Temporal Incompatibility of Quantum Superposition and Relativistic Causality in Toponium Formation

Abstract: Wave-particle duality, a cornerstone of quantum mechanics, faces a stringent test in toponium formation. Quantum superposition predicts instantaneous projection into bound states upon top quark pair creation, while relativistic causality requires a finite formation time of $\sim n^3 \times 10^{-25}$ s for the $nS$ states. This temporal conflict challenges the coexistence of wavelike and particlelike behavior at ultrashort timescales. Exploiting the top quark's intrinsic lifetime ($\tau_t \sim 5 \times 10^{-25}$ s) as a quantum chronometer, we simulate the cross-section ratio $R_b = \sigma(e^+e^- \to b\bar{b})/\sum_q \sigma(e^+e^- \to q\bar{q})$ ($q = u,d,s,c,b$) near $\sqrt{s} = 343$ GeV at future lepton colliders (CEPC/FCC-ee). Wavelike and particlelike scenarios yield distinct $R_b$ profiles, enabling $>5\sigma$ discrimination with 1500 fb$^{-1}$ of data. Preliminary LHC data provide independent $2$--$3\sigma$ support. This framework establishes a collider-based probe of quantum state formation with yoctosecond ($10^{-24}$ s) resolution, offering new insight into wavefunction collapse and relativistic quantum information.