Why I study the seventh dimension | Science



When we hear the word "dimension" we often think of science fiction, but it is a very present concept in our day to day life. For example, when buying a wardrobe, it is essential to know that it fits in the room where we go to put it. For this, we need to know its height, width and depth: these are the three habitual dimensions that we experience every day. However, there are many more important factors when purchasing furniture, such as its weight - especially if you have to climb it up the stairs -, its cost or its color. These and many other properties can be measured on a certain scale (the color can be assigned a number, using the wavelength), and can be considered dimensions.

In general, we can have as many dimensions as we want, and we should not worry about the idea of ​​adding more; it is just a way of describing additional properties of the object. In physics, an obvious dimension to take into account is time, since it is crucially important in any phenomenon of nature. To understand gravity it is essential to conceive the universe as a four dimensional object, eventually as the fourth dimension. Currently the additional dimensions seems to be the only plausible way to have a complete understanding of our universe.

I study, in particular, the seventh dimension. And why seven dimensions? The key is in the symmetry. The cubes and spheres have many symmetries, since their appearance is the same from many angles, but other geometric shapes, such as rectangles or rugby balls have less. The symmetries and dimensions are related: The types of symmetries that can occur depend to a large extent on the number of dimensions. Surprisingly, there is a certain type of symmetry of curved objects (called holonomy G2) that can only happen in seven dimensions.

Finding and understanding seven-dimensional objects with holonomy G2 is very complicated. However, it is possible to get an idea of ​​its configuration by looking at a simple object: soap bubbles. By gently blowing the soap film, if we get the bubble to form, little by little it becomes round. This form minimizes the area of ​​its surface, given the volume of air it contains. The spaces of seven dimensions with holonomy G2 that interest us also minimize a type of area or energy. Although it does not always work, I have demonstrated that it is possible to use the mechanism by which the bubble becomes round, which also turns out to be closely related to the way in which the heat dissipates in a room, to find the spaces of seven dimensions that interest us.

The cubes and spheres have many symmetries, since their appearance is the same from many angles, but other geometric shapes, such as rectangles or rugby balls have less

These objects also appear in modern theories about the shape of our universe. Specifically, in the string theory, one of the candidates to be the long-awaited theory of everything. This theory models elementary particles as "ropes", that is, objects of a dimension, which can be loops or open fragments, with loose ends. This has drastic consequences: we need many more dimensions to describe our universe, at least 10 in total. More worrying still is that there are several string theories in 10 dimensions, and what we are looking for is a single unified theory.

For this purpose the call has been devised Theory M, a proposal that brings together all the theories of strings of 10 dimensions, and that assumes that the universe has 11 dimensions. In its simplest version, the universe is composed on the one hand of four dimensions (the usual three of space and one of time) and a piece of seven dimensions, which, surprisingly, has to have holonomy G2. This link is opening fascinating new research that unite geometry in seven dimensions and physics.

Jason Lotay is a professor of mathematics in University College London (UCL)

Coffee and Theorems is a section dedicated to mathematics and the environment in which they are created, coordinated by the Institute of Mathematical Sciences (ICMAT), in which researchers and members of the center describe the latest advances in this discipline, share points of contact between mathematics and other social and cultural expressions and remind those who marked their development and knew how to transform coffee into theorems. The name evokes the definition of the Hungarian mathematician Alfred Rényi: "A mathematician is a machine that transforms coffee into theorems".

Editing and coordination: Agate Rudder (ICMAT)

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