The emergence of P = 4 and d0 = 3 from causal axioms P1P4 1 suggests thata metric structure may underlie this discrete geometry. This paper proceeds phe-nomenologically: we investigate the consequences of the hypothesis that the relationbetween emergent proper time τ , spatial displacement |Δpos|, and causal step dLtakes the form τ 2 + |Δpos|2 = dL2. All results are conditional on this hypothesisand a complementarity assumption stated explicitly in Section 2. This work does notreproduce the quantitative predictions of quantum mechanics or special relativity.It provides a structural perspective only.Under these two assumptions, of the eight possible combinations of sharp and un-sharp quantities, three are naturally consistent with known physics: the macrocosm(Special Relativity), the microcosm (Heisenberg uncertainty), and quantum entan-glement. This paper further suggests that wave-particle duality, the measurementproblem, and the special status of time in quantum mechanics may nd a naturalinterpretation within this framework.
Goran Amidzic (Fri,) studied this question.