Experimental Evidence for Maximal Surfaces in a 3 Dimensional Minkowski Space

Conventional physical dogma, justified by the local success of Newtonian dynamics for particles, assigns a Euclidean metric with signature (plus, plus, plus) to the three spatial dimensions. Minimal surfaces are of zero mean curvature and negative Gauss curvature in a Euclidean space, which supports affine evolutionary processes. However, experimental evidence now indicates that the non-affine dynamics of a fluid admits a better description in terms of a 3 dimensional space with a Minkowski metric of signature (plus, plus, minus). Three dimensional spaces with a Minkowski metric admit maximal surfaces of zero mean curvature, with conical or isolated singularities, and with positive Gauss curvature, in contrast to Euclidean 3D metrics. Such properties are also associated with the Hopf map, which generates two surfaces of zero mean curvature and positive Gauss curvature in a 4D Euclidean space. Falaco Solitons, easily created as topological defects in a swimming pool, are experimental artifacts of maximal surfaces (of zero mean curvature, but positive Gauss curvature) in a 3D Minkowski space. The topological defects in the otherwise flat surface of fluid density discontinuity appear as a pair of zero mean curvature surfaces, with a conical singularity at each end. The two conical singularies of the Falaco Soliton pair appear to be connected with a 1D string under tension. The singular conical points are associated with rotation (not translation)