A Third But Unmentioned Possibility

The old quandry of “discrete or continuous?” assumes an unwarranted binary set of possible answers. There is a third possibility: fractal. The discrete fractal models retain the continuous nature of physical reality, but they are non-differential, and so they can have “quantized” properties.

Another important idea is that space and time may be purely relational and continuous. Conversely, it may be the masses of fundamental objects of nature’s hierarchy that are approximately “quantized”. So discreteness is created by matter, not by space-time.

There is a ‘dog chasing its tail’ quality of the continuous versus discrete quandary. Perhaps the concept of fractal systems, when we include both the classical fractals with continuous self-similarity (large N systems, especially common in the InterScale region of nature’s hierarchy) and the newer discrete fractals with discrete self-similarity (most common at the ‘bottom’ of each cosmological Scale), offers a third possibility. Fractals seem to point to a hybrid modeling approach that resolves the continuous/discrete conundrum by arguing: (1) that strictly discrete or strictly continuous models are artificial idealizations, and (2) that they are both useful approximations that apply in appropriate circumstances. Because nature’s hierarchy has no ‘bottom’, we find an endless hierarchical succession of quasi-continuous fluids, which are composed of quasi-discrete particles, which have substructures that can be approximated by quasi-continuous fluids, which are composed of quasi-discrete particles, and so on forever.

So the answer may be continuous and discrete, but in a fractal context, which allows for both.