Multiple Dimensions

When someone mentions “different dimensions,” we tend to think of things like parallel universes — alternate realities that exist parallel to our own, but where things work or happened differently. However, the reality of dimensions and how they play a role in the ordering of our universe is really quite different from this popular characterization.

To break it down, dimensions are simply the different facets of what we perceive to be reality. We are immediately aware of the three dimensions that surround us on a daily basis – those that define the length, width, and depth of all objects in our universes (the x, y, and z axes, respectively).

Beyond these three visible dimensions, scientists believe that there may be many more. In fact, the theoretical framework of superstring theory posits that the universe exists in 10 different dimensions. These different aspects are what govern the universe, the fundamental forces of nature, and all the elementary particles contained within.

The first dimension, as already noted, is that which gives it length (i.e., the x-axis). A good description of a one-dimensional object is a straight line that exists only in terms of length and has no other discernible qualities.

Add to it a second dimension, height (i.e., the y-axis), and you get an object that becomes a two-dimensional shape (e.g., a square).

The third dimension involves depth (i.e., the z-axis), and it gives all objects a sense of area and a cross-section. The perfect example of this is a cube, which exists in three dimensions and has a length, a width, a depth, and, therefore, also a volume.

Beyond these three lie the seven dimensions that are not immediately apparent to us, but that can still be perceived as having a direct effect on the universe and reality as we know it.

Getting to Know the Other Dimensions

Scientists believe that the fourth dimension is time (we already know this one, for the most part), which governs the properties of all known matter at any given point. Along with the three other dimensions, knowing an object’s position in time is essential to plotting its position in the universe.

The other dimensions are where the deeper possibilities come into play, and explaining their interaction with the others is where things get particularly tricky for physicists.

According to string theory, the fifth and sixth dimensions are where the notion of possible worlds arises. If we could see on through to the fifth dimension, we would see a world slightly different from our own that would give us a means of measuring the similarity and differences between our world and other possible ones.

Image credit: Berkeley Center for Cosmological Physics

In the sixth, we would see a plane of possible worlds, where we could compare and position all the possible universes that start with the same initial conditions as this one (i.e., the Big Bang). In theory, if you could master the fifth and sixth dimensions, you could travel back in time or go to different futures.

In the seventh dimension, you have access to the possible worlds that start with different initial conditions. Whereas in the fifth and sixth dimensions the initial conditions were the same and subsequent actions were different, here, everything is different from the very beginning of time. The eighth dimension again gives us a plane of such possible universe histories, each of which begins with different initial conditions and branches out infinitely (that’s why they are called infinities).

In the ninth dimension, we can compare all the possible universe histories, starting with all the different possible laws of physics and initial conditions. In the tenth and final dimension, we arrive at the point at which everything possible and imaginable is covered. Beyond this, nothing can be imagined by us lowly mortals, which makes it the natural limitation to what we can conceive in terms of dimensions.

Making Sense of the Theory

The existence of these additional six dimensions that we cannot perceive is necessary for string theory in order for there to be consistency in nature. The fact that we can perceive only four dimensions of space can be explained by one of two mechanisms:

- The extra dimensions are compactified on a very small scale.
- Our world may live on a three-dimensional submanifold corresponding to a brane on which all known particles besides gravity would be restricted (a.k.a., brane theory).

If the extra dimensions are compactified, then the extra six dimensions must be in the form of a Calabi–Yau manifold. While imperceptible as far as our senses are concerned, they would have governed the formation of the universe from the very beginning. That’s why scientists believe that by peering back through time, using telescopes to spot light from the early universe (i.e., billions of years ago), they might be able to see how the existence of these additional dimensions could have influenced the evolution of the cosmos.

The existence of extra dimensions is explained using the Calabi-Yau manifold, in which all the intrinsic properties of elementary particles are hidden. Image Credit: A Hanson

Much like other candidates for a grand unifying theory (a.k.a., the theory of everything), the belief that the universe is made up of ten dimensions (or more, depending on which model of string theory you use) is an attempt to reconcile the standard model of particle physics with the existence of gravity. In short, it is an attempt to explain how all known forces (gravity, electromagnetism, the electromagnetic weak and strong force) within our universe interact and how other possible universes themselves might work.

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