A Minimum Kinetic Energy Requirement for Observable Coherent Orthogonalization: Reconciling Wigner Symmetry and the Margolus-Levitin Bound

This work investigates the interplay between Wigner’s symmetry theorem (enforcing unitary dynamics)and the Margolus-Levitin (M-L) bound (a quantum speed limit). We establish that for coherent evolution to an orthogonal state to be observable within a system’s environmentally limited coherence time ( τ_c), a minimum average energy E_min ≥ πħ / (2τ_c) is required. For systems where this energy is predominantly kinetic ( E = 1/2 m v^2), this translates to a minimum velocity v_min = √(πħ / (mτ_c)). This operational threshold underscores the synergy between intrinsic quantum dynamics and environmental constraints. While foundational, this v_min is often far exceeded by typical system velocities, highlighting that environmental decoherence generally remains the dominant practical challenge in observing quantum phenomena, as exemplified by macromolecular interferometry (e.g., C₆₀).