1.10 Quantum Time
Regarding the question of ‘instants’ of time, time being a linear continuum implies that there is a nondenumerable infinity of them. This means that between any two instants there is a third; time is continuous. However, for times shorter than about 10-43 seconds; the so-called Planck time, science has no experimental support that time holds its continuousness. But physicists agree that General Relativity must fail for durations shorter than the Planck time, though they don’t know exactly how and what is the substitute.
The idea that space or time (space-time) could be discrete has been recurring in scientific literature recently, but its origins go back to ancient philosophies. The new concepts brought about by Quantum Mechanics (e.g., the concept of indeterminacy or the uncertainty principle) suggested that space-time could be also quantized like energy. This was reinforced by the discovery of ultraviolet divergences in Quantum Field Theory (Zee 2003: 145-51), though many of the strange quantum concepts soon became acceptable aspects of continuum physics. In the 1980s, powerful computers inspired some new discrete thinking in physics. Complicated mathematical simulations performed on these super-computers paved the way for Lattice Theories to be applied to Quantum Mechanics, and included Quantum Gravity. In Quantum Gravity, Planck’s length is a minimum size beyond which no accurate measurements can be performed.
Hawking, however, sees no reason to abandon the continuum theories that have been so successful. But it may be possible to invent a discrete structure of space-time without abandoning the continuum theories if the discrete-continuum duality can be resolved, just as the wave-particle duality has been resolved by Quantum Mechanics.
The practical methods of the quantisation of time in modern scientific theories are based on some complicated mathematics such as lattice theories and cellular automata that are beyond the scope of this introduction (Wolfram 2002: 771). But it is good to note here that Ibn al-Arabi’s quantisation of time, as we shall see in section II.8, is unique and is based on a broader cosmological view (of the oneness of being) such that discreteness and continuousness are special cases of it (see also section VII.5).