The Indian physicist Sidharth (I liked the syllabic connotation) suggests that space and time are granular like free flowing sugar, not continuous like golden syrup, at their smallest scales. He discusses how the quantisation of time – the existence of the chronon as time’s smallest quantum – leads to an explanation of the arrow of time. Perhaps the chronon is only able to face one way in the ‘real’ world.
This quantised spacetime is fuzzy, underlain with the order of fractal geometry – a new way of ‘looking at the world’ were it possible.
Such bumpy fractal spacetime’s road maps is not familiar Euclidean geometry. Quantized fractal spacetime is non-Archimedean, or ultrametric: lengths and distances cannot be measured with a ruler. How far is it between 3 and 5? I live in Kuwait and feel close to Esther, who lives in England. What do we mean when we say “close” or “far”? In mathematics, we’re used to using “real” distances x-y, but there are others, which are called “p-adic” and measure the common ‘factors’ two numbers have. We don’t measure p-adic distances in kilometres, they are more like the distance between people on a family tree, where brothers and sisters are close to each other and cousins are further away. So, this quantized fractal spacetime is also noncommutative: its geometry, its spacetime, is not flat or ordered according to our usual formulas of geometry and algebra. The image is of a 3-adic tetrad, showing crystal planes and their ‘nearness’.
Funny old world, innit………….