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  • 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.