A Minimal Theorem System Deriving the LT as an EM Observation Map and the Relativistic Energy Equation from GT Universal Spacetime

This paper presents a minimal theorem system for Nakaza’s New Relativity Theory (NNRT). Relativistic time and relativistic length are not defined as attributes of real spacetime, and the invariance of the speed of light is not postulated as an independent principle. Instead, the Galilean transformation (GT) in universal time and universal space is adopted as the transformation law for real inertial motion, and a Lorentz-transformation (LT)-type relation is constructed on top of it as a measurement map between two inertial frames using electromagnetic (EM) waves. The existence of time and space can be recognized, but neither can be directly grasped and numerically characterized independently of a scale. In this paper, artificial standards such as clocks and length standards are defined independently, and the time and spatial coordinates obtained with those standards are taken as physically defined universal time and universal space. Measurement within a single inertial frame is complete with these universal standards and requires neither relativistic time nor relativistic length. By contrast, when the state of motion of another frame is measured by EM waves propagating across two relatively moving inertial frames, reciprocal redshift and blueshift arise in the forward and backward propagation directions, and an LT-type relation is derived as the corresponding measurement map. Furthermore, because the identity of the EM phase requires frequency and wave number to transform by the same Doppler factor, invariance of the speed of light is derived as a theorem of measurement rather than assumed as a principle. From this EM measurement map, the energy-momentum transformation is derived as a transformation of quantities conjugate to the action, and its invariant is connected to the classical inertial mass, thereby deriving 𝑚0𝑐2 without assuming it in advance. The quantity 𝑚0 belongs to the layer of real motion as an inertial property intrinsic to matter, whereas 𝑚0𝑐2 is positioned as an observational reference quantity in which that inertial property is expressed in energy dimensions within the EM measurement system. Consequently, 𝑚0𝑐2 does not mean that the mass 𝑚0 physically transforms into energy, nor does it mean that a massive body actually moves at the speed 𝑐. Finally, it is shown that the relativistic energy equation and the classical kinetic energy follow consistently from the two-layer structure consisting only of GT real motion and the EM measurement map.

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File2 in Japanese, under consideration