Dimensions vanish in quantum gravity: "Carlip suggests that this foam behaves similarly to the space-time close to a singularity, the object at the centre of a black hole. According to general relativity, gravity is so strong near a singularity that space-time becomes distorted. Under these conditions, light is so strongly bent that it can take an infinitely long time to travel between nearby points. This means neighbouring patches of space-time become effectively disconnected from one another, allowing them to expand and contract independently.
Carlip suggests that at the tiny length scales of quantum gravity, the same sort of disconnection happens between different regions of space. This in turn allows space at different points to expand or contract faster in one dimension than in the others.
As a result, over very short distances and timescales, the motion of a particle is dominated by one dimension, though this favoured dimension keeps changing randomly. This means that if you wait long enough or look at larger distance scales, space becomes effectively three-dimensional."
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