Cycles of Time: An Extraordinary New View of the Universe

by Roger Penrose

even the ordinary closely flat space-time of our experiences, if it were to be examined at the minute Planck scale, would be found to have a turbulent chaotic character, or perhaps a discrete granular one—or have some other kind of unfamiliar structure better described in some other way. Wheeler presented the case for quantum effects of gravity causing the space-time at the Planck level to curl up into topological complications that he viewed as a kind of ‘quantum foam’ of ‘wormholes’.[3.70] Others have suggested that some kind of discrete structure might manifest itself (like entangled, knotted ‘loops’,[3.71] spin foams,[3.72] lattice-like structure,[3.73] causal sets,[3.74] polyhedral structure,[3.75] etc.[3.76]), or that a mathematical structure, modelled on quantum-mechanical ideas, referred to as ‘non-commutative geometry’[3.77] might become relevant, or that higher-dimensional geometry might play a role, involving string-like or membrane-like ingredients,[3.78] or even that space-time itself might fade away completely, where our normal macroscopic picture of space-time arises only as a useful notion derived from a different more primitive geometric structure (as happens with ‘Machian’[3.79] theories and with ‘twistor’ theory[3.80]). It is clear from this multitude of very different alternative suggestions that there is no agreement whatsoever as to what might actually be going on in ‘space-time’ at the Planck scale.