A tale of two attoms (new hypotheses should not be half-hearted but doubled)
Quantum History starts with Atoms of matter confirmed by Perrin...
R. Brout Aug 1999
Motivated by the construction of spectral manifolds in noncommutative geometry, we introduce a higher degree Heisenberg commutation relation involving the Dirac operator and the Feynman slash of scalar fields. This commutation relation appears in two versions, one sided and two sided. It implies the quantization of the volume. In the one-sided case it implies that the manifold decomposes into a disconnected sum of spheres which will represent quanta of geometry. The two sided version in dimension 4 predicts the two algebras M_2(H) and M_4(C) which are the algebraic constituents of the Standard Model of particle physics. This taken together with the non-commutative algebra of functions allows one to reconstruct, using the spectral action, the Lagrangian of gravity coupled with the Standard Model. We show that any connected Riemannian Spin 4-manifold with quantized volume >4 (in suitable units) appears as an irreducible representation of the two-sided commutation relations in dimension 4 and that these representations give a seductive model of the "particle picture" for a theory of quantum gravity in which both the Einstein geometric standpoint and the Standard Model emerge from Quantum Mechanics.. Physical applications of this quantization scheme will follow in a separate publication.
(Submitted on 4 Nov 2014)
... we conclude that in noncommutative geometry the volume of the compact manifold is quantized in terms of Planck units. This solves a basic difficulty of the spectral action  whose huge cosmological term is now quantized and no longer contributes to the field equations...
One immediate application is that, in the path integration formulation of gravity, and in light of having only the traceless Einstein equation ..., integration over the scale factor is now replaced by a sum of the winding numbers with an appropriate weight factor. We note that for the present universe, the winding number equal to the number of Planck quanta would be ∼ 1061 
(Submitted on 8 Sep 2014 (v1), last revised 11 Feb 2015 (this version, v4))
... it is obvious that the multitude of sand having a magnitude equal to the sphere of the fixed stars which Aristarchus supposes is smaller than 1000 myriads of the eighth numbers*.King Gelon, to the many who have not also had a share of mathematics I suppose that these will not appear readily believable, but to those who have partaken of them and have thought deeply about the distances and sizes of the earth and sun and moon and the whole world this will be believable on the basis of demonstration. Hence, I thought that it is not inappropriate for you too to contemplate these things.
* 1000 myriads of the eighth numbers = 1063Archimedes3rd century B.C