Abstract
<title>Abstract</title> <p>We present a unified geometric reinterpretation of cosmic expansion in which spacetime is described as a four-dimensional Euclidean spatial manifold \(\:\left(x,y,z,w\right)\), with the observable universe represented by a finite-thickness hyperspherical wavefront propagating along the auxiliary spatial coordinate \(\:w\). Within this framework, physical time is not fundamental but emerges from progression along the expansion direction according to \(\:t=w/{v}_{H}\), where \(\:{v}_{H}\) is the characteristic expansion velocity. By modelling photon propagation across this expanding wavefront, we derive a spiral path-distance metric that reproduces the observed Type Ia supernova luminosity relation and the angular-diameter distance of the cosmic microwave background using a single, near-constant expansion velocity. The apparent accelerated expansion of the universe is interpreted as a geometric consequence of photon propagation rather than evidence for a cosmological constant or evolving expansion history. Gravity arises naturally as a localized geometric depression within the propagating wavefront, producing gravitational time dilation and recovering the weak-field behaviour of general relativity. Because the observable universe occupies a finite temporal window rather than an infinitesimally thin hypersurface, microscopic particles possess additional degrees of freedom within the expansion dimension. This provides a geometric interpretation of wave-particle duality, electron spin and quantum delocalization while preserving the established mathematical formalism of quantum mechanics. The characteristic width of this temporal window is proposed to satisfy an action relation \(\:m{v}_{H}d=nh\), yielding a fundamental length scale comparable to the Bohr diameter and suggesting the geometric correspondence \(\:\alpha\:={v}_{H}/\left(\pi\:c\right)\) between the cosmological expansion velocity and the electromagnetic fine-structure constant. The framework makes experimentally testable predictions, including a Planck-mass transition between quantum and classical behaviour and a finite geometric coherence boundary for quantum entanglement. Taken together, these results suggest that cosmological expansion, gravity and quantum phenomena may represent different manifestations of a common four-dimensional geometric structure.</p>