TEDxBoulder - Thad Roberts - Visualizing Eleven Dimensions

Transcriber: Robert Tucker Reviewer: Ariana Bleau Lugo Is anyone here interested in other

dimensions

? (Applause) Very good. Well, thank you all for your time... and your space. (laughs) Well, I'm glad one worked here. Alright. Let us imagine a world whose inhabitants live and die believing only in the existence of two spatial

dimensions

. A plane. These Flatlanders will see some pretty strange things happen; things that are impossible to explain within the limitations of their geometry. For example, imagine that one day some Flatlander scientists observe this: a set of colored lights that seem to appear randomly in different places along the horizon.

No matter how hard you try to make sense of these lights, you won't be able to find a theory that can explain them. Some of the smarter scientists might find a way to probabilistically describe the flashes. For example, for every 4 seconds, there is an 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 result, they begin 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 simply does not make sense.

They are right? Does the fact that they were forced to describe these lights probabilistically really mean that the world is indeterministic? The lesson we can learn from Flatland is that when we assume only part of the complete geometry of nature, deterministic events can appear fundamentally indeterministic. However, when we broaden our vision and access the full geometry of the system, the 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 may be like the Flatlanders.

Because it turns out that our world is riddled with mysteries that just don't seem to fit within the geometric assumptions we've made. Mysteries such as warped space-time, black holes, quantum tunnels of nature's constants, dark matter, dark energy, etc. The list is quite long. How do we answer these mysteries? Well, we have two options: we can hold on to our previous assumptions and invent new equations that exist somehow outside of the metric, as a vague attempt to explain what is going on, or we can take a bolder step, throw away our old assumptions and build a new model for reality.

One that already includes those phenomena. It's time to take that step. Because we are in the same situation as the inhabitants of Flatland. The probabilistic nature of quantum mechanics leads our scientists to believe that the world is ultimately indeterminate. That the closer we look, the more we find that nature simply doesn't make sense. Hmm... Maybe all these mysteries are actually telling us that there is more to the picture. That nature has a richer geometry than we have assumed. Perhaps the mysterious phenomena of our world could be explained by a richer geometry, with more dimensions. This would mean we're stuck in our own version of Flatland.

And if that's the case, how do we get out? At least conceptually? Well, the first step is to make sure we know exactly what a dimension is. A good question to start with is: What do x, y, and z have 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 position-independent descriptors. So z is a dimension because an object can stay still at x and y while moving in Z. So to suggest that there are other spatial dimensions is to say that it must be possible for an object to stay still at x, y, and z, but still move somewhere. another spatial sense.

But where could 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 quantified, that it is made of interactive pieces. If space is quantized, then it cannot be divided infinitely into smaller and smaller increments. Once we get to a fundamental size, we can't go any further and continue talking about distances in space. Let's consider an analogy: imagine that we have a piece of pure gold that we intend to cut in half again and again. Here we can consider two questions: 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?

They are two completely different questions, because once we get to a gold atom, we can't go any further without transcending the definition of gold. If space is quantized, the same applies. We cannot speak of distances in space less than the fundamental unit of space for the same reason that we cannot speak of quantities of gold less than 1 gold atom. Quantizing space leads us to a new geometric image. One like this, where the collection of these pieces, these quanta, come together to build the fabric of x, y and z. This geometry is

eleven

dimensions. So if you're watching this, you already have it.

It won't be out of your reach. We just need to make sense of what is happening. Note that there are three different types of volume and that all volumes are three-dimensional. The distance between any two points in space becomes equal to the number of quanta that are instantly between them. The volume within each quantum is interspatial and the volume in which the quanta move is superspatial. Notice how having perfect information about the x,y,z position only allows us to identify a single quantum of space. Note also that it is now possible for an object to move 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. That makes 9 spatial dimensions. 3 x, y, z volume dimensions, 3 superspace volume dimensions and 3 interspatial volume dimensions. Then we have time, which can be defined as the total number of resonances experienced in each quantum. And supertime allows us to describe its movement through superspace. Okay, I know this is a whirlwind, much faster than I'd like to do it, because there are so many details we can get into. But there is a significant advantage in being able to describe space as a medium that can possess density, distortions and undulations.

For example, we can now describe Einstein's curved spacetime without dimensionally reducing the image. Curvature is a change in the density of these spatial quanta. The denser the quanta become, the less they can resonate freely, so they experience less time. And in the regions of maximum density, and the quanta are completely packed together, as in black holes, they do not experience time. Gravity is simply the result of an object traveling in a straight line through curved space. Going directly through x,y,z space means that both the left and right sides travel the same distance and interact with the same number of quanta.

So when there is a density gradient in space, the straight path is the one that provides an equal spatial experience for all parts of a traveling object. Well, this is really important. If you've ever looked at a graph of Einstein's curvature, the curvature of spacetime, you may not have noticed that one of the dimensions was unlabeled. We assumed that we took a plane of our world and whenever there was mass in that plane we stretched it; If there was more mass, we stretched it more, to show how much curvature there is. But in what direction are we moving?

We got rid of the z dimension. We overlook that every time in our books. We didn't have to get rid of the z dimension here. We were able to show the curvature in its full form. And this is really important. Other mysteries that arise from this map, such as quantum tunnels. 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 could call it quantum tunneling. In the same way when we observe an electron, and then it disappears from the fabric of space and reappears somewhere else, and that other place may actually be beyond the boundary that it is not supposed to transcend.

OK? Can you use this image now? To solve that mystery? Can you see how the mysteries of our world can be transformed into elegant aspects of our new geometric image? All we have to do to make sense of those mysteries is change our geometric assumptions and quantify space. Well, this image also has something to say about where nature's constants come from; such as the speed of light, Planck's constant, the gravitational constant, etc. Since all units of expression, Newtons, Joules, Pascals, etc., can be reduced to five combinations of length, mass, time, amperes, and temperature, quantifying the structure of space means that those five expressions must also come in quantized units.

So this gives us five numbers that emerge from our geometric map. Natural consequences of our map, with units of one. There are two other numbers on 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 call zhe can be used to represent the maximum state of curvature. The reason we now have a maximum is because we have quantified the space. We cannot continue infinitely. What do these numbers do for us? Well, this long list here are the constants of nature, and if you've noticed, although they go by quite quickly, they are all made up of the five numbers that come from our geometry and the two numbers that come from the limits of curvature.

By the way, that is very important, for me it is a big problem. This means that the constants of nature come from the geometry of space; They are necessary consequences of the model. OK. This is really fun because there are so many jokes that it's hard to know exactly who will get caught where. But this new map allows us to explain gravity in a way that is now totally conceptual, you have the whole picture in your head, the black holes, the quantum tunnels, the constants of nature, and in case none of that appeals to you attention, or you've never heard of any of them before, you've definitely barely heard of dark matter and energy.

Those are also geometric consequences. Dark matter, when we look at distant galaxies and we look at the stars orbiting those galaxies, the stars on the edges move 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, which creates more gravity and produces those effects. But we cannot see the matter. That's why we call it dark matter. And we define dark matter as something that cannot be seen! 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 leap.

We took a leap, we said that space is quantized, but everything else went from there. Here we say that space is made up of fundamental parts, in the same way that we believe that air is made up of molecules. If that is true, then an automatic requirement is that you can have changes in density, this is where gravity comes from, but you must also have phase changes. And what stimulates a phase change? Well, temperature. When something cools enough, its geometric arrangement will change and it will change phase. A change in density here, in the outer regions of galaxies, is going to cause a gravitational field, because that's what gravitational fields are, they are changes in density.

OK? He skipped all that completely. And now we'll move on to dark energy, in 15 seconds. When we look at the cosmos, we see that distant light is redshifted, okay? It loses some of its energy as it travels toward us over billions of years. Now, how do we explain this red shift? Well, these days 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 redshift changes, from this distance to this distance to that distance. OK? And we also measure expansion that way.

But there is another way to explain the redshift. Just like there would be another way to explain how if you had a tuning fork tuned to middle C, and you went into 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 as the sound travels toward your ear. In this case, that seemed a little far-fetched because atmospheric pressure doesn't decrease quickly, but whenWe are talking about billions of years of light traveling through space, all we need are the same quanta to have a small amount of inelasticity and the red shift is imminent.

Alright, there's a lot more to explore in this, because if you're interested, feel free to visit this website and give as much feedback as you can. We are running out of time, so let me say that this model gives us a mental tool, a tool that can expand the reach of our imagination and perhaps even rekindle the romanticism of Einstein's quest. Thank you. (Applause)