If our space is a surface contained within a network, it is in effect a space within a larger space, which oddly enough isn’t a new idea. In 1919, Kaluza successfully derived Maxwell’s equations from relativity theory by expressing Einstein’s equations in four dimensions. He essentially unified quantum theory and relativity but his discovery was ignored because a physically real extra dimension would make gravity vary as an inverse cube so the solar system would collapse. Kaluza’s extra dimension was denied because it contradicted physical realism, so when mathematicians discovered that electromagnetism could be explained by complex numbers rotating into a fourth dimension, they called that dimension imaginary. This was then accepted because it didn’t contradict physical realism.

Klein then tried to rescue Kaluza’s extra dimension by saying it was compactified, curled up in a tiny circle so entering it returned you to the start but this was also seen as unlikely. Years later, when string theorists needed to explain the six extra dimensions their mathematics required, they suggested that space contains extra dimensions curled up within it. But why would nature create extra dimensions that do nothing except make our equations work?

In contrast, a virtual reality that appears on a screen surface is contained in a space with an extra dimension. If our space is a three-dimensional surface, there must be another non-physical dimension as well as the three physical dimensions of the virtual reality. Unlike string theory, this dimension extends at right angles to our space rather than curls up within it. Quantum space is the four-dimensional space that contains our three-dimensional space as a surface within it. It implies an extra dimension that we can no more enter than a game avatar can leave its screen world to enter ours.

Physicists express this idea by saying that space is a brane in a higher-dimensional bulk and conclude that if the extra dimension of that bulk is sequestered from our space, the gravity problem that denied Kaluza’s theory long ago can be avoided (Randall & Sundrum, 1999):

“Physicists have now returned to the idea that the three-dimensional world that surrounds us could be a three-dimensional slice of a higher dimensional world.” (L. Randall, 2005) p52

If this higher dimensional space is quantum space, our space is a polar surface rather than a Cartesian “slice”.