[MUSIC PLAYING] MATTHEW O'DOWD: This episode
is supported by Skillshare. It's 1928. Over the past quarter
century, the greatest geniuses of the modern era
discovered the two keys to the fundamental
nature of reality. Einstein's theory of special
and general relativity had changed forever
the way we think about motion, space, and time. And the emerging field
of quantum mechanics had radically altered
our understanding of the fundamental building
blocks of the universe. Yet, this year, 1928,
one brilliant insight would bring these theories
together and unveil the quantum fabric of reality. It would also predict the
existence of anti-matter. By the late 1920s,
Einstein and Planck had already shown that light is
a particle, as well as a wave. And Louis de Broglie had
shown that all matter has this dual wave-particle nature. Bohr, Heisenberg,
Born, Pauli, and others pieced together a
mathematical description for the weird nature
of subatomic particles. Then, in 1926, Erwin Schrodinger
wrote down his famous equation, the Schrodinger equation,
which breathed life into this emerging model. It describes how these
matter waves, represented as wave functions,
change over time, and allowed
physicists to predict the evolution of
quantum systems, such as the strange
interference pattern in the famous
double-slit experiment. Yet, everyone knew
there was a problem. First and most obvious,
the Schrodinger equation is totally incompatible
with Einstein's relativity. In relativity, the
dimensions of space and time are intrinsically connected
and they float into each other as frames of reference change. But the Schrodinger equation
tracks the evolution of a particle's wave
function according to one and only one
clock, typically the clock in the reference
frame of the observer. Relativity tells us
that the passage of time depends on velocity. So the Schrodinger equation only
works for slow-moving objects. That's a problem. Subatomic particles are
often moving at close to the speed of light. The other problem with
the Schrodinger equation is that it describes particles
as simple wave functions, distributions of
possible positions and momenta that have
no internal properties. Yet, we now know that
many elementary particles have an internal
property called spin. That doesn't mean that
they're actually rotating. But spin does result in a sort
of quantum angular momentum. For example, an electron's spin
causes them to align themselves with magnetic fields, just
like a rotating electric charge would. The axis of spin can point
in different directions; for example, up or down. The discovery of
quantum spin starts with an Austrian physicist
named Wolfgang Pauli. Pauli realized that to
explain electron energy levels in atoms, those electrons
must obey a rule that we call the Pauli
exclusion principle. It states that no electron
can occupy the same quantum state as another electron. In fact, it applies to all
particles called fermions. In the case of
electrons in atoms, it suggests that
we should only find one electron per
atomic orbital, if we count each orbital
as a quantum state. However, we actually observe
two electrons per orbital. And so Pauli realized there must
exist a hidden quantum state. Pauli introduced what we
call a new degree of freedom internal to electrons,
one that could take on one of two values. Let's call those
values up and down. That would allow two separate
electrons, one up, one down, to occupy the same
atomic energy level, without occupying the
same quantum state and therefore violating the
Pauli exclusion principle. Other physicists
soon figured out that this new quantum
state represented spin and the up and
down degrees of freedom were the direction of pointing
of the angular momentum axis. We now call these two component
wave functions, spinors. Now, it's OK to ignore spin in
the old Schrodinger equation and get approximate answers. But when a magnetic
field is present, spin direction becomes
very important. So for fast moving
electrons and for electrons in electromagnetic fields,
the Schrodinger equation gives the wrong answers. The problem consumed a brilliant
British physicist, Paul Dirac. He wanted a fully
relativistic version of the Schrodinger equation
that worked for electrons. In a way, he started
with relativity. He wrote down Einstein's
famous equation, E equals mc squared, but in its
full form, including momentum. He then used quantum
mechanical expressions for energy and momentum. The result was a huge mess. But Dirac stumbled upon
a single simple idea that caused the resulting
horrendous mathematics to collapse into an incredibly
simple, beautiful equation. That simplification
required Dirac to expand the internal workings
of the electron even further. Instead of having a
two-component spinor, up and down, as in Pauli's theory,
he needed four components. Now, he had no
idea what those two additional mysterious
components might mean. But the resulting
equation was so simple and elegant
that somehow Dirac knew that he was onto something. The resulting Dirac
equation describes the spacetime evolution of
this weird four-component particle-wave function,
represented by the symbol psi. It contains the marks of
both quantum mechanics, in the Planck constant,
and relativity, in the speed of light. The Dirac equation perfectly
predicts the motion of electrons at any speed, even
in an electromagnetic field. It was a major victory. But it opened up even more
questions than it answered. To begin with, what on earth
were those two extra degrees of freedom in the
four-component electron? The answer came from
trying to calculate the energy of the electron
using this equation. It predicted something
totally bizarre. It allowed electrons to exist
in states of negative energy. If true, that would lead
to some weird effects. For example, a lone
electron moving in an electromagnetic
field could keep releasing energy
as light infinitely, and sink lower and lower,
to infinite negative energy states. There was no bottom
to the energy well. Now, we know perfectly well
that this doesn't happen. Dirac came up with an
idea to explain this. We call it the Dirac sea. Imagine an infinitely deep
ocean of electrons that exists everywhere in the universe. These electrons occupy
all of the negative energy states, all the way from
negative infinity, up to zero. The only time we can actually
interact with an electron is when one has a positive
energy, which would leave it sitting on top of the sea. This is where the Pauli
exclusion principle comes back. If the energy states
of this imaginary ocean are all completely full,
then that one extra electron can't lose any more energy. It just floats on
top of the sea. The idea of the Dirac sea leads
to its own weird predictions. Remove one electron from the
surface and it leaves a hole. That hole should act like
a particle all by itself. It would be like an eddy on
the surface of a pool of water. It would move around. It would have inertia,
acting like it had the mass of the
missing electron. It would also act like it had
the opposite electric charge to the electron,
a positive charge. And if a positive
energy electron found one of these
holes, it would fall in, annihilating both, and releasing
all of the energy bound up in their masses. Of course, there is
something in our universe that acts exactly like
holes in the Dirac sea. It's called anti-matter. And Dirac had just
predicted its existence. Now, the Dirac sea itself
doesn't really exist. But it was one of
the first attempts to describe something very real,
the idea of a quantum field. We now know that every
elementary particle has an associated field,
that fills all of space. These fields are
more like membranes than infinitely deep oceans. They have a very definite
energy, usually zero. And the elementary particles
that we know and love are just regions where a
field has a bit more energy. That energy manifests as
vibrations in the field. Now, quantum field theory
is a very deep topic. And it'll be the subject
of upcoming episodes. But for now, let's get to
the bottom of these holes. Paul Dirac's negative
energy solutions describe anti-matter, not
holes in the Dirac sea. Only a few years after Dirac
wrote down his equation in 1928, the positron,
the anti-matter electron, was spotted in cosmic
rays by Carl Anderson. Anti-matter is very real. But what is it? Well, it's a vibration
in the same quantum field as its regular
matter counterpart. Anti-matter's existence
is fundamentally tied to these weird
four-component electrons that Dirac invented to
make his equation work. Those two extra
components correspond to the up and down
spins of the electron's anti-matter counterpart,
two spin directions for the electron, two for the
positron, a four component spinor. In fact, the electron and the
positron cannot exist without each other. They are two sides of the same
coin, positive and negative energy solutions of the
same type of vibration in the electron field. It's actually a tiny bit
more complicated than that, and way more awesome. But there will be time for
all of that in the future. So all elementary particles
have a quantum field and all have an
anti-matter counterpart. Just as with the holes
in the Dirac sea, anti-matter particles
have the same mass as their counterparts,
but opposite charge. That mass is very real. It's not negative mass
despite this negative energy description. When matter, anti-matter
counterparts find each other, they annihilate, releasing an
awful lot of very real energy. A penny of anti-matter
could be used to launch a good-sized
rocket into orbit. Dirac's incredible insight in
combining quantum mechanics and relativity reveal an entire
flip side of our universe, with its prediction
of anti-matter. It was also a key step in the
discovery of quantum field and quantum field theory
and the development of the standard model of
particle physics, which have become our best
description of the underlying workings of reality. And that's a quantum rabbit hole
that we'll jump into very soon, right here on "SpaceTime." I'd like to thank Skillshare
for sponsoring this episode. Skillshare is an online
learning community, with classes in design,
business photography, and more. Premium membership
includes unlimited access to thousands of classes and
is available starting at $10 a month. And you'll be able to learn
from anywhere by downloading the Android or iPhone app. My favorite thing I found so
far is Ian Norman's class, Nightscapes, which is all about
landscape astrophotography. This is so cool
because it shows us how to produce
beautiful starscape photographs using some pretty
simple camera equipment. My new plan is to
level up my skill in time for the solar
eclipse in August. To get a two-month free trial
and help support our show, click on the link
in the description or go to skillshare.com
and use the promo code SPACETIME at checkout. In the last episode,
we did a "Space-Time" journal club on a new paper
investigating whether the cold spot in the cosmic
microwave background was due to supervoids or a collision
with another universe. Let's discuss. A few people point
out that there are lots of cold
spots in the CMB map and that some look larger
than the actual cold spot. Well, first, let me point
out that the cold spot wasn't identified by the, "oh,
that bit looks a bit bluer than the rest method." Detailed statistical analysis
of the entire Planck CMB map pointed to that region as
being a significant outlier. It's the size of the
consistently low temperature region that's unusual. There are smaller
cooler regions that are consistent with
random fluctuations. Also, those wide spots
near the center of the map are the result of Doppler
shift due to Earth's motion through space. Unpronounceable username asks
whether colliding universes in the bubble universe
scenario means that we redefine
"universe" to be the bounded
post-inflationary pocket in a single true
infinite universe? Yeah. Vhsjpdfg, that's exactly it. I mean the definition
of universe is semantic. But this bubble universe idea
does suggest a greater universe beyond our bubble. The fact that there are probably
other bubbles in this scenario means it makes sense to
talk about those bubbles as separate universes and as
the whole ensemble, including the inflating part,
as a multiverse. Galdo145 asks whether bubble
universes with different vacuum energies would convert
to the lower energy state after colliding? The answer is yes. This is exactly
what we'd expect. The vacuum field can have
one or more local minima, where the vacuum energy can
come to a rest in an eternally inflating spacetime, halting
inflation in that patch. The vacuum energy
may come to a rest at different minima
in different bubbles or it can be a
false vacuum in one and the true vacuum
in the other. If two bubbles with different
vacuum energies collide, then the one with
the higher energy should convert to
the lower energy. For the lower energy
bubble, that's bad, at least in the
region of the collision, because a ton of energy
gets dumped into it from the high energy bubble. For the high energy
bubble, it's much worse because that change in
the vacuum energy state would propagate at
the speed of light to fill that universe,
fundamentally changing the way its
elementary particles behave. It would be like
reformatting a hard drive. Pradhyumn asks if I can
make a video recommending some good books
on space and time? Well, that's a good idea. But how about I just recommend
some stuff for today's episode. This is the "Quantum Divide"
by Chris Gerry and Kimberley Bruno. It explores the key
concepts in quantum physics through a description of
the most important quantum experiments ever made. And it's a rare popsci book that
provides a lot of real crunch, but also really delves into
the physical implications and the true meaning
of the results. Also, this could be one
of the greatest popsci books ever written. It's Richard Feynman's "The
Character of Physical Law." And one of Feynman's
greatest talents was his uncanny ability
to see the fundamentals beneath observed relationships. And he channels that
intuition through this book. Many of you noticed
that we misprinted the typical deviation of the
cosmic microwave background temperature by a little. I actually say the right
number, 20 microkelvin. But we put 20
millikelvin on screen. Sorry. We suck. But you guys, you're like a
scientific unit prefix hawks. We will try to keep
our accuracy to within a factor of a
thousand next time.
