Twin Paradox Without Paradox

Abstract

The twin paradox is generally regarded as a consequence of the geometry of Minkowski spacetime: the traveling twin follows a shorter worldline and therefore accumulates less proper time. While mathematically consistent, this explanation leaves a conceptual gap—it stipulates that clocks measure the metric interval without specifying why such a relation holds. The Ze interpretation closes this gap by reconstructing proper time from purely operational primitives. Time is defined not as a geometric coordinate but as a local count: tau = alpha * N, where N is the number of causally connected coincidence events registered by a stable counter and alpha is a conventional normalization coefficient. Motion redistributes a finite event budget between two orthogonal channels: temporal self-correlation (aging) and spatial cross-correlation (displacement). The total event count satisfies dN_total^2 = dN_temporal^2 + dN_spatial^2, from which the Lorentz factor gamma = dN_total / dN_temporal and the Minkowski interval ds^2 = dt^2 - dx^2/c^2 emerge as derived continuum approximations. Velocity is redefined as the event allocation ratio v/c = dN_spatial / dN_total. Within this framework, the twin scenario reduces to a comparison of two distinct causal chains sharing common endpoints. The traveling twin’s chain contains the same number of temporal self-correlations interspersed with additional spatial correlation events required by motion; these spatial events consume event budget without contributing to causal distance. Upon reunion, the counter comparison yields N_T < N_E directly and without paradox. The asymmetry is not a puzzle requiring reconciliation with a symmetric description—it is the empirical fact from which theorizing begins. The Ze interpretation is empirically equivalent to special relativity but provides a constructive mechanism for time dilation, eliminates the clock hypothesis as an independent postulate, aligns time ontology with metrological practice, and dissolves the twin paradox by reducing it to trivial arithmetic. The paradox vanishes not because it is resolved but because it was never there.