'Great fleas have little fleas upon their backs', with no foundational stopping point. Is the Universe like this the closer we look at it?

Have you ever wondered what the smallest thing is in the Universe? Maybe there is no such thing.

We’re used to observing objects that match us in size, like tables and chairs; and we can visually make out small’sh and big’sh objects, like grains of sand and mountains, at least with some perspective. But we have to notionalise things on an extreme scale, beyond our perception—the cosmos and its fundamental parts, quarks and neutrinos and all. We use numbers with plenty of zeros to characterise them; we infer their existences; but we don’t see them.

We might, then, dare to imagine that the Universe is stacked infinitely: a flea on a flea’s back on a flea’s back … divided and divided with no smallest part. And so goes this wonderful poem, Siphonaptera, by Augustus De Morgan:

Great fleas have little fleas upon their backs to bite 'em,
And little fleas have lesser fleas, and so ad infinitum.
And the great fleas themselves, in turn, have greater fleas to go on;
While these again have greater still, and greater still, and so on.

Is this possible? Some philosophers and physicists think so. The Universe, they say, is ‘gunky’. There is no largest part either: planets and stars and galaxies are perhaps smaller particles of an even bigger universe.

A fractured universe is already commonly accepted in quantum mechanics: fields underly ‘particles’ with no defined locations. Conversely, classical physicists see a grained universe: electrons are fundamental, indivisible particles, to the order of 10-15 m in size. But this is a false move, say quantum physicists, since the Universe is funkier than that: electrons are point particles of no spatial extents.

However, while quantum physicists like funk, they don’t necessarily like gunk! Their theories often entail indivisible building blocks (e.g. ‘ground states’ and properties). This is also true for string theory, whose building blocks are ‘vibrating strings’. A world that can be infinitely carved up threatens both worlds.

True or not, a gunky universe is fantastically different to the one we think we inhabit: no smallest or largest thing, just never-ending division.

What do you think?