Editing Infinite divisibility (section)

==In quantum 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 a set|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.<ref>{{cite arXiv |eprint=quant-ph/0009001v2 |title=Quantum Mechanics and the Cookie Cutter Paradigm|author=Ulrich Mohrhoff|year=2000}}</ref> This casts fresh light on the ancient [[Logic|conundrum]] of the divisibility of matter. The multiplicity of a material object&mdash;the number of its parts&mdash;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&mdash;[[quark]]s and [[electron]]s&mdash;are [[point particle]]s: 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 [[Quantum indeterminacy|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, according to the best currently accepted theory in physics, the [[Standard Model]], there is a distance (called the [[Planck length]], 1.616229(38)×10<sup>−35</sup> metres, named after one of the fathers of Quantum Theory, [[Max Planck]]) and therefore a time interval (the amount of time which light takes to traverse that distance in a vacuum, 5.39116(13)&nbsp;×&nbsp;10<sup>&minus;44</sup> seconds, known as the [[Planck time]]) at which the Standard Model is expected to break down – effectively making this the smallest physical scale about which meaningful statements can be currently made. To predict the physical behaviour of space-time and fundamental particles at smaller distances requires a new theory of [[Quantum Gravity]], which unifies the hitherto incompatible theories of Quantum Mechanics and General Relativity. {{Citation needed|date=October 2010}}