TEDxBoulder - Thad Roberts - Visualizing Eleven DimensionsMay 04, 2020
Transcriber: Robert Tucker Reviewer: Ariana Bleau Lugo Is anyone here interested in other
dimensions? (Applause) It's okay. Well, thank you all for your time... and your space. (Laughter) Well, I'm glad that one worked here. Good. 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 limitations of its geometry. For example, imagine that one day some Flatlander scientists observe this: a set of colored lights that seem to appear randomly at different places along the horizon.
No matter how hard they try to make sense of these lights, they won't be able to find a theory that can explain them. Some of the smartest scientists might find a way to describe the flashes probabilistically. 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 consequence, 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 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 seem fundamentally indeterministic. However, when we enlarge our view and access the complete 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 are 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, the quantum tunnel of 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 options: we can stick with our old assumptions and invent new equations that exist somehow outside the metric, as a vague attempt to explain what's going on, or we can go a bolder step, throw out our old assumptions, and build a new model for reality. One that already includes those phenomena. It is time to take that step. Because we are in the same situation as the Flatlanders.
The probabilistic nature of quantum mechanics makes our scientists believe that the world is ultimately indeterminate. That the closer we look, the more we find that nature just doesn't make sense. Hmm... Maybe all these mysteries are actually telling us that there's more to the picture. That nature has a richer geometry than we have supposed. Perhaps the mysterious phenomena in our world could actually be explained by 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 get 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 of position in one dimension does not imply a change of position in the other dimensions. Dimensions are position-independent descriptors. So z is a dimension because an object can be still in 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 be still in x, y, and z, but still moving 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 go no further and talk about distances in space. Let's consider an analogy: imagine we have a piece of pure gold that we want to cut in half over and over again. 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 to a gold atom, we can't go any further without transcending the definition of gold. If the space is quantized, then the same applies. We cannot talk about distances in space that are less than the fundamental unit of space for the same reason that we cannot talk about quantities of gold that are less than 1 gold atom. Quantizing space leads us to a new geometric image. One like this, where the collection of these pieces, these many, come together to build the fabric of x, y, and z. This geometry is
So if you're looking at this, you already have it. It will not be beyond you. We just have to make sense of what's going on. Notice that there are three different types of volume, and 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 x,y,z position only allows us to identify a single quantum of space. Also note 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 dimensions of volume x, y, z, 3 dimensions of superspatial volume and 3 dimensions of interspatial volume. 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 motion through superspace. Okay, I know this is a whirlwind, much faster than I'd like to, because there's so much detail 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 waves.
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 freely resonate, so they experience less time. And in the regions of maximum density, and the quanta are fully packed, such 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 straight through x, y, z space means that both your left and right sides travel the same distance, 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. OK, this is really a big problem. If you've ever seen a graph of Einstein's curvature, the curvature of space-time, you may not have noticed that one of the dimensions wasn't labeled. We assume that we took a plane of our world and every time there was mass on that plane we stretched it out; if there was more mass, we stretch it more, to show how much curvature there is. But what is the direction in which we are stretching?
We got rid of the z dimension. We overlook that every time in our books. Here, we didn't have to get rid of the z dimension. We have to show the curvature in its full form. And this is really a big problem. 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's gone, 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.
In the same way when we observe an electron, and then it disappears from the fabric of space and reappears in another place, and that other place may actually be beyond the limit that it is not supposed to be able to cross. OKAY? 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, quantize space. Well, this image also has something to say about the origin of the constants of nature; such as the speed of light, Planck's constant, the gravitational constant, etc.
Since all the units of expression, Newtons, Joules, Pascals, etc., can be reduced to five combinations of length, mass, time, amperes, 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 are derived 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 quantized space. We cannot go on infinitely. What do these numbers do for us? Well, this long list here are the constants of nature, and if you've noticed, even though they fly by pretty quickly, 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. By the way, that's a big problem, for me it's a big problem. This means that the constants of nature come from the geometry of space; are necessary consequences of the model.
IT'S OKAY. This is a lot of fun because there are so many jokes that 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 is now totally conceptual, you get the whole picture in your head, black holes, quantum tunnels, the constants of nature, and in case none of them you has caught your eye, or you've never heard of any of them before, you've definitely barely heard of dark matter and dark energy. Those are also geometric consequences. Dark matter, when we look at distant galaxies and look at the stars orbiting those galaxies, the stars 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, producing those effects. But we cannot 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 make that kind of leap. We made a leap, we said that space is quantized, but everything else fell apart. 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's true, then an automatic requirement is that it can have changes in density, that's where gravity comes from, but it must also have phase changes. And what stimulates a phase change? Well, the temperature. When something gets cold 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're changes in density. OKAY? Totally skipped through all of that. And now we'll move on to dark energy, in 15 seconds. When we look out into the cosmos, we see that distant light is redshifted, okay?
That it loses some of its energy as it travels towards us over billions of years. Now, how do we explain that redshift? Well, nowadays we say that it means that the universe is expanding. OKAY? 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. OKAY? And we also measure expansion that way. But there is another way to explain the redshift. 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 to your ear. Here, that seemed a bit over the top because atmospheric pressure doesn't decreaserapidly, but when we're talking about billions of light-years traveling through space, all we need are the quanta themselves to have a small amount of inelasticity and the redshift is imminent. Alright, there's a lot more to explore on this, because if you're interested, feel free to visit this website and give as much feedback as you can.
We are 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 romance of Einstein's quest. Thanks. (Applause)
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