a virtually unknown German mathematician, named Theodor Kaluza

suggested a very bold and, in some ways, a very bizarre idea.

He proposed that our universe

might actually have more than the three dimensions

that we are all aware of.

That is in addition to left, right, back, forth and up, down,

Kaluza proposed that there might be additional dimensions of space

that for some reason we don't yet see.

Now, when someone makes a bold and bizarre idea,

sometimes that's all it is -- bold and bizarre,

but it has nothing to do with the world around us.

This particular idea, however --

although we don't yet know whether it's right or wrong,

and at the end I'll discuss experiments which, in the next few years,

may tell us whether it's right or wrong --

this idea has had a major impact on physics in the last century

and continues to inform a lot of cutting-edge research.

So, I'd like to tell you something about the story of these extra dimensions.

So where do we go?

To begin we need a little bit of back story. Go to 1907.

This is a year when Einstein is basking in the glow

of having discovered the special theory of relativity

and decides to take on a new project,

to try to understand fully the grand, pervasive force of gravity.

And in that moment, there are many people around

who thought that that project had already been resolved.

Newton had given the world a theory of gravity in the late 1600s

that works well, describes the motion of planets,

the motion of the moon and so forth,

the motion of apocryphal of apples falling from trees,

hitting people on the head.

All of that could be described using Newton's work.

But Einstein realized that Newton had left something out of the story,

because even Newton had written

that although he understood how to calculate the effect of gravity,

he'd been unable to figure out how it really works.

How is it that the Sun, 93 million miles away,

[that] somehow it affects the motion of the Earth?

How does the Sun reach out across empty inert space and exert influence?

And that is a task to which Einstein set himself --

to figure out how gravity works.

And let me show you what it is that he found.

So Einstein found

that the medium that transmits gravity is space itself.

The idea goes like this:

imagine space is a substrate of all there is.

Einstein said space is nice and flat, if there's no matter present.

But if there is matter in the environment, such as the Sun,

it causes the fabric of space to warp, to curve.

And that communicates the force of gravity.

Even the Earth warps space around it.

Now look at the Moon.

The Moon is kept in orbit, according to these ideas,

because it rolls along a valley in the curved environment

that the Sun and the Moon and the Earth can all create by virtue of their presence.

We go to a full-frame view of this.

The Earth itself is kept in orbit

because it rolls along a valley in the environment that's curved

because of the Sun's presence.

That is this new idea about how gravity actually works.

Now, this idea was tested in 1919 through astronomical observations.

It really works. It describes the data.

And this gained Einstein prominence around the world.

And that is what got Kaluza thinking.

He, like Einstein, was in search of what we call a unified theory.

That's one theory

that might be able to describe all of nature's forces from one set of ideas,

one set of principles, one master equation, if you will.

So Kaluza said to himself,

Einstein has been able to describe gravity

in terms of warps and curves in space --

in fact, space and time, to be more precise.

Maybe I can play the same game with the other known force,

which was, at that time, known as the electromagnetic force --

we know of others today, but at that time

that was the only other one people were thinking about.

You know, the force responsible for electricity

and magnetic attraction and so forth.

So Kaluza says, maybe I can play the same game

and describe electromagnetic force in terms of warps and curves.

That raised a question: warps and curves in what?

Einstein had already used up space and time,

warps and curves, to describe gravity.

There didn't seem to be anything else to warp or curve.

So Kaluza said, well, maybe there are more dimensions of space.

He said, if I want to describe one more force,

maybe I need one more dimension.

So he imagined that the world had four dimensions of space, not three,

and imagined that electromagnetism was warps and curves

in that fourth dimension. Now here's the thing:

when he wrote down the equations describing warps and curves

in a universe with four space dimensions, not three,

he found the old equations that Einstein had already derived in three dimensions --

those were for gravity --

but he found one more equation because of the one more dimension.

And when he looked at that equation,

it was none other than the equation

that scientists had long known to describe the electromagnetic force.

Amazing -- it just popped out.

He was so excited by this realization

that he ran around his house screaming, "Victory!" --

that he had found the unified theory.

Now clearly, Kaluza was a man who took theory very seriously.

He, in fact --

there is a story that when he wanted to learn how to swim,

he read a book, a treatise on swimming --

(Laughter)

-- then dove into the ocean.

This is a man who would risk his life on theory.

Now, but for those of us who are a little bit more practically minded,

two questions immediately arise from his observation.

Number one: if there are more dimensions in space, where are they?

We don't seem to see them.

And number two: does this theory really work in detail,

when you try to apply it to the world around us?

Now, the first question was answered in 1926

by a fellow named Oskar Klein.

He suggested that dimensions might come in two varieties --

there might be big, easy-to-see dimensions,

but there might also be tiny, curled-up dimensions,

curled up so small, even though they're all around us,

that we don't see them.

Let me show you that one visually.

So, imagine you're looking at something

like a cable supporting a traffic light.

It's in Manhattan. You're in Central Park -- it's kind of irrelevant --

but the cable looks one-dimensional from a distant viewpoint,

but you and I all know that it does have some thickness.

It's very hard to see it, though, from far away.

But if we zoom in and take the perspective of, say,

a little ant walking around --

little ants are so small that they can access all of the dimensions --

the long dimension,

but also this clockwise, counter-clockwise direction.

And I hope you appreciate this.

It took so long to get these ants to do this.

(Laughter)

But this illustrates the fact that dimensions can be of two sorts:

big and small. And the idea that maybe the big dimensions around us

are the ones that we can easily see,

but there might be additional dimensions curled up,

sort of like the circular part of that cable,

so small that they have so far remained invisible.

Let me show you what that would look like.

So, if we take a look, say, at space itself --

I can only show, of course, two dimensions on a screen.

Some of you guys will fix that one day,

but anything that's not flat on a screen is a new dimension,

goes smaller, smaller, smaller,

and way down in the microscopic depths of space itself,

this is the idea,

you could have additional curled up dimensions --

here is a little shape of a circle -- so small that we don't see them.

But if you were a little ultra microscopic ant walking around,

you could walk in the big dimensions that we all know about --

that's like the grid part --

but you could also access the tiny curled-up dimension

that's so small that we can't see it with the naked eye

or even with any of our most refined equipment.

But deeply tucked into the fabric of space itself,

the idea is there could be more dimensions, as we see there.

Now that's an explanation

about how the universe could have more dimensions than the ones that we see.

But what about the second question that I asked:

does the theory actually work

when you try to apply it to the real world?

Well, it turns out that Einstein and Kaluza and many others

worked on trying to refine this framework

and apply it to the physics of the universe

as was understood at the time, and, in detail, it didn't work.

In detail, for instance,

they couldn't get the mass of the electron

to work out correctly in this theory.

So many people worked on it, but by the '40s, certainly by the '50s,

this strange but very compelling idea

of how to unify the laws of physics had gone away.

Until something wonderful happened in our age.

In our era, a new approach to unify the laws of physics

is being pursued by physicists such as myself,

many others around the world,

it's called superstring theory, as you were indicating.

And the wonderful thing is that superstring theory

has nothing to do at first sight with this idea of extra dimensions,

but when we study superstring theory,

we find that it resurrects the idea in a sparkling, new form.

So, let me just tell you how that goes.

Superstring theory -- what is it?

Well, it's a theory that tries to answer the question:

what are the basic, fundamental, indivisible, uncuttable constituents

making up everything in the world around us?

The idea is like this.

So, imagine we look at a familiar object, just a candle in a holder,

and imagine that we want to figure out what it is made of.

So we go on a journey deep inside the object and examine the constituents.

So deep inside -- we all know, you go sufficiently far down, you have atoms.

We also all know that atoms are not the end of the story.

They have little electrons that swarm around a central nucleus

with neutrons and protons.

Even the neutrons and protons have smaller particles inside of them known as quarks.

That is where conventional ideas stop.

Here is the new idea of string theory.

Deep inside any of these particles, there is something else.

This something else is this dancing filament of energy.

It looks like a vibrating string --

that's where the idea, string theory comes from.

And just like the vibrating strings that you just saw in a cello

can vibrate in different patterns,

these can also vibrate in different patterns.

They don't produce different musical notes.

Rather, they produce the different particles making up the world around us.

So if these ideas are correct,

this is what the ultra-microscopic landscape of the universe looks like.

It's built up of a huge number

of these little tiny filaments of vibrating energy,

vibrating in different frequencies.

The different frequencies produce the different particles.

The different particles are responsible

for all the richness in the world around us.

And there you see unification,

because matter particles, electrons and quarks,

radiation particles, photons, gravitons, are all built up from one entity.

So matter and the forces of nature all are put together

under the rubric of vibrating strings.

And that's what we mean by a unified theory.

Now here is the catch.

When you study the mathematics of string theory,

you find that it doesn't work