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.
If the virtual particle are not real, then which is the phisical origin of Hawking radiation? And can be the Hawking radiation the origins of dark matter?
I can watch any of these videos 10x each and still not understand half of the subject. :(