- Hi, I'm Sean Carroll.
I'm a theoretical physicist
here at the California
Institute of Technology.
I've been challenged to explain dimensions
to five different levels.
The idea of a dimension,
sometimes in pop culture
is misunderstood, like
there's an extra place
you can go, a mystical dimension
or something like that.
To a physicist or a mathematician,
a dimension is just the
direction you can go in.
Up down, left right, forward backward.
To you and me, we think there's
three dimensions around us,
but then physicists start
talking about extra dimensions.
How can you hide them?
Where might they be?
I'm hopeful that we're learn
something at each level.
[down-tempo music]
We're gonna talk about some science.
Do you like science?
- Yes, a lot.
- Oh, very good.
You've come to the right place.
So we're gonna think about physics.
Have you heard the word physics before?
Do you know what that is?
- Yeah, kind of.
- What's your idea what physics is?
- Um, I'm not so sure.
- Okay.
I just think of physics as
the study of everything.
What stuff is, what stuff does.
So today we're gonna talk about space,
and in particular the idea of dimensions.
Have you heard about dimensions?
- At the camp
I made a 3D printing one.
- 3D printing, good.
- So I don't choose the size,
all I had to do was the shape.
- But do you know what 3D means?
- It's three dimensional.
- Three dimensional, as opposed to,
what is ordinary printing?
- So, ordinary printing would be 2D.
- What do you say when
something is one dimensional?
What's an example of something
that's one dimensional?
- Hmm, I think one dimensional
might be a circle, I guess,
or maybe a line.
- A line is the perfect example
- Yeah, a line.
- Because it's one thing
that's straight, right?
- [Hank] Yeah.
- So here's some toys.
We're gonna build some dimensions, right?
So what would you say about this?
- That's one dimensional.
- Exactly.
It's not really one dimensional, right?
- So everything has to
be one or two dimensional
before it's three dimensional.
- And how would you find yourself,
like if someone said where are you,
could you use some words or ideas
to say where you are on that line?
- I think I would be maybe there,
since I'm facing it.
- But here's what I
want you to think about.
If I say I'm at this point on the line,
I could translate that into saying
I'm at the three centimeter point,
if I were here I'd be at
the four centimeter point,
the five centimeter point, right?
- Yeah.
- So every point, every
location on our little line--
- Has its own unit.
- Has its own unit, has one number.
- Yeah.
- We need one number to
tell you where we are.
That's one dimension.
That's what it means
to be one dimensional.
I only need to tell you one number
to figure out where we are.
- Unlike three dimensional,
you have to tell a lot
'cause if it's like a
sphere, you kind of have
to start using points.
- There you go. Exactly.
We're gonna build a little
two dimensional space.
You wanna do it?
You wanna do the honors here?
Why don't you put those
two lines together?
- If you make it
two dimensional is this, a corner.
- Exactly, there you go.
- Another way is if you
have space in between
is an angle.
- I think you should be in this chair
and you should be explaining this to me.
You're much better at this than I am.
- Yeah.
- So those are the dimensions.
That's how we think about dimensions.
Remember, we just needed one number
to find ourselves on the
line, we need two numbers
to find ourselves on the plane.
- I think that would be
an X or a Y axis, so--
- There you go.
So, do you think we could have
more than three dimensions?
- 3D is the maximum of
dimensions for shapes.
- Well, as far as we know.
- Yeah.
- This is why physicists
think about things
we don't know about.
We're wondering whether there
could be extra dimensions
you've never seen.
- Yeah.
- That are tinier than atoms.
So, okay.
So what have you learned?
What do you know about dimensions now?
How do you think about dimensions
in a slightly different
way than you did before?
- So at least everything
has a certain dimension.
- Yeah, do you think you'd be excited
if physicists said that they found
extra dimensions of space?
- That would be an amazing discovery.
The news would be spreaded
around the world rapidly.
- I think so.
I think you're right.
All right Hank, we want
you to keep up studying,
learn a lot of math and physics
and help us discover
new dimensions some day.
Does that sound like a fun idea?
- Yeah.
[playful music]
- Do you like science?
Is that something you think about?
- Yeah, I do.
- [Sean] What kind of science?
- I like biology and computer science.
- All right, you're in the wrong place.
[laughs]
We're not gonna be talking
about biology or computer science.
So we wanna talk about
the idea of dimensions.
Do you know what dimension is?
How we would define dimensions?
- I guess, I don't know
how to exactly define it,
but I know, like the first four.
- Right, you know the difference
between like one dimension
two dimensions, three
dimensions, et cetera.
So let's do a little experiment here.
So there's one dimension.
I'll give that to you.
Now, here's your task.
I'm going to give you another dimension,
and I'm gonna ask hold those two things
at right angles to each other.
It's easy to do.
Yeah, so there's no trick here.
[laughing]
- Yeah.
- I'm not trying to fool you here. Okay.
Now this is going to be slightly trickier.
I'm going to give you this.
I want you to hold all three of them
at right angles to all the others
at the same time.
- Um ...
- There you go.
So what that's doing is
when you had just two
that was describing a two
dimensional plane, right?
Like the two things pick out a plane,
the three things pick out
all three dimensional space.
I'm gonna give you one more,
and I'm gonna ask you
to hold that fourth one
so that it's at a right
angle to all the other three
at the same time.
- Um ...
- All right, now I am tricking you.
It can't be done.
- Yeah.
- Right?
You can't do it.
So we just experimentally proved
that space is three dimensional.
That's sort of what it means
to be three dimensional,
that there are three different
directions you can move in
and there's not four or
five or six directions
you can move in.
- Okay.
- There you go.
Three dimensional space, right?
- Mm-hmm.
- [Sean] So, have you thought
about using coordinates
in three dimensions?
- Yeah, I was actually doing SAT prep.
- There you go.
[laughing]
- It showed like the X
Y and Z axis as well.
- That's right.
So that's exactly what these would be.
Have you heard that there
are other coordinate systems
other than XYX?
- No.
- Well, we could also say how far we are
away from the center, just the distance.
And then the angle that
our little line makes
with let's say the X axis.
- Yeah.
- So that's a different way
of giving you two numbers
and locating yourself, and we
call those polar coordinates.
It's a different coordinate system.
What we want to do as physicists is look
for extra dimensions.
Can you imagine, can you think of any way
that there could be extra dimensions?
- Time?
- Time.
Yes, Einstein said that
we can think of time
as a fourth dimension, and
that's a very fascinating thing
that we could talk about all by itself.
But what about space?
What about the solar system?
Like, if you wanted to tell
me where a certain star was
in the sky, do you know how we do that?
- I have no idea.
- It's exactly the same thing
as latitude and longitude
but we put coordinates on the sky.
- Oh.
- So astronomers call them
right ascension and declination,
which are two terrible words,
but basically you've seen on the globe
where you draw latitude and longitude,
what it looks like.
- [Juliana] Yeah.
- [Sean] And sort of
the peels of an orange
kind of thing, right?
- [Juliana] Yeah.
- So you can define
something as, well you know,
how high above a certain
location on earth it is,
but the earth is rotating
and revolving around the sun
so we have to define separate
celestial coordinates.
- So, there's like how many
dimension would there be?
- We don't know.
You know, the optimistic
view is that there are six,
but the thing is, some of them might be
really, really, really,
really, really small,
like way too small for us to ever see.
- Yeah.
- And some of them might be medium sized
that hopefully we can see.
- Oh, okay.
So since it's all theoretical,
like this could not be three dimensional.
- Absolutely right.
And this is sort of the
state of uncertainty
that physicists are stuck living in.
- Oh. [laughs]
- You know, honestly
out there, if you go out
onto campus and talk to the physicists,
half of them will say probably
extra dimensions exist,
and half of them say no,
that's just nonsense.
- Oh. [laughs]
- [Sean] We really don't know.
- Yeah.
- Okay, after all this.
- [Juliana] Yeah.
- Someone comes up to you
on the street and says
what's a dimension?
- Oh, man.
I mean, I guess what I've learned today
is just that there are
not just three dimensions
or at least we think, I mean
everything's theoretical.
It's all just really kind of confusing.
- That's right, and you know,
if they're still bugging you
you can just like give them some sticks
and ask them to put them together.
- Oh yeah.
- [Sean] And that would shut them up.
- Yeah.
[down-tempo electronic music]
- Where do you go to school
and what do you study?
- I'm gonna be a sophomore
at Pomona College,
and I study math and physics.
- Oh, math and physics, okay.
What kind of physicist do you want to be?
Do you know?
- I really don't know.
I like theory and experimental
so it's kind of tough
for me to say.
- Usually if it's math and physics,
you end up as a theoretical
physicist, right?
- Yeah.
- Not an experimental one.
So, our theme here today is dimensions.
So this is great that you
have some math background
because mathematicians
think about dimensions
in a different way.
- Hopefully, yeah.
- So how would you explain to your friends
who are not math and physics majors,
like what is a dimension, yourself?
- My first intuitive thought
is what are the coordinates.
- Mm-hmm.
- So if we are looking at things,
if we're looking at like a dot,
or a line rather, that's one dimensional
because we can only measure it one way,
but then if we look at like a square
then we're increasing like that,
so it's basically what
coordinates we can use
to measure something.
- That's exactly right,
and so you've heard
of spacetime--
- Yeah.
- [Sean] Being four dimensional, right?
- Mm-hmm.
- Now, in some sense that's
kind of trivial to you and me,
because of course you have space,
which is three dimensional, you have time
which is one dimensional, so
spacetime is four dimensional.
But it didn't turn out,
it didn't occur to anyone
that that was a sensible way to talk
until really relativity.
This is the crucial thing, right?
Is that what Einstein realized is that
sure there's both time and
space, but how we divide
spacetime into time and
space can be different
for different people, and
really there's a real sense
in which four dimensional spacetime
is kind of a generalization
of three dimensional space.
And I think to really explain this
we're gonna need a blackboard.
- Okay.
- Let's bring one in.
[playful music]
All right.
The thing about relativity
is that they really want you to think
of spacetime as one four
dimensional thing, right?
It's kind of like space.
It's not just three dimensions of space
and one dimension of time.
- Why though?
- Why?
This is a very good question.
So, let's just start with space, right?
We know a little bit about space.
So here's my simple minded
way of drawing space
two dimensions, because that's how many
I can draw on the blackboard.
Let's say X and Y.
And what is special about
space, there's many things,
but one is that if I
have a curve or a path
between two points, there's a distance
that you can calculate, right?
And the distance between those two points
doesn't depend on your coordinates.
It doesn't depend on whether
you're in radial coordinates
or Cartesian coordinates, or whatever.
I'm allowed to imagine a curve
that does something like this
between those two points,
and if I were a person
walking on that curve,
I would have an odometer
with me maybe, and I would
know, you would know,
even without having done that,
this path is always gonna
be longer than that path.
There's a formula, Pythagoras' Theorem
that tells you what the
shortest distance path is.
That's the point.
The physical-ness of what is real
is the distance along a certain curve.
So spacetime is like that.
That's why it is useful
to think about spacetime.
- Okay.
- So let me draw spacetime.
Here's how we usually draw it.
I'll just say X, but all
of space is condensed
in this one direction,
and this is time, okay?
So if you're a little person
and you started some event, so you start,
you're located somewhere in space,
somewhere in the three
coordinates of space,
and whether you like it
or not, you're moving
through spacetime just by getting older.
- Yeah.
- When people ask me can
you travel through time?
I say yes, yesterday I traveled
24 hours into the future
and here I am, a day later.
So that's just this.
Okay, you're moving through
time, like it or not.
So what Einstein says
is look, I can travel
through spacetime in different ways,
like I could hop in a rocket ship
and fly out and then fly back,
and then I could meet you there.
So this is a different trajectory
through spacetime, right?
- Yeah.
- And it's almost exactly
like the space story.
The space story says there's a distance,
distance is different
along different curves.
Einstein says there's
something that measures
the length of these curves,
and we call it the proper time.
It is literally the
time that you would read
on your wristwatch.
- So it's kind of like
our fundamental time?
Or our base time?
- Well kind of.
What Einstein wants to get
across is there's no such thing
as fundamental, like
there's the universe's time,
this big letter T that
might tell you how old
the universe is, but then every individual
has a clock with them, and
they measure their own time
depending on how they're
moving through the universe.
- I see.
- And the crucial difference is
that time is not the same for
this person who stayed behind
and sat in their chair,
and this person who zoomed out there.
- Why is that, that
this one's shorter then?
- There is what we call
a metric on spacetime,
and when we talk about Euclidean space
versus a curved space,
versus a sphere or something,
that's a different metric.
And spacetime has its own metric
which says the following thing,
that the path between
two events in spacetime
that is a straight line, will
always be the longest time.
- I see.
Oh, okay.
- [Sean] That's the difference.
- All right.
- So when Einstein had this idea,
oh gravity could be
related to the curvature
of spacetime, he did some equations,
so he got it, that's a long story,
we'll put that aside.
What he figured out was
that rather than gravity
living on top of spacetime,
it's a manifestation
of the curvature of spacetime
so when you have like the
earth, the sun, the moon,
they cause a gravitational field,
they're actually warping
the spacetime around them.
They're giving it a different geometry.
- Would it be if I had like a spring
or not a spring, but like a sheet,
and I dropped a book in
the sheet, curves down?
- Yeah, exactly.
If you had a sheet that
was originally flat,
and you set a marble on it,
it would go in a straight line,
but then if you put something on it
so it warps it, that marble
is now gonna be deflected.
- I see.
- Einstein says that
gravity is just like that.
- I see.
- But there are no straight lines,
because spacetime itself is curved.
So do you think if you
had to explain relativity
what would you say?
- I think I'd go with
kind of the train paradox.
Let's say I'm stationary,
and someone's moving past me
on the train, they think
they're stationary on the train.
Like they think that
they're not accelerating,
but if they start walking
through the train cars,
then they are accelerating in their frame,
but then from my outside frame
where I'm completely removed,
I see they are accelerating.
So I guess that relativity
is all about perspective,
I guess in a way.
- Yeah, that's right.
And it goes exactly back to
what we drew on the board
where how those two people in
the train and on the ground
would divide spacetime up differently
to space and time.
- That was pretty good.
- [Sean] Yeah.
- I learned a lot.
- [Sean] It's a lot of
fun stuff to talk about.
[down-tempo electronic music]
So observational cosmology,
so like what do you look at?
- So, I work on two ground-based
surveys in the optical,
and we're basically
trying to make huge maps
of the universe so that
we can study dark energy.
- I'm sure you've heard
about extra dimensions
a little bit.
- I've heard it, yeah.
- Well I'm thinking about the idea
that there might be more than
three dimensions of space.
What is your impression
of theoretical physicists
who think about things like
extra dimensions of space
that they haven't ever seen?
- I get a little scared,
[laughing]
because I think how can
you prove these theories?
- Right.
- One theory I've heard of,
I don't know if this fits in
with that, is bubble universes.
- Mm-hmm.
- Is that an extra dimension?
Does that fit into that,
or is that something?
- It does.
In fact, one way that different universes
might be created and be
different from each other
is that different universes could have
effectively different
numbers of dimensions.
Like we have three dimensions around us,
but there's people out
there, aliens, who could live
in five dimensional universes.
- And are each of those dimensions,
are they governed by the
same laws of physics,
or is there like a separate
Lagrangian for each universe--
- It's a, yeah.
- [Bela] Or how does that work?
- We think that it would be,
no all of this is incredibly speculative,
and we don't know for sure.
But the idea is that
there is some deep down
underlying laws that are
universal and the same,
but they show up differently,
so they appear different.
So the specific particles
and forces and masses
would be completely
different in different parts
of the multiverse.
- Okay.
- Why in the world would
you think that there
are extra dimensions, right?
So you've heard of string theory?
- I have.
So string theory is basically a theory
of quantum gravity.
- Mm-hmm.
So we have quantum mechanics, right?
The theory of atoms and so
forth and how those work,
and then we have gravity,
and gravity doesn't
seem to fit in.
It's the one force of
nature that we can't really
easily fit into this quantum
mechanical framework,
so string theory is one of the best ideas.
- Right.
- That's the good news.
The bad news is that it only seems to work
if spacetime is ten dimensional.
[chuckles]
So you would say well then it's wrong.
It can't be right.
Spacetime is not ten-dimensional.
Spacetime is four dimensional.
We've observed that.
But instead, we say if
spacetime looks four dimensional
to us, but string theory,
which might be the best theory
we have of quantum gravity says
it must be ten dimensional,
maybe we can hide those
extra six dimensions somehow.
So here's how we could get lucky.
We could imagine that there
are extra dimensions of space
that are curled up somehow
that are so small that we can't see them.
This is actually an old idea.
It goes back to Kaluza and Klein
right after general relativity
was invented in 1915.
But there's a more recent idea that says
there could actually be
relatively large extra dimensions.
There could be extra
dimensions that are actually
that big, like a millimeter across
that you would not have noticed.
But here's the new, exciting idea.
So let's imagine, okay.
This is a piece of paper.
But let's imagine this
is our entire world.
So, in other words, our real
world is three dimensional,
but let's imagine that we're
just idealizing it down
to two dimensions, so we all live here.
You and I live here.
But let's imagine that we're
embedded in this bigger space.
So there are extra dimensions
that are actually big, okay?
And let's imagine that.
When I say we live on this
three dimensional world
what I mean is imagine that the particles
that you and I are made of,
right, the quarks, the leptons,
the electrons and everything,
all the forces we know about,
electromagnetism, the weak nuclear force,
the strong nuclear force,
imagine they can't leave this surface.
This is what we call a brane.
B-R-A-N-E.
Have you heard this word before?
- I've heard it, yeah.
- [Sean] Do you know where it comes from?
- No.
- From membranes, you know.
We have lines, one dimension.
We have two dimensional surfaces.
So if you have a line that is
a vibrating physical thing,
you call it a string, right?
- Right.
- If you have a two dimensional
surface that vibrates
and is a physical thing,
we call that a membrane.
Membrane theory goes back,
it never was as popular
as string theory, but it's
been around for a while.
But if you had extra dimensions of space,
then you can three
dimensional vibrating things,
and four dimensional vibrating things.
- So how do these strings
give rise to things
like mass and charge,
and basically give us
the properties of the
particles that we see?
- Well basically the strings
are the particles that we see.
It's exactly the same thing
as we said for the straw,
if you look at it far away
it looks one dimensional.
A little loop of string,
so a little one dimensional
circle that is vibrating.
If you look at it from
very, very far away,
it just looks like a particle.
So in string theory, an
electron is a little string.
A photon is a little string.
- So, is string theory
part of what they call
the Grand Unified Theory?
Is it supposed to be the last thing
that sort of unifies
all the forces together?
- Yes, string theory's even better.
So the phrase Grand Unified
Theory was coined in the 1970s
for theories that joined
electricity and magnetism.
So a good string theory is gravity plus
the Grand Unified Theory.
- Okay.
- It's even better.
It's the theory of everything.
What would you tell a friend of yours
if they asked you what dimensions are,
what extra dimensions
are, what a brane is?
- So we have three spatial dimensions.
A brane is sort of the next level.
So a brane is a higher dimensional object
that vibrates through space.
- That's right.
And we could live there.
The world we see around
us, the three dimensions
of space around us could reflect the fact
that we are somehow stuck
on a three dimensional brane
trying to escape.
- It was really cool to learn
about strings and branes
and how looking at gravity on small scales
is actually connected to what I do
in looking at gravity on
these cosmological scales,
and it's definitely something
I'm gonna think about
in my research.
[atmospheric electronic music]
- You're a string theorist,
so tell us what kind
of string theory you do, what it means
to be a string theorist.
- One of the things that's key
in the whole story of string theory
is the piece of it that talks about
quantum theories of gravity.
So I'm very excited about
what happens to spacetime,
what does it even mean
at the quantum level.
- Cool, so do you think a
lot about extra dimensions
in your everyday life?
- Uh, yes I do.
- And so when you think
about extra dimensions,
you put them together with
brains and different fields
wrapping around the extra
dimensions and so forth, right?
- Yes.
- You know, a lot of people,
a lot of string theorists,
they care a lot about
all the different ways
in which we could hide
the extra dimensions.
As someone who cares about cosmology,
I wanna start asking why
are the extra dimensions
small at all?
How did that happen?
Is this something you
think about yourself?
- Yes, well ultimately
we'd like to understand
the observable universe.
If string theory turns out to be the thing
that the universe cares about,
we'd like to know, with
all of these possibilities
that are in string theory,
how do we get the one
that looks like the world we live in?
- The thing I want to talk
about is this paper I wrote
with Matt Johnson and Lisa Randall
where we realize there's another way
to compactify extra dimensions
spontaneously, dynamically.
If you imagine starting
with this big piece of paper
you couldn't wrap up everything,
but within some region of
space you could make a tube.
- Okay.
- Right?
And down there in the tube it looks like
your long thing that is
compactified in one direction
and infinitely extending
in the other direction,
so there's one less
macroscopic dimension of space.
- Hmm. Okay, that's nice.
- [Sean] You think that
sounds plausible to you?
- It sounds like fun.
What I would immediately ask is
where do the large dimensions
come from in the first place?
Is that something you
address, or you just assume
that all the dimension are
large as a starting point?
- Yeah.
So we certainly assume
that they're all large
as a starting point, and
it's worse than that.
So in our paper we imagine you start
in de Sitter space.
You start in a universe with no matter,
no anything like that, just empty space
but with an energy that is positive
and all the dimensions are large.
- But where do they come from?
- It was always there.
- Why?
- Why not?
- Okay.
[laughing]
- Well you know, I think
that this is again, this is--
- You're replacing one prejudice
with a different prejudice.
- I would say that we
shouldn't be prejudiced
one way or the other.
- Just a large, ten or 11 dimensions
with a cosmological constant
doesn't seem like a
fundamental starting point.
It sounds like there needs to be something
to underlie that.
But it's a fun scenario.
- Yeah, so let me tell
you a little bit more
about the scenario.
So you know there are black holes, good?
Right?
- I've heard of them.
- [Sean] There are black branes as well.
- Indeed.
- Why don't you explain to
us what a black brane is?
- Well in some ways, it's
very much like a black hole
in that you have far away from it
you have these large just flat dimensions.
As you move in, there's
something in the interior.
It has, itself, higher dimensions,
and so because physicists love to joke
they thought, well it's like a membrane
but it can have many different dimensions.
Let's use P to stand in for
those number of dimensions,
and so they called them P-branes.
- Yeah, I've been trying to explain this
to lower levels, and they
always look at me like,
are you pulling my leg here a little bit?
Or is this the real thing that they use?
Yes, it is the real thing they use.
We study these branes in de Sitter space,
and so what we found is that
there are black brane solutions
which instead of having
a singularity inside
are non-singular, and
stable, and compactified.
Is this a familiar thing?
I know things like this
have been discussed, right?
- Yeah. Yeah.
So, a lot of the branes that
are relevant for studying
things to do with
anti-de Sitter spacetimes
in various dimensions actually start out
as these non-singular type brains,
and then you find in the core,
there's actually an
anti-de Sitter spacetime.
- Right.
Imagine that rather than
going down to a point,
it just asymptotes to some fixed radius
that continues infinitely far down there.
But then you can ask,
okay what about the rest
of the universe?
You have some sphere, some
two dimensions compactified,
and the balance between
the cosmological constant
and the electromagnetic field keeps it
at a fixed distance.
- Right. Good, good.
- But then the other dimensions,
the transverse dimensions,
don't need to be anti-de Sitter.
They can have either positive, zero,
or negative cosmological constant.
So you can basically get any
sort of cosmological solution
times a compactified sphere.
- Is it that these have the lowest action
of all the things that could possibly,
all the possible solutions?
- I guess.
I mean, maybe you'd think otherwise.
Again or maybe you could change my mind,
I think that as long as it can happen
it will happen some of the time, right?
- Okay, that's fair.
- I mean it's one of the
things that could happen, so
I mean it obviously,
You know, we know--
- It's quantum, baby.
- It's quantum.
[laughing]
It's a loud, it's of a loud
it's gonna happen.
- I still laugh from
Keanu Reeves I'm afraid.
[laughing]
- Someone probably wrote it for him.
So it's possible that if you
do have this starting point
of an empty de Sitter space
with positive cosmological
constants and fields lying around
you inevitably get a multiverse.
It just happens, you know,
it's just part of quantum
nucleation to different things,
and then maybe you need to explain
why we live in this universe
rather than some other one
via the anthropic principle
or something like that.
So how does our kind
of, you know, low-tech
old fashioned way of making
new universes intersect
with the kinds of things
you'd think about.
- Well, it's interesting
because there's a lot
of activity going on
inspired by things we learned
from working in anti-de Sitter space
where the cosmological
constant has the wrong sign.
So you will find that there
are a number of papers
as many of which you've probably read,
probably you've read
more of them than I have,
which try then to take the
different kinds of brains,
these extended solutions, and
they're many different kinds
doing different things, we
understand well enough now
that we can put them
together in various ways.
They intersect, they
dissolve inside each other,
they wrap each other.
- They overlap, they wrap around.
- They overlap, and you
do them in all sorts
of different ways and show
that you can construct
four dimensional universes
with a cosmological constant
of your desire, depending upon
how you did the construction.
- I know not everyone buys that, right?
- Not everyone buys it.
There's a big discussion in
the literature right now.
- And if we put aside for the second
the concerns of our colleagues
in other parts of physics,
and it's just amongst us chickens,
what do you think about
the future of cosmology
and string theory, and the dynamics
of these extra dimensions?
- I think it's gonna
get way more interesting
than we're currently able
to grapple with right now,
and I think there are hints of it.
There could be a
description of the physics
that might be our early universe
that is like that molecular description.
And then from that emerges flat spacetimes
maybe four, maybe some mechanism tells you
it's four and not something else.
I think that's where we're going.
- If the viewers wanted to
know more about how spacetime
can emerge from quantum mechanics,
they could read the graphic
novel you just wrote.
- Right, yes.
I wrote and drew a graphic
novel called "The Dialogues:
"Conversations About
the Nature of Universe."
- And I just wrote a book
called "Something Deeply Hidden"
about many worlds, quantum mechanics,
and how spacetime can emerge from it.
Plenty of reading material
for the audience out there.
- Excellent.
[down-tempo electronic music]
- So that was fun.
I hope that everyone did learn something.
I know that I did.
It was very nice to see
how the idea of dimensions
and space resonates in different ways
with different people,
all the way up to talking
to Clifford about the
forefront of modern research.
I really do think that we're not done
understanding how dimensions work.
There are three dimensions
of space, why that?
Why not two?
Why not 27?
I think that we really
don't yet have the data
or ideas to think about this,
but we're creeping up on it.
I'm optimistic about
progress in the near future.
[atmospheric electronic music]
- I'm a professor at the
University of Waterloo.
- And I'm a sleep scientist at UCSF.
- Today I've been challenged
to explain lasers--
- To explain the topic of sleep
at five different levels.
