Time Symmetry, Retrocausality and the Emergent: Arrow of Time the Quantum Time-Symmetric Interpretation (QTSI)

TL;DR

The Quantum Time-Symmetric Interpretation (QTSI) addresses how time-symmetric quantum laws can yield an emergent arrow of causality. It introduces a two-component temporal state $\Psi(t)=(\psi_{+},\psi_{-})$ coupled by a mixing parameter $\Delta(\phi)$, with a retrocausal coherence time $\tau_{RC}=\hbar/|\Delta(\phi)|$; environmental amplification controlled by $\phi$ suppresses the backward component, producing classical causality while preserving time symmetry at the microscopic level. The theory is built on a SU(1,1) biespinor framework, yielding dynamical equations and Noetherian conservation that prevent signalling, and it integrates historical ideas from Wheeler–Feynman, Aharonov, and Price. It predicts observable signatures in temporal echoes and cavity-based experiments, and proposes a disciplined experimental program to extract $\tau_{RC}$, map $\Delta(\phi)$, and test against higher-order path models, thereby offering a falsifiable route to assess retrocausal influences within standard quantum mechanics. Overall, QTSI aims to unify time symmetry, measurement, and irreversibility into a concrete dynamical picture with testable predictions about advanced echoes and the emergence of the quantum arrow of time.

Abstract

Microscopic quantum laws are time-symmetric: nothing in the Schrödinger equation or its relativistic extensions distinguishes future from past. Yet measurements produce irreversible records, an apparently one-way causal flow, and the familiar notion that causes precede effects. Within the Quantum Time-Symmetric Interpretation (QTSI), this asymmetry is not fundamental but emergent. Isolated quantum systems are described by a two-component temporal state containing forward- and backward-propagating amplitudes. Their mixing, governed by a parameter $Δ(φ)$, defines a retrocausal coherence time $τ_{RC}(φ)$ beyond which advanced components are suppressed. As the system couples to amplifying environments characterized by a macroscopic parameter $φ$, $Δ(φ)$ decreases and the backward component is dynamically eliminated, giving rise to classical causality and effective collapse. QTSI aligns naturally with time-symmetric approaches from Wheeler--Feynman, Aharonov, and Price, agrees with all weak-measurement and quantum eraser results in their operational regimes, and predicts specific signatures in temporal echoes and chaotic cavities. Detailed formal and experimental developments appear in the Supplementary Addenda.