Noether’s Theorem [1] states: “For every continuous symmetry of the laws of physics, there must exist a conservation law”. This theorem is used in classroom physics to illustrate how one can derive conservation laws from symmetries, e.g. conservation of angular momentum from the symmetry of angular isotropy. However, as is well known, Noether’s theorem itself has an important symmetry! For every conservation law, there must exist a continuous symmetry. In the case of angular momentum, the conserved quantity, spin, cannot vary continuously. The angular momentum of any object can only be changed by some integer multiple of ħ/2 (spin ½) [2] . In DM it is clear that the microscopic informational process can exactly conserve quantities such as angular momentum. RUCAs can be designed so that units of ħ are neither created nor destroyed. This is because in DM we can have discrete atoms of angular momentum where the basic process conserves those atoms. Of course, the existence of a cellular array implies angular anisotropy, but this is only at a most microscopic level. A variant of Noether’s Theorem implies that exact conservation of discrete angular momentum must enforce asymptotic continuous angular isotropy as one looks at processes some level above the scale of the cellular array. Similarly, absolute microscopic conservation of discrete units of momentum must enforce asymptotic continuous translational symmetry. Conservation of discrete units of energy does the same for asymptotic continuous time symmetry. DM opens the possibility of experiments that can provide ways to measure absolute angular orientation and absolute translation with respect to the underlying grid of the DM RUCA.
