[MUSIC PLAYING]
[APPLAUSE]
SEAN CARROLL: Thanks.
It's great to be here at Google.
I've used your service
on the internet.
[LAUGHTER]
And yeah, I want to talk
about quantum mechanics.
And I'm presuming that--
I know there are some
experts in the audience.
I'm presuming that there are
many complete non-experts.
But probably even the
most complete non-experts
have heard the phrase
"quantum mechanics"
and know that there are
many books out there
on quantum mechanics.
And why in the world does
the world need another book
on quantum mechanics?
And I think that
the answer is that I
don't like any of
the other books,
especially because,
what they tend to do
is to emphasize how difficult
it is to make sense of quantum
mechanics, how surprising and
spooky and mysterious it is.
And I admit that there are
things about quantum mechanics
that are hard to wrap
our minds around.
But I don't think there's
anything intrinsically
unintelligible about it.
So the message of my book is
that you can understand quantum
mechanics, not that you can't.
Of course, I am flying in the
face of my esteemed predecessor
at Caltech, Richard
Feynman, who thinks,
"I think I can safely
say that nobody
understands quantum mechanics."
And I know what he means.
You know, he's not wrong.
We-- quantum mechanics, for
those of you who don't know,
is this wonderfully successful
theory that we developed mostly
over the first quarter of
the 20th century that's
supposed to apply to
everything in the universe,
but really becomes
manifest and necessary
when we look at
microscopic things,
when we look at electrons
or atoms or very, very
small-scale things.
And we can use this theory
to extraordinary precision.
We can make
predictions that have
been tested to 12 decimal
places of accuracy.
Quantum mechanics is
absolutely necessary
to understand why the sun
shines or how transistors work
or why this table is solid, OK?
So why does Feynman say this?
Because even though we
can use quantum mechanics
to make predictions,
if you ask physicists,
but what's really
happening, they don't know.
And that's OK.
It's OK not to know things,
but when you don't know,
what you should try to do is
to learn, is to figure it out.
And as a field, physics
has decided not to do that.
Rather than taking
people who are trying
to understand quantum
mechanics at the deepest level
and treat them as the
superstars and most
important people
in the field, they
push them out of the field.
They've decided that
trying to understand
quantum mechanics
at a deep level
is not our job as physicists.
It's only to make predictions.
I think that this is bad.
The analogy I like to
use is with Aesop's fable
of "The Fox and the Grapes."
If you remember this one,
the Fox sees the grapes,
and would like to eat these
juicy, wonderful grapes,
and jumps up, but
can't reach the grapes.
The Fox is unable to
get to the grapes.
So the Fox says, you know what?
I never really wanted
those grapes anyway.
They were probably sour.
The Fox represents
physicists, and the grapes
represent understanding
quantum mechanics.
We used to try very hard to
understand quantum mechanics,
and we subsequently stopped,
and I think that was a mistake.
So let me tell you how we
got to quantum mechanics.
This is a fake version
of the history,
but it gives you an idea.
So by 1909, we had this
picture of the atom, which
is the same cartoon
you will always see
when people talk about atoms.
I think it's literally the
logo of the Atomic Energy
Commission or the Nuclear
Regulatory Commission.
There is a nucleus, a middle
of the atom, which we now know
is full of protons and neutrons,
and there are electrons
orbiting around the atom, OK?
The problem is that,
even though this
is consistent with
certain pieces of data,
it can't be true as the
final answer, at least,
according to the standards of
classical Newtonian mechanics
because these electrons
zooming around in orbits
should be emitting
electromagnetic waves.
When you take a charged
particle like an electron,
and you shake it in any way, it
has an electric field radiating
out in all directions.
So when you move the
electron, the field adjusts.
And when you move
it up and down,
the field waves,
and we see those.
That's where the light
that we're seeing right now
comes from, from
vibrating electrons.
So these electrons that are
moving around in circles
should be emitting light.
And that means they
should be losing energy,
and they should spiral in
to the nucleus of the atom.
And you can calculate how
quickly that should happen.
It's about 10 to the
minus 11 seconds, which
is a very short period of time.
So in other words,
according to the rules
of classical mechanics
applied to the Rutherford
model of the atom,
all matter should
be dramatically unstable.
You and the chair you're sitting
on and this table and the Earth
itself should
collapse into a point
in a tiny fraction of a second.
That prediction does
not fit the data,
so we need to do
something better.
There were many
ideas batted around.
What we eventually
hit upon was, don't
think of the electron as a
point particle in an orbit.
Think of the electron as a wave.
In particular, we dubbed
this the wave function,
which is the most
boring, uninspiring name
for the most important
thing in all of physics.
The wave function
is the idea that,
rather than being in an orbit
around the nucleus of the atom,
think of the electron as
being described by a wave that
is spread out around the atom.
And just like a
violin string that you
pluck in different ways--
a string that is tied
down at both ends
has, I guess, the
fundamental frequency
that it can vibrate at.
And then there are
overtones, harmonics,
that it can vibrate
at in different ways.
The point is that there's a
discrete set of different ways
it can vibrate.
Likewise, if you think of
the electron as a wave,
rather than as a
particle, there's
a discrete set of shapes that
wave can have in the atom.
And there's a
minimum energy shape.
So rather than just spiraling
in to the center of the nucleus,
the electron goes to its
minimum energy configuration,
which is still spread out.
It's the shape in the upper left
here, spherically symmetric.
These other shapes
are higher-energy.
Versions of the wave
function of the electron.
And then it just
sits there forever.
And if you remember
high school chemistry,
you were tortured by
pictures of electrons
doing these things and
the various orbitals
that they could be in.
And so this became
a way of thinking
about why matter is stable.
Even better, a couple of
years later, Erwin Schrodinger
came up with an equation for how
these orbitals, electron wave
functions, actually behave.
And I give you the details
of the Schrodinger equation,
because I know you
all want to go off
and solve it in your spare time.
There are people here at
Google who spend a lot of time
solving this equation
on quantum computers.
And you don't need to know
the details of the Schrodinger
equation if you are not a
quantum mechanical expert.
What you need to know is that
there is an equation, OK?
So physicists love
equations for good reasons.
It's because you can go from
the idea, the original idea,
the electron is a
wave around the atom,
and now you can just
apply it widely.
You can apply it to
any other circumstance.
You can take the wave
function doing anything.
And you can let it evolve.
You can solve this equation.
In words, the Schrodinger
equation says,
any one wave can be decomposed
into different energy parts.
And every energy part
evolves at a separate rate.
So the energy of the wave
is proportional to how fast
it evolves.
That's the Schrodinger equation.
That's the entire thing.
And so this equation still--
you know, suggested in 1926--
is still right, as
far as anyone knows.
It's one of the fundamental
rules of nature.
So you might think that
we're, like, triumphant,
that quantum mechanics is
basically done, that we
know that now electrons are
not particles; they're waves.
This is the equation we obey.
That's what you want in
a good physical theory,
an understanding of what nature
is and which equation it obeys.
The problem is the
data don't stop there.
So this is a
wonderful little image
of a chunk of uranium
in a cloud chamber, OK?
So a cloud chamber has
some pressurized gas in it
that, when a charged particle
moves through the gas,
it ionizes the
particles around it,
and it creates a
little track, OK?
So if you have a
chunk of uranium--
it's radioactive--
it will actually
emit electrons and alpha
particles and things like that.
And you can use the Schrodinger
equation to say, well,
what does the wave function of
the emitted electron look like?
The answer is, it looks
like a spherical wave.
The electron wave function
comes out in all directions
more or less equally.
There's details, but
that's the basic story.
But then you look at it.
You never see an electron coming
out in all directions equally.
What you see in this
picture are straight lines,
trajectories, as if the
electron is a particle again.
What's up with that?
We still have not answered this
question, what's up with that?
This is the sad part about
the modern understanding
of quantum mechanics.
So what people
said was, look, it
looks like the way that
electrons behave in their wave
functions is different
when you're not looking
at them, like when
they're in the nucleus,
around the nucleus of an atom,
versus when you are looking
at them, like when they're in
a bubble chamber or a cloud
chamber, OK?
Now, surely that can't
be the final answer.
But what the strategy adopted by
physicist in the 1920s was is,
yes, that's the final answer.
So they invented an idea
called the collapse of the wave
function.
They said, sure, wave
functions for electrons
or whatever, they obey the
Schrodinger equation when
you're not looking at them.
But when you measure a
quantum mechanical system,
its wave function suddenly
and unpredictably changes.
And rather than
predicting exactly what's
going to be able to happen,
you can predict the probability
of different things happening.
And the probability
is largest where
the wave function was largest.
And after the
measurement has occurred,
the wave function
changes to be localized
where you observed it.
So on the left here, you have
a picture of a wave function
that might be all spread
out for an electron.
You imagine measuring the
position of the electron.
Its wave function
collapses somewhere.
And if you looked at
it again right away,
you would see it
in the same place.
So this is the attempt to
understand why electrons
are all spread out
in wave functions
when you're not looking at
them, but look like particles
when you do look at them.
Because the act of measurement
is something special.
It really does something to the
particle in a particular way.
So this is what's called the
"textbook" or "Copenhagen"
interpretation of
quantum mechanics.
This is what we teach
our undergraduates.
I'm not, like, going to
reveal the truth, you know?
This is what we
actually tell our kids.
This is what I was told.
The rules of quantum
mechanics, according
to this way of thinking,
come in two groups.
There's one set of rules
for when you're not
observing the system.
Those rules say that the
electron is described
by wave functions, or
whatever quantum system,
there's a wave function.
And that wave function obeys
the Schrodinger equation.
And that's exactly in
parallel with the rules
of classical mechanics.
In classical mechanics,
there's a system,
and it obeys some equations.
And that's it.
Those are all the rules.
In quantum mechanics,
you have those rules,
but then there's
extra rules for what
happens when you measure or
look at or observe the system.
You can only measure
certain things.
When you do, the wave
function collapses.
And the best you can do is
to predict the probability
of a certain collapse.
That's the Copenhagen
interpretation.
This is clearly unacceptable as
a fundamental theory of nature.
I mean, what are
you talking about?
It's fine for making
predictions and building things,
but it's clearly not
the final answer.
This was the point of contention
in the famous Bohr-Einstein
debates in the '20s and '30s.
Niels Bohr was the founder
and defender of the Copenhagen
interpretation.
Einstein said, look, that's
fine as far as it goes,
but clearly it has
not gone far enough.
We need to look harder.
This is why the title of my book
is "Something Deeply Hidden."
There's something else going on
that we haven't yet explicated,
and Bohr and his friends
said, no, no, no.
It's fine.
Don't worry about it.
And Bohr and his friends
totally won the public relations
battle.
But I think that
Einstein was actually
right in this
particular dispute.
So let me just
mention two reasons
why the Copenhagen
interpretation by itself
can't be the right final answer.
There's what we might
call the reality problem.
We started by saying
that electrons should
be thought of as wave
functions, but what
is the wave function, really?
Is the wave function a
complete description of nature?
In other words, is
there an isomorphism
between the mathematical
formalism of a wave function
and what reality is doing?
Or is it part of nature,
but not the whole part?
Maybe there's other
variables there.
That's what Einstein
himself thought.
He thought that there
was a wave function,
but there were also particles.
So the wave function
described what
happened when you
weren't looking at them,
but when you measure the thing,
you see the actual particle.
And in the modern
version, these are called
hidden variable theories.
Bohmian mechanics is
the most famous version.
But maybe the wave function
doesn't represent reality
in any way.
There's other
people who say, just
use the wave function
to make predictions.
Don't think of it
as part of reality.
So the fact is that, even
professional physicists who
use quantum mechanics
everyday, can't tell you
what it says about reality.
And if you ask them, they
will tell you in all honesty,
bless their hearts, that they
don't care about reality.
All they care about is making
predictions for observations.
I think that's a bad attitude
to have, but I'm in the minority
there.
The other problem is called
the measurement problem.
And this one is even more
obvious as a problem.
What do you mean,
make a measurement
or look at something?
Like, what counts
as a measurement?
Who is able to do measurements?
Is it just people?
Do you need to be human?
Do you need to be conscious?
What about when you're asleep?
Can cats make measurements?
What about video cameras?
What if I don't look
at it very closely?
What if I glance at it?
Does that count
as a measurement?
How fast does it happen?
When does it happen?
A well-defined, rigorous
theory of physics
should answer all
of these questions.
And the Copenhagen
interpretation
doesn't answer any of them.
It just says, don't
worry about that.
You know a measurement
when you see it.
I think that's not
quite good enough
to be a fundamental
theory of nature.
So there are different
alternatives.
These days-- this was all put
together in the 1920s, right?
These days, we actually
have perfectly well-defined
theoretical physics frameworks
that do answer these questions.
The problem is, we
have more than one,
and we are having trouble
deciding between them.
So I am not going to be, in
any sense, fair in this talk.
I'm just going to tell
you my favorite one
and let you know
there are others.
Buy the book if you
want to see the others.
OK.
Here is my favorite.
It came from Hugh Everett,
who was a graduate student
and was incredibly
criticized for his ideas
and that left the
field right away.
And so Hugh Everett
says the following.
He says, here is the solution
to all of your quantum problems.
Chill out.
Stop working so hard.
You're trying too hard
with all this stuff.
You've made up a whole
separate set of rules
about quantum mechanics
for what happens when you
measure or observe a system.
Just erase all those rules.
Just forget about them.
You want to know
what reality is?
It's the wave function.
Do you want to know
what wave functions do?
They obey the Schrodinger
equation, and that's it.
That's all you need to know.
So in other words, this is
the Everett interpretation
of quantum mechanics.
There's only one set of rules.
They're always obeyed.
And all it says is, there
are wave functions obeying
the Schrodinger equation.
Now, there's a problem with
this interpretation, which
is why it was not invented by
Bohr or Einstein in the 1930s,
in that, it doesn't seem to
quite map onto our experience,
right?
Like, we saw the cloud chamber
with all the little particles
moving.
They don't look like they're
obeying Schrodinger's equation,
so what's going on?
And Everett says,
there are two things
that you've forgotten
about that are already
built into quantum mechanics.
He doesn't add anything, right?
He erased some rules.
He says, there are two
things that are already there
in quantum mechanics that, if
you just take them seriously,
everything will be fine.
One thing is, you, yourself
are a quantum system, right?
You are part of the wave
function of the universe.
You are not a classical system.
In Copenhagen, depending on who
is talking and what time of day
it was, they would admit that
they treated the observer
as classical.
There's even something called
the Heisenberg cut, advocated
by Werner Heisenberg,
that separates
the classical, macroscopic
world of observers
from the microscopic
quantum world.
And Everett says,
look, you might be big
and made of a lot of
atoms, but the atoms
you're made of obey the
rules of quantum mechanics,
so you do, too.
Treat yourself as
quantum mechanical.
And the other point that
he wanted to emphasize
was entanglement--
again, a feature
of quantum mechanics,
not anything that he
added to the theory.
So let me mention what
entanglement says.
My favorite example
is the Higgs boson,
because I wrote a
book about that, OK?
The Higgs boson, we
discovered back in 2012,
and the reason it's
my favorite example
is because the Higgs boson
is a spinless particle.
Every elementary particle
comes with a quantity
called spin, which is really
just like the spin of the Earth
or a spinning top or
anything like that.
Except, when you get down
to that microscopic realm,
spin comes in definite,
quantized values.
So the spin of the Higgs
boson is exactly 0.
The spin of an electron is 1/2.
Which means that, if you
observe the spin of an electron
in quantum mechanics,
it will either
be spinning clockwise
by amount 1/2
or spinning counterclockwise by.
An amount 1/2.
And we call these
spin up and spin down.
So we know from the observations
and from the theory, the Higgs
boson can decay into two
electrons, technically,
an electron and an
anti-electron, a positron,
so the charge is conserved.
But let's ignore
that complication.
So one particle with 0 spin
is decaying into two particles
with spin 1/2.
But spin is conserved.
Spin is angular momentum.
It's part of that, right?
So it must be that when
the Higgs boson decays
into an electron and
an anti-electron,
they're each spinning, but
they'd better be spinning
in opposite directions.
The total spin
has to add up to 0
because that's what it was for
the Higgs boson all by itself.
Now, we don't know
which way it is, right?
Like, one electron is spin down,
and the other one is spin up.
But we don't know which
is up and which is down.
So if you go through the
Schrodinger equation, what
you find is that it's
not one or the other.
It's a superposition of both.
One of the crucial features
of quantum mechanics
is that you have different
pieces of the universe.
But unlike in
classical mechanics,
the different pieces don't have
their own individual states
that we can talk about.
Rather, there's only
one quantum state.
There's only one wave function
of the entire universe.
So when you talk about what
the two electrons are doing,
you need to talk about
both of them at once.
So you know that electron
one might be spin up
or might be spin down.
There's a 50/50 chance.
You know that electron two
might be spin up or spin down.
There's a 50/50 chance.
But you also know that they're
not spinning the same way.
So if you measure the
spin of electron one
and find that it's
spinning up, you instantly
know that electron
two is spinning down.
And this state of the Higgs
boson decaying into something
is that it decays into a
superposition of spin up
for electron one, spin
down for electron two,
plus spin down for electron
one, spin up for electron two.
That's entanglement.
What is happening
to particle one
is entangled with what's
happening to particle two.
They're not independent
from each other.
This is so important,
let me say exactly
the same thing again in
slightly different words
to drive it home.
There's only one wave
function, the wave function
of the universe, what Everett
called the universal wave
function.
His first title for his
thesis was "The Theory
of the Universal Wave Function,"
but his advisor did not
let him get away with that.
So the lesson is,
you might think
that if you have two
electrons, and you don't know
the spin of either
one, but you know
they can be in superpositions,
you might say, well,
electron one is in a
superposition of up and down.
Electron two is in a
superposition of up and down.
Quantum mechanics says
there's not two separate wave
functions for the two
electrons; there's only one,
and they are entangled
in the following way.
And this was actually invented
or at least appreciated
by Einstein.
Einstein and Schrodinger
wrote letters back and forth.
Because despite playing
fundamental roles
in the origin of
quantum mechanics,
neither Einstein nor
Schrodinger liked how
quantum mechanics was going.
They didn't like the
Copenhagen interpretation.
And so the origin
of entanglement
was in Einstein's effort to show
that quantum mechanics couldn't
be complete as yet.
Because you can
send one of these
particles light years
away from the other one.
And if you measure
the spin of one,
you instantly know
the spin of the other.
And Einstein says,
look, I'm Einstein.
I know about this thing
called relativity.
You can't send information
faster than the speed of light.
How does it know way over there?
And that's the spooky action
at a distance that he invented.
But it's there.
It's true.
It's part of quantum
mechanics, and you can actually
test it experimentally.
So let me show you, then,
how entanglement explains
the measurement problem
according to the Everett
interpretation.
And we're going to
use Schrodinger's cat
to explain this.
You've probably heard of the
thought experiment put forward
by Erwin Schrodinger.
He has a box.
He puts the cat in the
box, closes the box.
And there's a little
apparatus there
that has a quantum
wave function that
has a probability
of opening some vial
and emitting gas into the
box or not doing that.
The gas Schrodinger decided
to contemplate was cyanide.
So the cat's either
alive or dead.
His daughter
literally said later,
I think my father
just didn't like cats.
[LAUGHTER]
There's no reason to kill the
cat in the thought experiment.
It plays no role.
So in my version of the thought
experiment, it's sleeping gas.
AUDIENCE: Aww.
SEAN CARROLL: And what
happens is, there's
a quantum system that evolves
into a superposition of having
decayed or not.
So there is a Geiger counter
or some other detector
that evolves into a
superposition of having clicked
or not.
So the box and the gas
evolve into a superposition
of having been emitted or not.
So the cat evolves
into a superposition
of being awake or being asleep.
The whole mess is
just designed to take
a superposition of a tiny,
microscopic quantum system
and amplify it to a
macroscopic world.
It doesn't matter
that it's a cat.
Honestly, the Geiger
counter or the box by itself
would have worked
perfectly well.
But remember, Schrodinger
was unhappy about quantum
mechanics.
The point of the
Schrodinger's cat experiment
was not to go, like, look how
weird quantum mechanics is.
Schrodinger said, what
you're telling me, Mr. Bohr,
is that when I open the box,
before I opened the box,
the cat was in a superposition
of awake or asleep.
And after I open
the box, it suddenly
snaps into either
awake or asleep.
Surely, you don't
believe that, right?
That was his point.
And so in other words, if you
knew about classical mechanics,
it could be perfectly
plausible to say,
there's a cat in the box.
It might be awake.
It might be asleep,
but I don't know.
But the only two possible states
of the cat are, it's awake
or it's asleep.
In quantum mechanics, we
have a new possibility
of this superposition,
that the cat
can be in a combination
of awake and asleep.
And then we tell
a story about what
happens when we open the box
and measure that superposition.
And that story is very
different in Copenhagen
versus in Everett.
So in Copenhagen, we treat
the observer as classical.
So I'm putting classical things
in square brackets and quantum
things in parentheses.
So the role of the observer
here is played by Niels Bohr.
And we start with a system
where the cat is quantum
and in a superposition.
And Niels Bohr is classical, and
he has not yet opened the box.
He opens the box, and that's
observation or measurement.
And according to the
Copenhagen interpretation,
the wave function collapses.
And after that measurement,
either the cat was awake
and the observer measured it to
be awake, or the cat was asleep
and the observer
saw it sleeping.
Those are the two
possibilities, and there's
a certain probability
you can calculate.
So Everett says, ignore all
of this business about wave
functions collapsing.
Just obey the
Schrodinger equation.
Just ask what the Schrodinger
equation would predict
for this particular setup.
So there's no collapse, and
there's only one wave function,
and the observer is
quantum in their own right.
So this is Hugh
Everett now playing
the role of the observer.
So measurement in Everett's
version of quantum mechanics
is just obeying the
laws of physics.
It's just, open the box and
let Schrodinger's equation do
its work.
And what happens inevitably--
and everyone agrees on this--
is that the wave
function of the universe
evolves to a superposition
of the cat was awake,
and the observer saw the cat
awake; and the cat was asleep,
and the observer
saw the cat asleep.
Again, if you obey the
Schrodinger equation,
that's what happens.
No ifs, ands, or buts.
The problem is, it looks like
you, if you're the observer,
would be in a
superposition of having
seen two different things.
And nobody in the
history of human beings
has ever felt like they
are in a superposition
of having seen one thing
or having seen another.
So the immediate rejection
of Everett's theory
was because it
doesn't fit the data.
It doesn't explain
our experience.
It doesn't explain why we see
tracks that look like particles
in the cloud chamber.
So miraculously,
Everett got it right,
despite the fact that, in some
sense, he had no right to.
The real explanation
for this comes
from decoherence, which is a
process which really wasn't
understood until the 1970s.
Remember, I said that the
point of quantum mechanics
is there's only
one wave function
for the whole universe,
not separate wave
functions for separate pieces.
And then I put into
the wave function
the cat and the observer.
I really should put in the
entire rest of the universe,
right, to be strictly correct.
So here's the entire
rest of the universe.
It's usually, in this context,
called the environment,
so I made a picture of grass.
But really, what
you should think of
is the light coming from
these light bulbs or the air
in the room, like,
all the stuff,
all the degrees of freedom
that we're not explicitly
keeping track of, that are
bumping into us all the time,
but we don't know where every
single individual photon is.
So long before we open the box,
in the box, there are photons.
There are air
molecules, et cetera.
They will interact with the cat.
And they will interact
with the cat differently
depending on whether the
cat's awake or asleep.
Because the cat is in different
locations in the box, right?
So a photon will
hit it or will not
hit it depending on whether
the cat is awake or asleep.
So the environment becomes
entangled with the cat
long before you open the box.
And then you finally
open the box,
and you say what you're
doing is called measurement.
But really you're just
becoming entangled
with the two different quantum
states that were always there.
Now, why does it matter?
It looks a lot like this
equation at the bottom
is very similar to the
equation we had before.
What matters is that
these two different states
of the environment--
well, let me put it this way.
The environment is doing two
different, separate things
in the two parts of the wave
function, the part where
the cat's awake and the
part where the cat's asleep.
The technical term is that
these two environment states
are orthogonal to each other.
You can show mathematically this
will happen very, very quickly.
And what that means is
that the separate two
terms in this equation
evolve separately.
They obey their own
equations of motion.
If something happens in one
part of that sum of two terms,
it does not affect anything
happening in the other term.
So Everett says, this is the
prediction of the Schrodinger
equation, and it's right.
Believe it.
This is the final answer.
What you haven't realized
is, you're asking,
why don't I feel like I
am in a superposition?
The answer is, because
there are now two of you.
There is one of you
that saw the cat awake
and one of you that
saw the cat asleep.
It's as if these two different
parts of the superposition
describe different worlds.
So the crucial part
here is that Everett
doesn't put the worlds in.
The Everett interpretation--
I'm not really
revealing a surprise here.
It's sometimes called the
many-worlds interpretation
of quantum mechanics.
He never called it that.
The name was not invented
until 1970 by Bryce DeWitt.
The point is, if you just
have the Schrodinger equation
and you just follow
what it does.
The worlds appear,
like it or not.
They were always there.
Everett just points out that
they naturally come to be.
The process of decoherence
separates the wave function
into distinct branches
that no longer interact
with each other, so they are,
for all intents and purposes,
separate worlds.
Now, there's a
bunch of questions
you can ask about the
many-worlds interpretation.
Some of them are
easier to answer.
Some of them are hard.
Many of them are
hard, to be honest.
But I'm not going to
dwell on all of them.
I just want to give you a
flavor for how we answer them.
So one question is, how
many worlds are there?
We don't know is
the short answer.
We don't even know whether
the number of worlds
is finite or infinite, OK?
The straightforward
and simple answer
is that there are
infinitely many worlds.
This is what Everett
himself would have believed.
At the technical
level, for those of you
who do know a little bit
about quantum mechanics,
the question is, what
is the dimensionality
of Hilbert space, the space
of all the possible wave
functions?
For simple systems
like an electron
in nonrelativistic quantum
mechanics or quantum field
theory, Hilbert space is almost
always infinite-dimensional.
And therefore, for all
intents and purposes,
there are an infinite
number of worlds.
But we don't know that for sure.
And people like me think
that quantum gravity implies
that the Hilbert space is
actually finite-dimensional.
So maybe there's only a
finite number of worlds.
But even if it's
a finite number,
it's a really,
really big number.
So rather than thinking of
the splitting, the branching
of the wave function, as
happening at special events
where you work hard
to make it happen,
it's happening all the time.
There are radioactive decays in
your body roughly 5,000 times
a second, and every one of those
duplicates the universe, OK?
So rather than
thinking of, like,
bang, a special event
that splits the universe,
there's a constant whooshing
as the universe is subdivided.
And that's the way
to think about it.
It's not a duplication of the
world with twice as much energy
and everything.
There's a certain amount of
world-ness in the equations,
and it's being subdivided and
differentiated as time goes on.
Think of the world
as splitting, not as
being copied in some way.
Now, there are some
objections that I
think I can easily answer.
One is that there's just
too many universes-- sorry,
I don't like it.
This is not a very
scientifically respectable
worry.
But I get it.
The problem is that there's
enough stuff going on
in one universe.
Doesn't it seem, like,
ontologically extravagant
to add all this extra stuff in?
The response to this is that
once you believe quantum
mechanics, the potential for all
these worlds was always there.
Once you believe that electrons
can be in superpositions,
you should believe that people
can be in superpositions
and worlds can be
in superposititons.
Hilbert space is
the name we attach
to the space of all
possible wave functions.
It's not any bigger
in many-worlds
than it is in Copenhagen or
anyone else's interpretation
of quantum mechanics.
It's just that many-worlds
lets the wave function
be wherever it wants
to be in Hilbert space.
So this might be an objection
to quantum mechanics,
but it's not an objection
to many-worlds, per se.
The second question is, how
can you test this theory?
You're saying there's all these
other worlds out there that I
can't interact with.
Doesn't that violate
the spirit of science,
that I should be able
to test my predictions?
Well, there's a longer
conversation here,
but let's appeal to Karl
Popper, the philosopher who
said that a good scientific
theory should be falsifiable.
Of course, every scientific
theory makes some predictions
that you can't test.
The question is, are there any
experiments you could imagine
doing that could give
you answers that would
cause you to reject the theory?
And remember, all Everett
is is the statement,
there are wave
functions, and they
obey the Schrodinger equation.
That's the world.
So this is the most falsifiable
theory ever invented.
All you have to
do is either find
variables other than
the wave function,
or find the wave function doing
something other than obeying
the Schrodinger equation.
And there are
ongoing experiments
to do exactly these things.
Karl Popper himself
was a huge fan
of the Everett interpretation.
He thought that the
Copenhagen interpretation was
a philosophical monstrosity.
So in terms of
testability, Everett
is just as good as anyone
else's interpretation
of quantum mechanics.
Now, so those are, I think,
the easily answered objections.
There are two other
questions that are harder.
I'm going to just do, like,
one minute on one of them
and then a couple of
minutes on the other one.
The first hard question
is, where does probability
come from?
So as an empirical
matter, when we
do measurements on
quantum systems,
it is certainly true
that the best we can do
is to predict the probability
of certain measurement outcomes.
And in Copenhagen, that's
because we put in a postulate
into the theory that says
there's a probability rule, OK?
Everett-- all the postulates
are, there's a wave function.
It obeys the
Schrodinger equation.
There's no mention
of probability.
In fact, the Schrodinger
equation is 100% deterministic.
If I know the wave function
at one moment of time,
I can predict it at
any other moment.
There's nothing probabilistic
about the dynamics.
So how in the world
does probability
enter what we know about quantum
mechanics from experience?
The answer is this idea of
self-locating uncertainty.
You can indeed know
everything there
is to know about
the wave function,
and there's still
something you don't know,
which is where you are
within the wave function.
So let's go back to the
cat and the observer
after decoherence happened
but before the observer knows
what branch of the wave
function they're on.
Decoherence happens
really, really fast.
Typical timescales
are less than 10
to the minus 20 seconds in
a big, macroscopic system
that you're not
trying to protect.
So before the observer opens the
box, decoherence has happened,
and the wave function
has branched.
So there's already two branches
of the wave function, the cat
awake branch and the
cat asleep branch.
But because the
observer hasn't looked,
there are two copies of the
observer that are exactly
identical with each other.
Because the observer
has not opened the box,
if you ask the observer,
which branch are you on,
cat awake or cat
asleep, they don't know.
They are identical.
So even though they
know the entire wave
function of the
universe, they don't
know which branch they're on.
That is self-locating
uncertainty.
And you can ask, given some
reasonable assumptions,
is there a uniquely
rational way to assign
credences,
probabilities, to being
on one branch or the other?
And you go through the
math, and the answer
is yes, and guess what?
It's exactly the
same as the postulate
that you had in the
Copenhagen interpretation--
the probability is given by
the wave function squared.
So it is very natural
for probability
to arise even though the
underlying dynamics are
completely deterministic.
Now, the harder question is, how
do we relate Everettian quantum
mechanics to the world
of-- the classical world
we see of tables and chairs?
And this is a tough one
for me to get across
because most of my
fellow physicists
don't even think
this is a problem.
I think it's the
hardest problem,
and we should all be
thinking about it.
But we all grow up tending
to think about the world
classically.
So we look around.
We see there are cats.
There are trees.
There are people.
Those are the
starting point when
we try to describe the world.
So when even
professional physicists
make quantum mechanical
models of reality, of, spins
or materials or
particles, they start
with some classical description,
and then they quantize it.
So you start with
some classical stuff,
and then there's
rules that you're
taught in graduate school
or undergraduate education
for turning that into
a good quantum theory.
And at the end of the day,
you have a wave function,
which mathematically is a
vector living in Hilbert space,
living in this giant
dimensional vector space.
Presumably that's cheating.
Presumably nature doesn't
start with a classical theory
and quantize it.
Nature has no need for that.
Nature just is quantum
mechanical from the start,
right?
So in some sense, you
should be starting
with a wave function
thought of as a vector
in some abstract Hilbert
space and deriving
the rest of the world.
This is how nature
actually works.
That turns out to be
really, really hard.
And it's harder in many-worlds
than it is in other approaches
to quantum mechanics.
In other approaches
to quantum mechanics,
whether it's Copenhagen or
hidden variables or whatever,
they sneak in some features
of the classical world
into the definition
of the theory.
Despite the fact that
there are many worlds, when
it comes to assumptions,
when it comes
to pieces of the
theory itself, Everett
is the leanest and meanest.
Wave functions in the
Schrodinger equation,
and that's it.
Every other approach to quantum
mechanics adds extra stuff,
and that extra stuff
gives you a handle
on why the world looks
classical in a certain way.
In Everett, you
have to work harder.
"Why does the world
look classical at all?"
is a perfectly good question.
So keep that question in mind.
Why does the world
of classical at all?
There's another
question that we have,
which is quantum gravity, right?
I'm sure that you might
have heard, depending
on which street corners
you hang out on,
that we don't yet
have a good quantum
theory of gravity itself.
We can take this procedure
I mentioned over here,
and it works for
every force of nature
and every piece of matter in
nature other than gravity.
For electromagnetism,
the nuclear forces,
particles that we know
about, electrons and quarks
and so forth, you start
with a classical theory,
you quantize it, you
get a reasonable answer.
For gravity, the best
classical theory we have
is Einstein's general
theory of relativity.
And his point is that gravity is
a feature of spacetime itself.
Namely, it is the
curvature of spacetime.
Spacetime curves and warps and
responds to matter and energy,
and we experience that curvature
as the force of gravity.
So he has a perfectly
good classical theory.
We can put it into our black
box, and we can quantize it,
and we get a terrible mess.
It doesn't work.
We have not yet
successfully taken
classical general
relativity and applied
the usual rules of quantization
in a successful way.
That's why people are driven
to consider alternatives,
like string theory or loop
quantum gravity, et cetera.
Those have made some
progress, but none of them
is obviously the right
answer in any sense.
So let me suggest
the following thing--
that maybe these two problems
cancel each other out.
The problem being, we don't
understand quantum mechanics,
and we don't understand
quantum gravity.
Well, why in the world should
we understand quantum gravity
if we don't even understand
quantum mechanics, right?
Maybe this fact
that, in Everett, you
should start from a quantum wave
function and emerge out of it
the classical world,
is really the right way
to think about gravity.
In other words, don't
quantize gravity
in the sense of starting
with some classical model
and turning it into
a quantum theory.
Start with some quantum theory
and finding gravity within it.
Well, we're allowed to
take clues from the world
as we do know it, where
quantum field theory
is the best way we have of
thinking about particles
and forces, right?
If it weren't for gravity,
quantum field theory
is the way nature works.
So here's a picture of a field.
This is the magnetic field, OK?
If you have a magnet.
There's an invisible
force field around it.
We know that because you put the
magnet near your refrigerator,
and it reaches out and grabs it.
Likewise, there's a
gravitational field,
an electric field, et cetera.
In modern physics,
everything is fields.
So even particles, even
matter, like electrons
and quarks and neutrinos--
there are fields that
fill all of space.
And what you perceive
as a particle is really
a vibration in that field.
So the fundamental
ingredients of nature,
according to modern
physics, are fields
filling space vibrating
in certain ways,
in a quantum mechanical
framework, the whole thing we
call a quantum field theory.
And there's an
immediate consequence
of that, which is that
empty space is fun.
It's full and lively, and
it's a busy place, OK?
If the world were
made of particles,
you can imagine
there are particles,
and the space in between
them is just space.
It's just sitting there,
and nothing is happening.
If the world is made of fields,
fields fill all of space.
And even where you
say space is empty,
and there's nothing there,
what you really mean
is that there are fields
there, but they're
in their lowest-energy state.
They're in their vacuum state.
And we can take space
and subdivide it
into little regions and talk
about what the fields are
doing in every region.
What you mean by a
particle is that the field
is vibrating more than it
does in its vacuum state.
But in most of space, it's
just sitting there quietly.
And there's a feature that
you can find in quantum field
theory that different
regions of space,
the fields that are
vibrating there,
are entangled with each other.
And the amount of
entanglement is
related to the
distance between them,
to the geometry of space itself.
If two regions of
space are nearby,
they will be highly entangled.
If they're far away,
they're not very entangled.
That is the conventional
story of quantum field theory.
Now, let's ask ourselves,
can we use this
as a clue to find gravity,
to emerge space itself?
The point is, we
can't put space in.
We have to find it
in the wave function.
So the idea, the suggestion is,
we can turn this idea around,
the relationship between
geometry and entanglement.
Rather than saying,
when two parts of space
are close together they're
highly entangled, we say,
when two quantum
parts of Hilbert space
are highly entangled,
they are close together.
That's what it means
to be close together.
And if you do that for all the
different parts of the wave
function, a geometry
emerges on space.
And you cross your fingers.
If everything works
out nicely, it's
the kind of
three-dimensional space
that you and I know
and love and live in.
So we can easily imagine a
relationship between geometry
and entanglement.
There is also a relationship
between entanglement
and energy.
Remember, I said that, in
the vacuum, in empty space,
there's a very specific
entanglement structure
in quantum field theory.
If you want to put a
particle somewhere--
so you want to add some energy
to a region of space by putting
a particle there--
you basically have to
break the entanglement
of that little
vibrating quantum field
with the rest of
its surroundings.
So you decrease the amount
of entanglement in a region,
and you necessarily add
energy and vice versa.
There's a direct correlation
between the amount
of entanglement somewhere and
what we would traditionally
refer to as the energy.
So look what we got.
By referring to
entanglement rather than
begging the question, by
assuming space and stuff
like that, we find that
there is a relationship
between the geometry
of emergent space
and the amount of entanglement.
There is separately a
relationship between the energy
and the amount of entanglement.
Therefore, there
is a relationship
between the amount of
geometry-- the geometry of space
and the amount of
energy in one region.
Modulo some mathematical
details that I
encourage you to check out.
But that's general relativity.
That's what Einstein said.
He said that the
geometry of space
is sourced by the amount
of stuff, energy and matter
and so forth.
What I'm saying here
is that, if you didn't
know that there was
any such thing as space
and you treated space as
something that emerged
naturally from the quantum
mechanical entanglement
between different parts of the
wave function of the universe,
the natural consequence would
be that space has a geometry,
and it's curved and that
geometry obeys an equation that
is very similar to Einstein's
equation of general relativity.
Now, we haven't proven this.
Truth in advertising.
This is an ongoing research
program that is not done yet.
We've made progress, but the
progress is the following.
Rather than saying,
this is true,
we have a long list
of assumptions.
And if all those assumptions are
correct, then this is true, OK?
So it's full employment
for graduate students
in the future generations.
They need to prove every one
of our assumptions is true.
But it's very encouraging
to me to imagine
that the problem with
quantum gravity was just
that we shouldn't be
quantizing gravity at all.
We should be taking
quantum mechanics seriously
and finding it.
So I know that there's probably
some details there that I
went through too quickly.
So happily, you can buy my book,
which I think is free to you.
I think you're giving
away copies for free.
But all the details
are in there.
The details that are not in
there are referenced in there.
It's an exciting time.
I think that we're
actually making
progress for the first time in
understanding how nature works.
And taking reality
seriously turns out
to be a smart strategy for
theoretical physicists.
Thank you very much.
[APPLAUSE]
And we have time for questions.
SPEAKER 1: Yes,
we have some time.
So does anyone have a question?
Hi.
Look alive.
SEAN CARROLL: That
seems very dangerous.
AUDIENCE: (LAUGHING)
It's very soft.
SEAN CARROLL: We live
on the edge here.
AUDIENCE: OK.
So many-worlds
theory is the fodder
for a lot of science fiction.
Just off the top
of your head, where
does modern science
fiction get it right,
and where does it get it wrong?
SEAN CARROLL: Yeah.
So that's a very good question.
Modern science
fiction almost always
gets it wrong for the
following very good reason--
that once the worlds
branch, according
to the real, true
theory of Everett,
they can't talk to
each other anymore.
So you can download--
if you have an iPhone,
there is an app called
Universe Splitter, where
it will send a signal to a
beamsplitter that will send
a photon either left or right.
And if you agree ahead of
time, if the photons go
left, I'm going to have
Chinese food for dinner;
if the photon goes right, I'm
going to have pizza for dinner,
there will be a
universe in which you
had Chinese food for
dinner and a universe
in which you had pizza.
But you can no longer
talk to the other one
and say, well, how
was yours, right?
So that does not make for very
good drama when that happens.
Now, there are-- maybe
the Schrodinger equation
isn't quite right.
Steven Weinberg, the
famous physicist,
suggested a modification of
the Schrodinger equation.
And Joe Polchinski,
another famous physicist
pointed out that, if that
modification were true,
it would enable communications
between different branches
of the wave function, which
he called an Everett phone.
So that's a perfectly
respectable thing
to write a TV show or
a movie about if that's
what you want to do.
[LAUGHTER]
It's crossed my mind, yeah.
AUDIENCE: If the, uh--
so if there's just a
single wave function
and the universe is just
a ton of forking events
that are creating all these
different universes, I guess,
is the implication
then that there
was ever or is ever
just a single point
or instance of entropy or, like,
true probability or randomness
that occurred?
SEAN CARROLL: Yeah,
well, I think the way
that I would put it is, there
is absolutely a direction
of time in this picture, right?
There were fewer
separate branches
of the wave function in the past
than there are in the future.
Now, there's separately
an arrow of time
given by statistical mechanics,
given by entropy increasing.
Entropy used to be
low, and it's growing.
I think it's the same thing.
I think both cases
are just facts
that the initial conditions
of our observable universe, 14
billion years ago near the big
bang, were highly non-generic,
were very special
and very low-entropy.
And nobody knows
why in either case.
But whatever caused the wave
function in the universe
to have few branches and the
physical thermodynamic entropy
of the universe to be low
explains everything since then.
AUDIENCE: So my question
is related to this one.
So if the branching needs
to happen constantly,
does that mean some sort of
serialization needs to be done?
Like--
SEAN CARROLL: Some what?
AUDIENCE: Serialization.
Like events need to
wait for each other
before they can branch the wave.
Like, how do you explain that?
SEAN CARROLL: Yeah, so I'm going
to give you the correct answer,
and it's going to
be unsatisfying, OK?
Let me make it concrete by
thinking about the Higgs bosons
and decaying and the EPR
experiment where Einstein said,
look, I'm going to take
particle one and particle two,
separate them by
many light years,
and observe particle one.
And you're telling
me, instantly,
particle two changes.
You can prove a theorem that
says that cannot be used
for communication.
You cannot send
information that way,
because the observer of
particle two doesn't know what
the result was
from particle one.
But following my
philosophy that we
want to understand
what's really happening,
you're still allowed to ask
what's really happening, OK?
So the answer is,
the wave function
of the universe branches.
What you want to
know is, should I
think of branching
when I observe particle
one as happening simultaneously
throughout the whole universe,
or am I allowed to
think of it as sort
of spreading within the light
cone of that particular point?
The answer is, either way.
The answer is that
the whole idea
of branches of the
wave function are
convenient human constructs.
Everett's idea is that
physics is just the wave
function of the whole universe.
And this is what it means to
say that the classical world,
the branches of the wave
function, are emergent.
They are approximate
descriptions
that give us a handle
on what's happening
in a convenient way that is
based on a lot less information
than just giving us the whole
wave function of the universe.
So you can slice up the wave
function of the universe
by letting it branch
instantaneously
throughout space.
Or you can keep things moving
slower than the speed of light.
Both descriptions give
exactly the same predictions
for every conceivable
experiment.
It's up-- whatever
makes you feel better.
[LAUGHTER]
I told you that it
would be unsatisfying.
AUDIENCE: That's not satisfying.
You were right.
AUDIENCE: OK.
So I was curious what you might
think are some of the most,
I guess, telling criticisms
of this view of the universe.
SEAN CARROLL: Yeah.
I think I would say that
there are two big looming--
I don't even want to say
problems-- but research
questions that have not
been completely answered,
both of which I talked
about, one of which
is the probability question.
I gave you my favorite
answer, but there's definitely
perfectly legitimate worries
and very smart people
who worry about that.
The best worry is the
following simple-minded one,
which I think is
simple-minded, but it's
hard to answer, which
is, look, OK, fine.
You say that there's
self-locating uncertainty.
And one of these branches,
I don't know which one,
and you say there's a good
way to assign probabilities
to being on one or the other.
But what forces me to
assign them that way?
Like, why can't I
just say I don't know?
Like, what's wrong with
saying, like, I don't know.
I'm on some branch.
Why, in my exper--
how do I-- am
being forced to map
this particular mathematical
fact about the wave function
onto my experience of flipping
coins or measuring spins.
That's a perfectly
good objection.
And the other one is
this structure question.
Like I said, we, made some
bold assertions and assumptions
and derived curved spacetime.
It's only in the
weak field limit.
We don't yet have
things like black holes.
And there's still a bunch of
questions that are just tricky.
Like, one thing
that we assume is
that the Hamiltonian,
the fundamental energy
function of the universe, takes
a very specific form, which
seems to be experimentally true.
But if you want to be
really broad-minded,
you say, well, why?
Why does the-- why do the laws
of physics look like that?
Why is there locality at all?
Why is there space at all?
And there's no answer
there in Everett.
There's no answer there is
anyone else's theory, either,
by the way.
But the ability to
answer this question
is more obvious in Everett,
and we haven't answered it yet.
AUDIENCE: If you assume a
finite-dimensional Hilbert
space for the universe,
is there a notion of--
and you're sort of
branching all the time--
is there a notion of running out
a room and some of the branches
coming back and
hitting each other?
SEAN CARROLL: There
absolutely is.
So if there's a finite
number of branches possible,
and branching is
happening all the time,
math theorems tell us we're
going to run out of branches.
Happily, we're nowhere
close to doing that.
And what it would
look like-- it's
just the approach to
thermal equilibrium
within any one branch.
What happens is all
the branches become
indistinguishable
from each other
because equilibrium
looks the same no matter
where you started, right?
So in some very real
sense, once that happens,
it's not so much that
branches re-fuse together
as there's no difference
between the different branches.
There's no obvious way
to divide the universe
into branches at all.
AUDIENCE: Why can you
say with such confidence
that we're not close to that?
SEAN CARROLL: Because it doesn't
look like thermal equilibrium.
I mean, happily.
There are still stars
shining in the sky.
That's why.
Anything else?
I can sign books if we have any
minutes left over, but yeah.
[LAUGHTER]
AUDIENCE: This is kind of a
different style of question,
but--
so I think quantum mechanics
has a reputation as being a very
arcane thing, discipline.
SEAN CARROLL: Yeah.
AUDIENCE: And yet,
I think the kind
of thinking that is fit for
theoretical physics is probably
pretty widespread and common.
And I think this mainly
because I'm a software engineer
and because I find myself at
home reading and listening
to theoretical physics
books and things.
You know, bad theories
smell bad in the same way
that bad software smells bad.
So if this is really the most
important problem in science,
arguably, how do we have
a sea change that allows,
regular old people who
like thinking this way
to do something about
it and isn't just, like,
increasing the number of
crackpots in the world?
SEAN CARROLL: Yeah, I mean,
this is a good question.
And it would be easy
to joke about it,
but it's hard to give
the right answer.
Here's the good news.
Of course, quantum
mechanics involves math--
complex analysis, linear
algebra, and so forth.
But it's not that hard math.
And furthermore, these
kinds of questions,
these foundations of
physics questions, the math
is not the obstacle.
It's really like-- it's
undergraduate math.
And you can get, as a
professional theoretical
physicist, into field theory
your string theory or whatever,
and the math gets
harder and harder.
But none of that's really
relevant here, honestly.
So I think that, if you're
an honest autodidactic who
wants to study quantum
mechanics from a textbook
and learn enough of
it to think deeply
about the foundations of physics
questions, it's very doable.
I mean, one of the best--
two of the best books on
foundations of physics
are David Albert's book "Quantum
Mechanics and Experience"
and David Wallace's book
"The Emergent Multiverse."
And they're both
pretty accessible
to people who like
matrices and calculus.
So I would say, get those,
read them, take them seriously,
and see what you have to do.
AUDIENCE: I was just going
to make an observation
that I enjoy a
podcast that talks
about a lot of these
things called "Mindscape."
So people--
SEAN CARROLL: Yes,
I have a podcast.
Somehow I didn't mention that.
Thank you.
Thank you.
Your $5 is in the mail.
[LAUGHTER]
Subscribe to my podcast.
I talk sometimes about
quantum mechanics.
But other times I talk
about music or movies
or whatever we want to
talk about that day.
So it's a fun scape of the mind.
Thank you very
much for having me.
[APPLAUSE]
