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We can clearly observe 4 dimensions.

  • 3 spacial dimensions (objects, including us, have length, width, and depth)
  • 1 time dimension (objects exist over a period of time)

All things in the universe, from ordinary matter to exotic dark matter and dark energy, and even electromagnetic radiation, which travels through the universe at the time-bending speed of light, are subject to these four dimensions even if some may engage with them in different ways.

One of the most mind-bending implications of string theory is that it requires between ten and eleven dimensions to exist in the universe. There are a few different versions of string theory, some of which differ in the number of dimensions they predict. I’m going to focus on the latest theory that has superseded the others, called M-theory. It requires eleven dimensions to exist in the universe.

Some things only become possible if you change your assumptions about the playing field.

For instance, it is impossible to draw a triangle with three right angles on a piece of paper.

But it becomes possible if you draw it on a ball. The difference is that you’ve added another dimension – depth, and this makes the previously impossible shape possible.

A ‘spherical triangle’

Why does M-theory need eleven dimensions?

Any other number of dimensions makes the mathematics of string theory produces intelligible results. Just like how considering time as a fourth dimension allows general relativity to explain gravity, considering eleven dimensions allows string theory to explain all the forces at once. With eleven dimensions, the maths suddenly makes sense.

What it does not tell us is how these dimensions fit into the universe that we see around us. There are two leading explanations, called compact dimensions (i.e. “they’re tiny”) and hyperspace (i.e. “they’re enormous”).

It’s like we’ve learned that a triangle with three right angles is possible, and the only explanation is that the universe has eleven dimensions.

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Compact dimensions

One explanation is that there are tiny six-dimensional shapes called Calabi-Yau manifolds everywhere. They are about the size of the Planck length, and repeat again and again at every point in our regular four dimensional universe. Strings sit on the surface of these shapes, where they vibrate and interact with each other across all of these dimensions. The fact that these strings are on such a crazy six-dimensional shape allows them to pull off weird and wonderful moves between dimensions that let them create the fundamental particles of the Standard Model.

The further you zoom out from this very tiny world and into our own macroscopic world, the more these extra dimensions appear β€˜compactified’. This means that they just get too small for us to see, like how a garden hose viewed at a far distance does not appear to have any depth. In this way the extra dimensions appear to be rolled into the four dimensions that we observe.

An artist’s representation of a Calabi-Yau manifold, a six-dimensional shape.

Branes in hyperspace

The other explanation is the more interesting of the two. It explains that the four dimensions that we perceive as our universe are just the surface of an object called a D3-brane. This ‘brane’ is one of many that exist simultaneously, next to each other like slide magazines in an old slide projector.

The universe that we see may be just one slide of a ‘hyperspace’ that contains many others. Pictured: The Kodak Carousel slide projector. The space that contains all of these branes is called β€˜hyperspace’ or the β€˜bulk’.

Certain kinds of strings are attached only to the four dimensions of our local brane, and they become the fundamental particles described in the Standard Model. But there is another kind of string that is not attached to our brane; it floats free in hyperspace and interacts with our brane only as it moves through it, making it’s influence much weaker than the others. It is this kind of string that forms the graviton, the particle responsible for gravity.

This explanation is interesting, as it predicts the presense of other branes. These we can imagine as parallel universes, and they may be infinite in number.

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