Here is the transcript of theoretical physicist Thad Roberts’ TEDx Talk: Visualizing Eleven Dimensions at TEDxBoulder.
Listen to the MP3 Audio here: Thad Roberts on Visualizing Eleven Dimensions at TEDxBoulder
Does anybody here happen to be interested in other dimensions? All right.
Well, thank you all for your time and your space. Good, I’m glad that one worked here.
All right. 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, et cetera. 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 can 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 going to 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.