Is there a fifth dimension? | Arlie Petters | TEDxNCSSM

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How can we tell if there is a fifth dimension and where exactly in space-time it exists? What is the role of black holes in that? Arlie O. Petters explains.

It's truly a delight to be here.

I want to pose a very simple
but provocative question.

You're sitting there, I am standing here.

We're experiencing
a three-dimensional space:

length, width, and height.

We also have on our watches,
so there is another dimension - time.

So, we are here
in a four-dimensional world.

I would like to ask
a very simple question:

can there be a fifth dimension?

This extra dimension would not
just be a dimension of time,

but we're thinking a dimension of space.

But isn't that a weird question?

Can you imagine moving in a direction
beyond length, width, and height?

That is a provocative question
of today's story.

Let us begin by taking a look
at a little bit of issues

that would relate
to a higher dimensional object.

So let us begin
with the following picture.

We have a wire cube,
and we're going to shine light on it.

What you're seeing below
is a shadow of that wire cube.

But it's not just an ordinary shadow.

It's a special one that captures

the extra properties of the full object.

So, if you count the vertices
in this cube, you'll see the number

of vertices in that shadow.

If you count the edges in that cube,
you will see the exact number.

In fact, this shadow has a name.

It's called a Schlegel diagram.

Now, the question arises:

what would be the shadow
of a four-dimensional cube?

A tesseract that we're all familiar with.

In that case, the shadow
will not appear in the ground.

It would sit in three-dimensional space.

And that shadow
would look something like this.

Some of you have seen this picture.

It's a diagram that also captures
the higher dimensional properties

of this four-dimensional cube.

Again, you can count the vertices,
the edges, the faces, and so on.

This is a picture
that has captured the ideas

of architects, artists, and so on.

If next time you're in Paris,

you should take a look at the Grand Arch.

You will see that this
was the winning entry

by the architect Spreckelsen
for the competition

of the Grand Arch set out by Mitterrand.

It is actually a five-dimensional
representation of this object

that can sit in a five-dimensional space.

So, this is the kind of thing
that we would like to address

from a physics point of view.

And in order to do that,

let us begin by taking a look
at Einstein's theory of gravity.

When you look at
how gravity acts on light,

there is something
very peculiar that happens.

We all grew up thinking
that light follows a straight line.

But one of the profound things
that Einstein showed us

is when you have light traveling in space,
the gravity of objects will bend it.

And he was the first person
to give the correct calculation

of the bending angle.

I'd like to share with you
an essay that he wrote in 1936

that most people are not aware of.

In this essay in fact he was 57 years old.

He showed that if you have an object,

so in this case you have a satellite
and here we are on Earth.

Notice when a signal travels to Earth,

it's bent by the gravitational
field of the Sun.

But let us imagine now
that you have a star.

He looked more closely
at that bending and discovered

that you would see double images
of this background source of light.

You would have a cosmic mirage.

In the same essay, which was
just a page and a half,

he also observed that if the source
of light sits on the line of sight,

so here we have the source
on the line of sight

and here it is off the line of sight.

When it's off the line of sight
you see two images.

When it's on the line of sight
it appears formally very bright.

And so bright it looks like a ring.

I would like to take that essay
and re-interpret it.

This is what is going on.

There is actually a shadow pattern

being created at the location
of the source.

And this shadow pattern
is actually being generated

by the action of gravity on light.

In other words, objects in the Universe
scare shadows throughout the cosmos.

And these shadows are different
from the Schlegel diagrams

that I showed you earlier.

These are natural things in the Universe.

And so in this case,
here in the background,

I am just showing you
the pattern created by a star.

So if you cut across here,
your brightness will do this,

it will go to a peak and then drop.

What does this shadow pattern
look like, say, due to 30 stars?

Here is an image that was generated
from a complete analysis

of the equations that come
from Einstein's theory of gravity.

So if you look at these, it may remind you

of when you look at light
glittering on a side of a boat,

when you're in a harbor.

But these are produced in the Universe.

If you have a 100,000 stars,
this is what it would look like.

It's getting more and more complex.

We know that stars have planets.

If you include the planets,

the shadows will begin
to pick up micro-structures

and this is an example
of what it would look like.

Doesn't that remind you
of the neural network of a brain?

As we had from an earlier speaker?

It's just amazing the profound
similarities that appear in science.

This is the basic idea

that will sit inside the question
of higher dimensions.

Well, the basic question sits

with the theory of Brane-World Gravity.

In this world, you have
length, width, height, time

and then is an extra one
that we all call the fifth dimension.

The shadow patterns you just saw,
that comes from Einstein's theory.

And in that theory,
we're in a four-dimensional universe.

The question is what happens
with the shadow patterns

in a five dimensional world?

And would that help us to address
the question of knowing scientifically

that there is an extra dimension,
the physical space?

So, here is Brane-World Gravity
in a nutshell.

The word brane, b-r-a-n-e,
is a shorthand for membrane.

And I am going to briefly
show you a picture

that's the Randall–Sundrum
Formulation of that theory.

And what it says is that our Universe

sits in this five-dimensional world.

Here I represented our Universe
by this flat sheet.

So this flat sheet is actually
a four-dimensional entity.

And you can have another brane,
a parallel universe to ours.

And so then this direction would represent
the direction of the fifth dimension.

And so as we stand here or sit here,
you're experiencing physical space

in our universe so we are locked on here.

But then how would we know
there is something off that?

That is the question.

And the key is to take a look
at this issue

of how gravity acts on light.

I'll share with you some research done
by the astronomer Charles Keeton

and myself by taking
a gravitational lensing approach

to trying to figure out: can we know
there is a fifth dimension?

And the story begins with the Big Bang.

Early in the Universe,
temperatures were extremely hot.

The Universe was extremely dense.

And these densities were uneven.

The areas that were more dense actually
collapsed and created black holes.

And in this environment,

you have these microscopic
black holes being formed.

In particular,

if the Universe is five-dimensional,

you would have five-dimensional
braneworld black holes being formed.

If the Universe is four-dimensional,

you will have microscopic
regular black holes

you know about from Einstein's theory

being formed.

And so the question is how could we tell
the difference between the two.

The strategy is to try and find
a braneworld black hole

by looking for its signature,
its fingerprint on light.

And we approach this problem

by using a very simple law

about the behavior of these objects
from the early universe to now.

And it has to do with the following issue.

Imagine you have a black hole
that's probably the size of a nucleus,

but the mass of an asteroid.

So, this is a very powerful object.

When such objects were formed

in the early universe,
in Einstein's theory,

they would have fizzled out by today.

And that is because they are very hot,

and they radiate energy
according to a certain law.

And that law is governed
by the four-dimensional properties

of Einstein's theory.

If however, that microscopic black hole

is five-dimensional,
if it's formed in a context

of braneworld theory, it would be cooler

and therefore,
would not fizzle out to today

if it has a mass
of that of an asteroid or less;

and so the idea is
that today such objects,

from a braneworld point of view
would exist.

And now we want to find
how they will act on the light.

The basic idea is this:

Imagine you have a still pond

and you drop a pebble.

It is going to create ripples,

and those ripples are actually going
to give you the key signature,

the key fingerprint of these black holes.

The same way
how you'll have in this pattern

the waves that are going out.

You have the lows and the highs,
and then it dies off towards the end.

The braneworld black holes
would do a similar thing.

And here's a cartoon of what its signature
and light would look like.

It is different from the signature
and light that the star would create;

than the one in Einstein's essay,

because here the braneworld black hole
is microscopic, but it has a lot of mass.

It can have a very powerful
gravitational field.

And so when you look
at this pattern in the background,

you can actually predict
the signature it's going to have.

And this is what it looks like.

It's going to do the following,
just as in a wave.

You'll see the wiggles like that.

And if there's no braneworld black hole,

you're going to have a constant signal
that cuts across in this way.

And so what we did is to take
the question of an extra dimension

into one of searching for an object
from that extra dimension;

namely, a microscopic
braneworld black hole.

And we are able to fingerprint it
by its action on light.

This prediction is actually
accessible to current technology.

We have a satellite in orbit right now,
the FERMI Space Telescope.

And this can measure energies
in a very high range,

in what's called a 200 MeV range.

And it's exactly in that range

that we are predicting
this wiggle ought to exist.

And so the story
really is saying the following:

if we find evidence for this wiggle,

it is going to favor this five-dimensional
point of view of the Universe.

Imagine, there was a point
when we thought the Universe

had certain properties
beginning with Earth.

In the old days, remember, the Universe
was really the Earth and the stars

and you thought the Earth is flat,
and then there was this provocative idea,

that it's round.

I believe that we are
at a similar stage,

where, if you find evidence
for a fifth dimension,

you are going to now have
an entire paradigm shift

of our understanding of reality.

Thank you.

(applause)