Symmetric Recovery of the Time Mode After Local Dynamical Redistribution: A Supplementary Note on the Four-Mode Interpretation of Special Relativity

抄録

In a previous study, the Four-Mode Theory proposed that the age difference in the twin paradox originates from differences in the history of Time-Mode redistribution rather than from symmetric inertial relative motion itself. However, the previous work intentionally left unresolved whether a locally redistributed Time Mode remains asymmetric after dynamical processes cease or gradually returns to its reference state.

The present supplementary note proposes the Symmetric Recovery Principle, according to which redistribution of the Time Mode occurs only while local dynamical processes such as acceleration, deceleration, gravitational interaction, or continuous changes in trajectory are active. Once these processes cease and the system returns to ideal symmetric inertial motion, the redistributed portion of the Time Mode is hypothesized to be gradually restored, allowing the local Time Mode to recover toward its reference state.

Within this interpretation, the age difference observed in the twin paradox is understood as the accumulated consequence of temporary reductions in the locally available Time Mode during periods of dynamical redistribution rather than as a permanent asymmetry persisting throughout subsequent inertial motion. In contrast, continuously curved motion, such as orbital motion or circular trajectories, may maintain a prolonged redistribution state because dynamical interaction remains continuously present.

This supplementary interpretation preserves the conceptual framework of the previous Four-Mode interpretation while providing a clearer description of the recovery process following local dynamical redistribution. The proposal remains qualitative and requires future quantitative formulation through constitutive laws and field equations.