**Authors:** Theodore J. St. John

Motion is a form of energy that can be described mathematically and graphically as the ratio of a change in space with respect to a change in time. It can also be described as the ratio of temporal frequency (inverse time) to spatial frequency (inverse space). Graphically, these are conformal projections of a single concept (motion) onto two pairs of orthogonal scales. The first pair is linear and the second is the inverse of the first. If the speed of light is the motion being projected, then all four scales are graphically linked by the diagonal line (the “world line” in Minkowski terminology). By graphing both pairs on the same graph, I pair up the linear temporal scale with the inverse spatial frequency scale at the first increment, t = 1 = fs, on the horizontal axis and then pair up the linear spatial scale with the inverse temporal frequency scale at s = 1 = ft on the vertical axis. Then I scaled the inverse domain by Planck’s constant (2 pi) in natural units and identified these as the energy of a quantum unit, E=hft on the horizontal and E=hcfs on the vertical. Each axis therefore represents the Hermitian adjoint of two domains, the linear domain and its inverse. Then I represented each frequency domain as a circle (polar coordinates), which is a conformal projection of its corresponding linear domain, and thus a conformal back-projection of motion. Since I scaled each inverse scale by 2pi they each represent the circle of convergence of the exponential function eR which has a radius of convergence at R=2pi. The pair of circles is superimposed at the origin of the S-T domain so their superposition, the product of these two circles, represents a plane wave as the quantum wave function. This quantum unit is what I identified as a holomorphic unit. The reflections of motion from the linear space-time domain are phase-shifted enough that they converge at a point (1/c2), that is offset from the origin by a scale factor of 1/c, which is the fine-structure constant in natural units. The spatial offset from the zero spatial frequency locus provides the spatial frequency grating necessary to form a holographic image. The shift in the phase also creates a difference between the divergent projection (the projection of motion outward) and the gradient of the inverse domain, which produces the curl-field resulting in a field that has morphed into a particle with a physical boundary.

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