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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."
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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.