inertial observer
far from the black hole sees the radiation. This is because that
distant point of space-time is smoothly connected to the
space-time near the horizon. I mean, it's all
one big space-time. The only observers who
don't see Hawking radiation are those plummeting in freefall
towards the event horizon. But if an accelerating
Rindler observer is in the same location
as an inertial observer, the former will see that patch
of space filled with radiation, but the latter will see an
empty vacuum in the same patch. At first glance,
this disagreement seems like a huge conflict. What if the Rindler
observer accelerates fast enough that they are burned
to a crisp by Unruh radiation? Does the inertial
observer see some sort of spontaneous combustion? Where does that energy
appear to come from if not from particles? A little less gruesomely,
imagine the Rindler observer has a particle detector. Every time an Unruh
particle hits the detector, it would click. And the inertial observer
would agree that it clicked, but they wouldn't see the
particle that triggered it. And this is actually the case. It's been worked out
with math and everything. The proof uses something called
an Unruh-DeWitt detector. This is a fancy name
for a particle in a box. This particle is coupled to
the quantum field of interest, meaning it can exchange
energy with that field. That means the particle can be
excited into a higher energy quantum state when it
encounters a particle associated with that field. So as the detector accelerates,
Unruh particles appear. The detector particle gets
excited by an Unruh particle, causing the detector to click. But what does this look like
for someone not accelerating but in the same patch of space? Well, they also see the
accelerating detector click, but they argue that it's
for a very different reason. When they perform the
relativistic field theory calculation to understand the
coupling between the detector particle and the field,
they get that there's a sort of drag or friction
turn between the detector and the field that results
from the acceleration. That causes energy to be dumped
into the detector particle. The source of that energy
is the acceleration itself. The upshot is that the
very existence of particles is observer-dependent. Here's a specific example. A charged particle accelerating
in a magnetic field emits radiation,
bremsstrahlung radiation. An inertial observer sees
the charged particle itself radiating, its energy extracted
from the magnetic field. But an observer
accelerating with that charged particle sees it
absorbing Unruh particles and then spitting
them out again. The Rindler and
inertial observers disagree on the
source of the energy even if they agree
on the final result. So how strong is
Unruh radiation? Well, don't worry too much. You need to accelerate
at a rate of 10 to the power of 20
meters per second squared to increase the temperature
via a single degree Kelvin. It's difficult to directly
observe Unruh particles, although analogies
have been observed even in classical systems, like this
really cool study with water waves. One more thing. According to Einstein's
equivalence principle, remaining stationary in
a gravitational field is equivalent to
acceleration in free space. That means you right now are
bathed in a very tiny amount of Unruh radiation. But there's one
place in the universe where the gravitational
acceleration can get that high, and that's right above the
event horizon of a black hole. If you hover close enough
to that event horizon, you would actually be
bathed in Unruh radiation. Here we get to a really
interesting question. What's the relationship
between the Unruh particle seen by someone
hovering at the event horizon and the particles
of Hawking radiation seen by a distant observer? Well, it's a great
question, but it's one we're gonna have
to come back to. Right now I have to
jet but not too fast, lest I combust in a
Fulling-Davies-Unruh thermal bath as I accelerate to that
future point in space-time. [ELECTRONIC MUSIC]
