Submitted:
14 September 2026
Posted:
15 September 2026
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Abstract
Spacetime is conventionally treated as a four-dimensional background within which matter and gravitational phenomena occur. Space-Clock Field Theory (SCFT-A) advances a field-first alternative: the Lorentzian metric is the gravitational field, and physical space is the clock-orthogonal spatial state of that field, rather than an independent background container in which gravity resides. A dynamical scalar clock \(T\) selects the physical foliation and distinguishes cosmological clock-field time \(T\) from matter proper time \(t\), the invariant time measured along material worldlines. Along homogeneous clock-comoving trajectories, the two physical times satisfy \(dT=Q\,dt\), so that \(\mathcal N_T\equiv dt/dT=Q^{-1}\) and \(H_T=H/Q\). Because \(T\) carries stress, conjugate momentum, conserved charge, and gravitational backreaction, this distinction changes relational observables and cannot be removed by a coordinate transformation. The theory's central reciprocal statement is: As physical space expands, cosmological time contracts or moves slower; as physical space contracts, cosmological time expands or moves faster. The expanding branch obeys the on-shell response \(d\mathcal N_T/dH<0\).