The Breathing Universe: 307_Relativistic Limits of the Breathing Universe

This paper analyzes the relativistic limit of the Breathing Universe Model (BUM) and demonstrates how standard special and general relativity emerge as controlled limiting cases of a more general dynamic vacuum-tension framework. In BUM, spacetime is governed by a time- and context-dependent vacuum tension field H(t), replacing the interpretation of the speed of light squared as a fundamental constant with that of an equilibrium stiffness of spacetime. Starting from the generalized mass–energy relation written in text form as E equals m times H, the paper shows that Lorentz symmetry arises uniquely when H becomes locally constant and isotropic in the free-propagation limit. Under these conditions, invariant signal propagation, linearity, and phase-coherence conservation together constrain admissible transformations to the Lorentz group, excluding Galilean and superluminal alternatives without additional assumptions. Relativistic time dilation, length contraction, and energy–momentum relations are recovered exactly, while deviations are suppressed below observable thresholds when H varies only on cosmological timescales. The work further clarifies the role of relativistic causality within a breathing spacetime, demonstrating that global oscillations of H(t) do not permit local violations of light-speed limits because clocks and rulers co-evolve with the vacuum tension. Apparent paradoxes related to variable constants are resolved by identifying measurable quantities as ratios of co-scaling fields rather than absolute values. By explicitly deriving special and general relativity as emergent regimes of a dynamic vacuum, this paper positions the Breathing Universe Model as an extension rather than a modification of relativistic physics. Relativity is shown to be the locally frozen expression of a deeper oscillatory geometry, preserving all established tests while opening a pathway to controlled, testable departures at cosmological scales.