The Physical Meaning of 𝒎𝟎𝒄𝟐 and an Observational Reconstruction of Relativity and Quantum Theory

This paper begins with a question concerning the physical meaning of 𝑚0𝑐2 as it appears in the relativistic energy relation 𝐸2 = 𝑝2𝑐2 + 𝑚0 2𝑐4 . The numerical relations 𝐸 = 𝑚0𝑐2 and 𝐸 = 𝛥𝑚𝑐2 are supported by precise experiments, but the ontology to which these mathematical quantities are assigned is a separate issue. This question leads directly to a reconsideration of the standard relativistic picture in which the relativistic time and relativistic length introduced by Einstein in 1905, and later geometrized as spacetime after Minkowski, are attributed to the physical world itself. The same issue appears in quantum theory. The relativistic energy–momentum relation connects to relativistic quantum-wave structures and, in the nonrelativistic regime, to Schrödinger mechanics; however, it does not follow uniquely from the mathematics that the wave function, probability, and uncertainty must be interpreted as properties of reality itself. The present paper identifies a common root of these two problems in the identification of mathematically observed quantities with reality itself. The Nakaza New Relativity Theory (NNRT) places an invariant real spacetime, consisting of universal time and universal space, as its physical basis. It does not, however, assume an absolute rest frame or an ether, and it regards all inertial frames as physically equivalent. In contrast, time, distance, phase, frequency, wavenumber, arrival time, and related quantities constructed through actual measurement are separated as quantities of measurement spacetime. The logical boundary between observational agreement and ontological identification is formulated here as the Observational–Ontological Non-Uniqueness Proposition (OONP). Taking the phase–action correspondence 𝛩 = 𝑆 ℏ⁄ , ��𝜇(𝛩) = 𝜕𝜇𝛩, and 𝑃𝜇(𝛷) = ℏ𝑘𝜇(𝛩) as a common bridge, the dispersion structure of a single Fourier mode is organized as relativistic observation, whereas the superposition of multiple modes and Fourier duality are organized as quantum observation. In this framework, 𝛥𝑥𝛥𝑝 ≥ ℏ 2⁄ is first interpreted as a bandwidth–localization constraint of a phasebased observational representation, while the Born rule, Hilbert space, and unitary evolution are retained as standard quantum mathematics in the quantum-observational layer. Furthermore, 𝑚0𝑐2 is reconstructed as the phase-invariant base scale 𝐵𝛷 = ℏ√𝜔2 − 𝑐2𝑘2=𝑚0𝑐2. What this paper changes is neither established mathematics nor experimental values. NNRT explicitly rejects the physical definition according to which relativistic time, relativistic length, and relativistic spacetime are properties of real time and real space themselves. It therefore proposes that these concepts be removed from the foundational description of real spacetime and be confined to the mathematics of measurement and observation. Keywords: NNRT, 𝑚0𝑐2, OONP, measurement spacetime, invariant real spacetime, phase, action, Fourier transform, uncertainty principle, Born rule, relativity, quantum mechanics.

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