Shapes Beyond Sine: Hilbert's Space Filling Curve

Traditional approaches in periodic function mapping and the understanding of how oscillatory behavior are modeled mean two things. One: the basic ideas of periodicity are tied to a cosine and sine approach. Two: interpretations of physical waves come from recursion relations and differential expressions. The innovations that modern physicists who study fractals bring to the forefront of eikonals are the multi-valued and space filling curve of Hilbert. Physical waves have to move past the spherical approach of Huygens to a more encompassing fractal representation that describes their filling the null void of space. What this means is that the two standard modeling paradigms are rooted in something that does not create space filling content. The curve that involves a hyper-dimensional solution, or one that has a space filling curve that moves through dimensions, can solve the Aharonov-Bohm magnetic vector potential QED problem.

This is all too complicated. Waves are not as simple as what was originally proposed. The relations of Maxwell neglect quantum spin and are in need of modification. General Physics is working to develop a space filling curve model of frequency spaces that are incident on POPOP wavelength shifters to detect subtle changes in photon characteristics based upon a polynomial Hamilton interaction and second quantization. This means that waves have structure that interacts with spacing on the order of nanometers and Ångstroms. All waves have curvature and their evenness and symmetry harken in an era of understanding quadrature based physics as the beginning of understanding how fields and particles are two sides of the same coin. In other words, the nature of states is wavelike and their waves are Hilbert space filling curves. These curves, when Taylor expanded, to first order are sine and cosine eigenfunctions, with their Kelvin Helmholtz and Raleigh Jeans instabilities manifestations of quadrature based curve formation.

Again, General Physics is working on describing the nature of wavelength shifting to develop a phased array quantum sensor radar device, something we have discussed with Zurich Instruments. Here, POPOP and wavelength analysis in a regular lattice are connected to data acquisition circuitry in a molecular sensor. The quantum electronics allow for the detection of wavelength behavior and sensitive perturbation of space filling curves that are approximated with polynomials to high order. Look for more information to come.