Infinite Divisibility - in Physics

In Physics

Until the discovery of quantum mechanics, no distinction was made between the question of whether matter is infinitely divisible and the question of whether matter can be cut into smaller parts ad infinitum.

As a result, the Greek word átomos (ἄτομος), which literally means "uncuttable", is usually translated as "indivisible". Whereas the modern atom is indeed divisible, it actually is uncuttable: there is no partition of space such that its parts correspond to material parts of the atom. In other words, the quantum-mechanical description of matter no longer conforms to the cookie cutter paradigm. This casts fresh light on the ancient conundrum of the divisibility of matter. The multiplicity of a material object — the number of its parts — depends on the existence, not of delimiting surfaces, but of internal spatial relations (relative positions between parts), and these lack determinate values. According to the Standard Model of particle physics, the particles that make up an atom — quarks and electrons — are point particles: they do not take up space. What makes an atom nevertheless take up space is not any spatially extended "stuff" that "occupies space", and that might be cut into smaller and smaller pieces, but the indeterminacy of its internal spatial relations.

Physical space is often regarded as infinitely divisible: it is thought that any region in space, no matter how small, could be further split. Time is similarly considered as infinitely divisible.

However, the pioneering work of Max Planck (1858–1947) in the field of quantum physics suggests that there is, in fact, a minimum distance (now called the Planck length, 1.616 × 10−35 metres) and therefore a minimum time interval (the amount of time which light takes to traverse that distance in a vacuum, 5.391 × 10−44 seconds, known as the Planck time) smaller than which meaningful measurement is impossible.