Quantum Interference in Time

Lawrence Paul Horwitz

Ivars Peterson

lichao

This paper presents a theory of quantum interference based on Time-Scale Dynamics, aiming to explain the essence of phenomena such as the double-slit experiment from first principles. The core physical picture is that interference is not an inherent property of waves, nor an effect of consciousness, but a structural consequence of whether different evolutionary paths still share the same intrinsic time scale τ. The theory is built upon the fundamental "stability-activity" contradiction (S \times A \geq C_d) and the resulting spontaneous time-scale differentiation of systems (\tau-clustering). We demonstrate that when two (or more) evolutionary paths have equal \tau values, their statistical weights form a superimposable structure, manifesting as interference fringes. Measurement (or any structural coupling) essentially introduces \tau-splitting, destroying time-structural equivalence and causing interference to vanish. The theory naturally derives the Born rule, explains the necessity of three-dimensional space, and unifies concepts such as quantum interference, wavefunction collapse, and decoherence as statistical manifestations of time-scale structures. Complete Python implementations are provided, supporting computational verification of all conclusions. Keywords: time scale; quantum interference; \tau-structure; Born rule; three-dimensional space; emergent symmetry

T. Legero, Tatjana Wilk, Axel Kuhn +1 more

Shivani Singh, C. M. Chandrashekar

One-dimensional discrete-time quantum walk has played an important role in development of quantum algorithms and protocols for different quantum simulations. The speedup observed in quantum walk algorithms is attributed to quantum interference and coherence of the wave packet in position space. Similarly, localization in quantum walk due to disorder is also attributed to quantum interference effect. Therefore, it is intriguing to have a closer look and understand the way quantum interference manifests in different forms of quantum walk dynamics. Quantum coherence in the system is responsible for quantum interference in the system. Here we will use coherence measure to quantify the interference in the discrete-time quantum walk. We show coherence in the position and coin space, together and independently, and present the contribution of coherence to the quantum interference in the system. This study helps us to differentiate the localization seen in one dimensional discrete-time quantum walks due to different forms of disorders and topological effects.

Robert B. Griffiths