Let me tell you a story about virtual particles.
It may or may not be true.
Out there in the emptiest places of the universe,
phantom particles appear and vanish again out of nowhere.
They borrow the energy for their existence
so briefly that they cheat the watch fly of the universe.
Near black holes, virtual matter and antimatter pairs
are separated by the event horizon
to create Hawking radiation.
And every time two particles interact,
an infinite number of virtual particles
mediate infinite versions of that one interaction.
Virtual particles sound pretty cool,
I guess, but is this really how they work?
Seriously, what are virtual particles?
Sometimes our mathematical hacks point to strange new aspects
of reality.
For example, Max Planck used a quantization trick
to figure out the spectrum of light emitted by hot objects.
The quantization part of his math trick
was meant to disappear in the final form of the equation,
but it remained.
It proved fundamental.
That math hack turned out to represent the very real quantum
nature of the photon.
This insight led to the discovery
of all quantum physics.
A more recent mathematical hack is the virtual particle.
They started out as a trick to make
impossible calculations in quantum field theory possible--
possible, at least, for the sort of people who can do
quantum field theory.
So will virtual particles also prove
to represent a new underlying aspect of reality?
Now, we're going to go pretty deep in this one,
but it will bring us closer to a better
understanding of the quantum nature of reality.
So stick with me.
First, let's get to the origin of virtual particles.
So quantum field theory is the machinery
behind the standard model of particle physics.
In it, particles are excitations in fundamental fields
that exist everywhere in space.
In particle interactions, packets of energy
are exchanged between these fields.
For example, two electrons-- excitations in the electron
field--
will repel each other by exchanging energy
through the electromagnetic field.
That process is kind of a mess.
Each electron jiggles the electromagnetic field,
and those jiggles have a back reaction
that jiggles each electron, which
in turn affects the way the electrons jiggle the EM field
ad infinitum.
It's a hopelessly tangled feedback cycle
of reaction and back reaction, and it's
impossible to calculate it perfectly.
But it is possible to approximate it--
in fact, with astonishing accuracy.
That's where perturbation theory comes in.
It's our mathematical hack.
The hack is to approximate this single multilayered mess
of an interaction by adding together a set of much
simpler idealized interactions.
Those interactions are mediated by virtual particles.
In that sense, virtual particles are the building blocks
of our approximation of the behavior of quantum fields.
Let's do an example.
In the case of the interacting electrons,
you start by saying each electron interacts once
with the EM field, transferring between them energy momentum
and one photon worth of quantum properties in a single packet
that we call a virtual photon.
Then you add the effects of doing this transfer in two,
three, four packets, as well as every other idealized field
interaction that you can imagine.
Every one of these interactions is
described with a simple excitation and transfer
of particles--
virtual particles.
The hope is that by adding together
the contributions of enough of these,
you can approximate the messy state of the field
in the true interaction.
We call these idealized interactions
intermediate states or virtual states of the field.
But in reality, the field never exists in these states.
The virtual particles never exist independently.
Instead, virtual particles are the mathematical building
blocks we use to approximate the complex states of interacting
fields.
Maybe you recognize these things--
Feynman diagrams.
We've definitely talked about them before.
Richard Feynman came up with them
as a bookkeeping tool to keep track
of which intermediate states are important in your calculation
of an interaction and which you can ignore.
Particles that either enter or leave these diagrams
are our real particles.
All those that both start and end within the diagram
are virtual particles.
Feynman diagrams are an absolutely essential tool
in most modern quantum field theory calculations,
but they also add to the misconception
about virtual particles.
They sure make it look like virtual particles are doing
regular particle stuff like traveling through space
but that's just not the case.
Virtual particles share some properties
with their real counterparts-- in particular, quantum numbers
like charge and spin, but they don't
need to obey Einstein's relationship between energy
mass and momentum.
In fact, they ignore a lot of the physics of real particles.
They can have any mass.
And they can even travel faster than light
or backwards in time.
This isn't because they're magic.
It's because they aren't physical.
Virtual particles are our mathematical representation
of the quantum mechanical behavior of fields,
and that behavior is weird.
Here's a really good illustration of this weirdness.
In our first example, we looked at two electrons
repelling each other.
One electron throws a virtual photon
at the other one causing them to be deflected from each other
like a game of quantum dodgeball.
But what about attractive forces?
What about an electron and a positron?
How can throwing photons between particles
cause them to be drawn together?
Let's look at the fine and diagram
of a single virtual photon passing
from electron to positron.
To calculate the effect of this, you
add together the possible effect of
every possible virtual photon being emitted by the electron
and absorbed by the positron.
Bizarrely, that includes photons that
are pointing in the wrong direction
to even make the journey.
Their momenta are pointing from positron
to electron rather than electron to positron.
And you also count photons emitted by the positron
but pointing away from the electron.
These are the virtual photons that ultimately
provide the attractive force.
But how do they make the journey between the particles?
Uh, they don't-- there is no journey per se.
These virtual particles sort of exist everywhere
at once, which is confusing.
Each one of these infinite possible virtual particles
represents a quantum of energy in
a single possible vibrational mode of the underlying quantum
field.
In a way, a virtual particle represents a pure excitation
of the field, an idealized case of perfectly defined momentum.
The Heisenberg uncertainty principle
tells us that the perfectly defined momenta
of virtual particles means completely undefined position.
In contrast, real particles are mixed up
combinations of many excitations,
many different momentum modes.
And that uncertain momentum gives them
real locations, real trajectories through space.
Our virtual photon doesn't have a location,
so it doesn't travel a real path.
It can move between our electron and positron
even if its momentum is pointing in the wrong direction.
It's a bit like the photon starts out
moving in the wrong direction and then quantum
tunnels between the particles, kicking them
towards each other like a teleporting boomerang.
But even that description is way too physical and Australian.
No individual virtual photon can be
credited with producing the attractive force.
In fact, you only see that force in the sum
of all possible virtual photons over all possible Feynman
diagrams.
Bizarrely, you also have to include the case
where the electron and the positron
totally ignore each other to even see an attractive force.
Did I mention that quantum mechanics is weird?
So that's the deal with virtual particles in particle
interactions, but we also hear about the role
of virtual particles in a complete vacuum.
You might have heard the quantum vacuum described
as his roiling ocean of virtual particle-antiparticle pairs
popping into and out of existence, the so-called vacuum
fluctuations or zero point fluctuations.
What's the deal with that?
So the quantum fields are composed
of these vibrational modes of all different
frequencies/momenta that can be excited to become particles.
These modes also exist in the vacuum
just without the excitations.
Each mode should have 0 energy in a vacuum,
but in quantum mechanics, nothing can be so exact--
thanks, again, to the Heisenberg uncertainty principle.
In order to remain "uncertain," there
has to be a slight chance that when you look at a vacuum,
any given mode will have non-zero energy.
This leads to a non-zero average energy called, confusingly,
the zero point energy.
So there's a chance that when measured
the vacuum will appear to have energy and so have particles.
But the key word here is "measured."
Do those particles exist if you're not looking?
Or more to the point, do vacuum fluctuations
produce actual particles when there's nothing else around?
The answer seems to be no--
at least, as far as you can answer such a question.
In the math of QFT, the perfect vacuum is a steady state.
It doesn't change over time.
It has a constant zero point energy.
Regarding its particle content, it
remains in a steady state of uncertainty.
It's a quantum state in a superposition
of "yep particles" and "nope, no particles."
The quantum state is not fluctuating on its own,
but it will randomly collapse into one of these possibilities
when something interacts with the vacuum.
This is a pretty subtle point, but it
makes a huge difference in how we think about the vacuum.
Virtual particles are not popping
into and out of existence in the absence of any else.
Instead, they're fanciful way of talking
about what might happen if something
interacts with the vacuum.
The classic example of this is Hawking radiation.
Stephen Hawking himself was the first to use virtual particles
as an intuitive way to describe his radiation.
He painted a picture of virtual matter-antimatter pairs being
separated by the black hole event horizon,
allowing one of the pair to escape to beautiful freedom
and reality.
But Hawking himself also cautioned
against taking this picture too seriously.
In his actual mathematical derivation,
he instead talks about vibrational modes
of the quantum vacuum being cut off by the event horizon.
This disturbance of the vacuum generates particles.
But without the black hole, the vacuum stays a vacuum.
A similar perturbation of the quantum vacuum
is also seen in the Casimir and Unruh effects.
We also did episodes on these, and just like with Hawking
radiation, you don't need for virtual particles
to have an independent existence to explain these effects.
So to recap, virtual particles are best
thought of as a mathematical device
to represent the behavior of quantum fields.
The original idea of virtual particles
came about as a calculation tool in perturbation theory
as we tried to approximate the behavior of quantum fields.
Now, in the case of Max Planck discovery of the quantum
nature of photons, it turned out that a mathematical artifact
represented new real physics--
the quantum nature of the photon in that case.
Planck knew that he was onto something
because there was no way to express his Planck
law without an artifact of that quantum nature--
namely, the Planck constant.
So what about virtual particles?
If they represent a physical reality,
then there should be no way to do quantum field theory
calculations without them.
It turns out there is a version of quantum field theory that
doesn't use virtual particles at all.
That will be the family of lattice field theories
in which space-time itself is defined on discrete grid.
It doesn't rely on perturbation theory,
and so it doesn't use virtual particles while ultimately
giving the same results.
Ergo, virtual particles are probably
just a mathematical artifact.
There is no good reason to believe
that virtual particles exist outside the math we
use to approximate the behavior of quantum fields.
At best, they can be interpreted as a small component
of possibility space for a quantum field
doing something real.
That said, for something that doesn't exist,
they're surprisingly useful for describing the weird underlying
machinery in our quantum space-time.
Last week we talked about the latest thinking on the Fermi
paradox and what conclusions we can really
draw about this persistently annoying lack of aliens.
Let's see what you had to say.
A few people say that the Fermi paradox isn't really
even paradoxical with some common objections
about the behavior of aliens, saying things
like the window of strong radio emission
for any civilization is too short to overlap
with us or aliens probably don't build Dyson swarms
or aliens probably don't build Von Neumann probes
or aliens probably don't colonize widely
and, in general, that aliens probably
stay quiet or use technologies undetectable to us.
Any and, perhaps, all of these may be true
but that misses the point.
The point is that the overwhelming majority
of every civilization that ever developed
would have to observe all of these conditions
in order for us to see nothing.
Remember, guys, it only takes a single rocket happy individual
to execute one of these projects, a single Musk
or Bezos or Branson or Milner from potentially thousands
of generations and potentially millions of civilizations
to play their hands, tentacle, pseudo pods,
whatever to a big space project.
All of these arguments of aliens probably
don't do this or that are what we call a soft filter.
Something that may be unlikely for any given civilization
but given enough civilizations that thing becomes inevitable.
These arguments on alien psychology are soft filters.
The Fermi paradox must be explained
by a very long chain of soft filters that
add up to extremely small probability or one
or more hard filters.
A hard filter is a step in development
that's so unlikely it can cut off
nearly all progress for development
of life or civilization.
Paper Dragon points out that not enough attention
is paid to one particular possible great filter.
That's the transition from what we'd
call not intelligent to intelligent life.
It's a good point because we have very little capacity
to assess the likelihood of that transition.
Humans are the only species to have ever built a society
with anything close to the technological capacity
to be seen by other species.
Was there some extreme fluke in the development
of Homo sapiens and our technological ascendance
that was an extreme fluke?
Maybe, though, it's not right to say
that it took the span of life on Earth
for this fluke to happen--
as if we were rolling the dice every Millennium
and only now came up sixes.
A lot of that time, life was evolving towards the point
that it could become intelligent.
There are now many tool using species, including primates,
birds, octopuses, dolphins.
And we aren't the only species to have evolved language, art,
and imagination.
Our extinct Homo-cousins, Neanderthals, Denisovans, et
cetera had various levels of the above.
But again, we just don't know.
It really could be that modern Homo sapiens underwent
an improbable genetic or cultural evolutionary movement
that qualifies as a great filter.
A few of you pointed out that our depiction
of the binary star system was wrong.
They were apparently orbiting a center of mass that
wasn't even between the stars.
So that was actually a three star system.
One star had collapsed into a black hole, which
is why you couldn't see it.
It was totally there though-- try increasing your screen
resolution.