Visualizing Eleven Dimensions: Thad Roberts at TEDxBoulder

In this talk Thad Roberts reveals a theory that could prove to be the key in simplification of the various complexities of quantum mechanics, space, and time.

Does anybody here happen to be interested
in other dimensions?

(Applause)

Alright.

Well, thank you all
for your time... and your space.

(Laughter)

Good, I'm glad that one worked here.

Alright.

Imagine a world
whose inhabitants live and die

believing only in the existence
of two spatial dimensions.

A plane.

These Flatlanders are going to see
some pretty strange things happen;

things that are impossible to explain
within the constraints of their geometry.

For example, imagine that one day,
some Flatlander scientists observe this:

A set of colorful lights
that appear to randomly appear

in different locations along the horizon.

No matter how hard they try
to make sense of these lights,

they'll be unable to come up
with a theory that can explain them.

Some of the more clever scientists

might come up with a way
to probabilistically describe the flashes.

For example, for every 4 seconds,

there's 11% chance that a red flash
will occur somewhere on the line.

But no Flatlander will be able
to determine exactly when

or where the next red light will be seen.

As a consequence, they start to think

that the world contains
a sense of indeterminacy,

that the reason
these lights cannot be explained,

is that at the fundamental level
nature just doesn't make sense.

Are they right?
Does the fact that they were forced

to describe these lights probabilistically

actually mean that
the world is indeterministic?

The lesson we can learn from Flatland

is that when we assume only
a portion of nature's full geometry,

deterministic events can appear
fundamentally indeterministic.

However, when we expand our view

and gain access
to the full geometry of the system,

indeterminacy disappears.

As you can see, we can now
determine exactly when and where

the next red light
will be seen on this line.

We are here tonight

to consider the possibility
that we are like the Flatlanders.

Because, as it turns out,
our world is riddled with mysteries

that just don't seem to fit inside
the geometric assumptions we have made.

Mysteries like warped space-time,
black holes, quantum tunneling

the constants of nature,
dark matter, dark energy, etc.

The list is quite long.

How do we respond to these mysteries?

Well, we have two choices:

We can either cling
to our previous assumptions,

and invent new equations
that exist somehow outside of the metric,

as a vague attempt
to explain what's going on,

or we could take a bolder step,
throw out our old assumptions,

and construct a new blueprint for reality.

One that already includes
those phenomena.

It's time to take that step.

Because we are in the same situation
as the Flatlanders.

The probabilistic nature
of quantum mechanics

has our scientists believing

that deep down,
the world is indeterminant.

That the closer we look,
the more we will find

that nature just doesn't make sense.

Hmm...

Perhaps all of these mysteries
are actually telling us

that there's more to the picture.

That nature has a richer geometry
than we have assumed.

Maybe the mysterious phenomena
in our world

could actually be explained
by a richer geometry,

with more dimensions.

This would mean that we are stuck
in our own version of Flatland.

And if that's the case,
how do we pop ourselves out?

At least conceptually?

Well, the first step is to make sure
that we know exactly what a dimension is.

A good question to start with is:

What is it about x, y and z
that makes them spatial dimensions?

The answer is that a change in position
in one dimension

does not imply a change in position
in the other dimensions.

Dimensions are independent descriptors
of position.

So z is a dimension because an object
can be holding still in x and y

while it's moving in Z.

So, to suggest that
there are other spatial dimensions

is to say that it must be possible
for an object

to be holding still in x, y and z,

yet still moving about
in some other spatial sense.

But where might these
other dimensions be?

To solve that mystery,
we need to make a fundamental adjustment

to our geometric assumptions about space.

We need to assume that space
is literally and physically quantized,

that it's made of interactive pieces.

If space is quantized,

then it cannot be infinitely divided
into smaller and smaller increments.

Once we get down to a fundamental size,

we cannot go any further

and still be talking
about distances in space.

Let's consider an analogy:

Imagine we have a chunk of pure gold

that we mean to cut in half
over and over.

We can entertain two questions here:

How many times can we cut
what we have in half?

and: How many times can we cut
what we have in half and still have gold?

These are
two completely different questions,

because once we get down
to one atom of gold,

we cannot go any further

without transcending
the definition of gold.

If space is quantized,
then the same thing applies.

We cannot talk about distances in space

that are less than
the fundamental unit of space

for the same reason
we cannot talk about amounts of gold

that are less than 1 atom of gold.

Quantizing space brings us
to a new geometric picture.

One like this,

where the collection of these pieces,
these quanta,

come together to construct
the fabric of x, y and z.

This geometry is eleven-dimensional.

So if you're seeing this, you already
got it. It's not gonna be beyond you.

We just need to make sense
of what's going on.

Notice that there are
three distinct types of volume

and all volumes
are three-dimensional.

Distance between any two points in space
becomes equal to the number of quanta

that are instantaneously between them.

The volume inside each quantum
is interspatial,

and the volume that
the quanta move about in is superspatial.

Notice how having perfect information
about x, y, z position,

only enables us to identify
a single quantum of space.

Also notice that it's now possible
for an object

to be moving about interspatially
or superspatially

without changing
its x, y, z position at all.

This means that
there are 9 independent ways

for an object to move about.

That makes 9 spatial dimensions.

3 dimensions of x, y, z volume,
3 dimensions of superspatial volume,

and 3 dimensions of interspatial volume.

Then we have time,
which can be defined as

the whole number of resonations
experienced at each quantum.

And super-time allows us to describe
their motion through super-space.

OK, I know this is a whirlwind,
a lot faster than I'd like to do it,

because there are so many details
we can go into.

But there's a significant advantage
to being able to describe space

as a medium that can possess
density, distortions and ripples.

For example, we can now describe
Einstein's curved space-time

without dimensionally
reducing the picture.

Curvature is a change
in the density of these space quanta.

The denser the quanta get,
the less they can freely resonate

so they experience less time.

And in the regions
of maximum density,

and the quanta are all
packed completely together,

like in black holes,
they experience no time.

Gravity is simply the result
of an object traveling straight

through curved space.

Going straight through x, y, z space

means both your left side
and your right side

travel the same distance,
interact with the same number of quanta.

So, when a density gradient
exists in space,

the straight path is the one
that provides an equal spatial experience

for all parts of a traveling object.

OK, this is a really big deal.

If you've ever looked at a graph
of Einstein curvature before,

space-time curvature,

you may have not noticed that one
of the dimensions was unlabeled.

We assumed we took
a plane of our world

and anytime there was mass in that plane
we'll stretch it;

if there was more mass,
we stretch it more,

to show how much curvature there is.

But what's the direction
we're stretching in?

We got rid of the z dimension.

We blow over that every single time
in our books.

Here, we didn't have to get rid
of the z dimension.

We got to show curvature
in its full form.

And this is a really big deal.

Other mysteries
that pop out of this map,

like quantum tunneling –

Remember our Flatlanders?

Well, they'll see a red light appear
somewhere on the horizon

and then it'll disappear,
and as far as they're concerned,

it's gone from the universe.

But if a red light appears again
somewhere else on the line,

they might call it quantum tunneling,

The same way when we watch an electron,

and then it disappears
from the fabric of space

and reappears somewhere else,
and that somewhere else

can actually be beyond the boundary that
it's not supposed to be able to get beyond.

OK? Can you use this picture now?
To solve that mystery?

Can you see how the mysteries of our world
can transform into elegant aspects

of our new geometric picture?

All we have to do
to make sense of those mysteries

is to change our geometric assumptions,
to quantize space.

OK, this picture also
has something to say

about where the constants
of nature come from;

like the speed of light, Planck's constant,
the gravitational constant and so on.

Since all units of expression,
Newtons, Joules, Pascals, etc,

can be reduced to five combinations

of length, mass, time,
ampere and temperature,

quantizing the fabric of space,

means that those five expressions
must also come in quantized units.

So, this gives us five numbers
that stem from our geometric map.

Natural consequences of our map,
with units of one.

There's two other numbers in our map.

Numbers that reflect
the limits of curvature.

Pi can be used to represent
the minimum state of curvature,

or zero curvature,
while a number we are calling zhe,

can be used to represent
the maximum state of curvature.

The reason we now have a maximum
is because we've quantized space.

We can't infinitely continue to go on.

What do these numbers do for us?

Well, this long list here
is the constants of nature,

and if you've noticed, even though
they're flying by pretty fast,

they're all made up of the five numbers

that come from our geometry
and the two numbers

that come from the limits of curvature.

That's a really big deal by the way,
to me it's a really big deal.

This means that the constants of nature

come from the geometry of space;

they're necessary consequences
of the model.

OK. This is a lot of fun
because there are so many punch lines,

it's hard to know exactly
who's going to get caught where.

But, this new map,

allows us to explain gravity,

in a way that's
totally conceptual now,

you get the whole picture in your head,

black holes, quantum tunneling,
the constants of nature,

and in case none of those
caught your fancy,

or you've never heard
of any of them before,

you've definitely just barely heard
about dark matter and dark energy.

Those too are geometric consequences.

Dark matter,
when we look at distant galaxies,

and watch the stars
that orbit about in those galaxies,

the stars out at the edges
are moving too fast,

they seem to have extra gravity.

How do we explain this?
Well, we couldn't, so we say

there must be some other matter there,
creating more gravity,

making those effects.
But we can't see the matter.

So we call it dark matter. And we define
dark matter as something you can't see!

Which is fine, it's a good step,
it's a good start,

but here in our model we didn't have to
take that kind of a leap.

We took a leap,
we said space is quantized,

but everything else
fell out from that.

Here, we're saying,
space is made up of fundamental parts,

just the same way we believe air
is made out of molecules.

If that's true,
then an automatic requirement is

you can have changes in density,
this is where gravity comes from,

but you should also have phase changes.

And what stimulates a phase change?

Well, temperature.

When something gets cold enough,
its geometric arrangement will change,

and it will change phase.

A change in the density here,
at the outer regions of the galaxies,

is going to cause
a gravitational field,

because that's what
gravitational fields are,

they're changes in density.

OK?

Totally skipped through all that.

And now we'll go to dark energy,
in 15 seconds.

When we look out into the cosmos,
we see that distant light

is red shifted, OK?

That it loses some of its energy
as it's traveling to us

for billions of years.

Now how do we explain
that red shift?

Well, currently we say it means
the universe is expanding. OK?

All of our claims that the universe
is expanding come from this,

from measurements of how
the red shift changes,

out of this distance
to this distance to that distance.

OK? And also we measure
the expansion that way.

But there's another way
to explain red shift.

Just like there'd be another way
to explain how if I had a tuning fork

tuned to middle C,

and I went in a tunnel
and you could hear... a B note.

Sure, you could say it's because
I'm moving away from you inside the tunnel,

but it could also be because
the pressure of the atmosphere

is decreasing while the sound
is traveling to your ear.

Here, that seemed
a little far fetched

because atmospheric pressure
doesn't decrease fast,

but when we're talking billions of years
of light traveling through space,

all we need are the quanta themselves

to have a small amount of inelasticity
and red shift is imminent.

Alright, there's a lot more
to explore in this,

because if you're interested,
feel free to check out this website

and give all the feedback you can.

We're out of time so let me just say,
that this blueprint gives us a mental tool,

a tool that can expand
the reach of our imagination,

and, maybe, even respark
the romanticism of Einstein's quest.

Thank you.

(Applause)