Why space has exactly three dimensions - physics-math - 26 September 2013 - New Scientist

Why space has exactly three dimensions - physics-math - 26 September 2013 - New Scientist: Quantum states are described not by 1D real numbers, which all lie on a single line, but by 2D complex numbers that represent points on a plane. The way these numbers interact to produce a complete description of objects such as photons that can be in more than one state at once naturally sketches out a 3D sphere describing all those possible states. Perhaps this result is just emphasising how the dimensionality of basic quantum objects and the dimensionality of space happen to be the same.

Müller thinks not: he thinks it points to an inextricable link between space's geometry and the degree of probability inherent in quantum theory. If so, the roots of relativity and quantum theory would be embedded in the way information is exchanged in the cosmos, suggesting where to look for any unifying theories. "It offers a clue that the notion of information will be an important part of quantum gravity," says Müller.