# The Great Unsolved Problems in Physics: Extra Dimensions

| January 23, 2013

In this series of articles I would like to take a look at the fascinating unsolved problems in physics. An overview of such outstanding problems as the theory of quantum gravity, the mystery of dark energy or the origin of time can be both fun and beneficial, so let’s take a look at some of these problems and how physicists are attempting to tackle them.

One of the most popular unsolved problems, at least judging by a number of science fiction movies mentioning it, is the existence of extra dimension. But let’s start at the beginning — what is a dimension? Perhaps the easiest answer would be it is the minimum number of coordinates needed to specify any point in space. So, as it seems at the first glance, we are living in a 3 dimensional universe.

Theodor Kaluza

The interesting thing is that a higher than three number of dimensions can be absolutely useful in physics. And the greatest example of this is the special theory of relativity created by Albert Einstein. In relativity, events are described not only in space, but in time as well. To understand this more intuitively, let’s imagine we need to meet a person for a dinner. What is the minimum required information to come to a meeting? Well, firstly it’s obviously the location of the meeting, which could be specified by 2 coordinates on a map. However, if your meeting is a building with more than one floor, then obviously the number of the floor is needed — that’s a third coordinate. But wait, we forgot something — to actually meet someone, you need to know the time of the meeting. So we have 4 coordinates, or 4 dimensions in total. And this is basically what space-time of special relativity is all about — time can be treated as a 4th dimension, forming space-time with other 3 dimensions (which can also be thought as length, width, height). Of course time is in many ways a different dimension — we can’t move in time freely (it always goes forward) nor we can really grasp it. Nevertheless, Einstein’s space-time with 4 dimensions works astoundingly well, so why is there a need for more dimensions?

To answer this question, we have to go back in time to 1921, when the young German physicist Theodor Kaluza was working on the unification of the theories of gravity and electromagnetism. And rather surprisingly he found out that if the theory of relativity was extended to 5 dimensions rather than 4 it could actually described Maxwell’s laws as well. It was a marvelous discovery, which was admired by Einstein himself. Unfortunately, despite the great interest from physicists, the theory soon ran into major problems (read more about that in this great article).

A nice video about extra dimensions
However, physicists did not abandoned the idea of extra dimensions, as it kept on appearing in various theoretical physics problems, often suggesting elegant solutions.  The list of theories employing extra dimensions includes Randall–Sundrum model, some models of particle physics and, of course, the superstring theory.  Randall-Sundrum model addresses the idea of why gravity is so weak compared to other fundamental forces by employing extra spatial dimensions, whereas the superstring theory requires a high number of extra dimensions for mathematical consistency.

Ok, this is all cool, but is there actually a way to test these claims? To be honest, that’s a really hard question. The problem is that string theory describes these strings that are so small that it is really hard to invent any direct test for the theory. Nonetheless physicists have a variety of ideas how to test the string theory and other theories with predictions of extra dimensions ( more on this here, here and here). Despite this, however, there is no widely accepted confirmation of either extra dimensions or string theory as of today. Hopefully  some new experimental tests will be invented in the near future, as the problem really is fascinating.