Scale Invariance, Self-Similarity

The laws of physics from the large cosmos to the small covalent bond are ruled by forces of attraction. What governs the scales is symmetry and order from fundamental epiphenomenal emergent conatus. These conatus are the impulse interactions of Leibniz and the Enlightenment thinkers, perfectly coincident and symmetric in the order out of chaos, the unity from multiplicity. This is not making much sense. Let's get simple. Colleagues have discussed laws of physics that work in the small and large scale. Like the inverse square relation of Coulomb and Netwon, or the continuity equation of Fermi electrons and bulk fluid material in the Navier Stokes equation, scale invariance is all around us. The coastlines of countries resemble the grains of sand, the lipid bilayer appears as the Golgi apparatus, and the organization of circuits emerges like an urban cityscape.

Scale invariant phenomena are related to self-similar structures in that the rules governing their behavior are not dependent on the size of the system. Of course, we have to move to Planck Wheeler coordinates to get a good understanding of the mechanisms behind cosmological and quantum phenomena but we might be able to see some of the interactions from our dislocation or spontaneous symmetry breaking of scale and dimension here in the laboratory. From subtle changes in the energy of a fusion plasma's heat capacity, we get a probe into disappearing string energy and relativistic history geodesic structures hiding in plain sight. What appears is a fundamental test of nested events in a fusion experiment that allows us to witness singularities at orders of magnitude larger number than previously possible in colliders. Probing scale invariance in multiple dimensions, including time, means discovering the nature of reality as nested in fundamental constants with symmetry from some logical lemma.