Relational Emergent Time for Quantum System: A Multi-Observer, Gravitational, and Cosmological Framework

TL;DR

The paper tackles the problem of time in quantum mechanics versus relativity by building a relational, clock-based emergent-time framework in which a globally timeless quantum state gives rise to observer-specific temporal flow. Time for each subsystem emerges from correlations with an internal clock, yielding effective Schrödinger dynamics that reproduce standard evolution while incorporating relativistic time dilation and cosmological expansion. The approach unifies gravitational, kinematic, and expansion effects within a single formalism and extends naturally to multiple observers, massless particles, and cosmological settings. Its main contribution is a coherent, relativistically compatible account of temporal flow grounded in quantum correlations, with potential implications for foundations, metrology, and cosmology. The framework advances a paradigm where time is not external but a relational quantity derived from entanglement with a global clock, opening avenues for experimental and theoretical exploration of temporal physics in diverse regimes.

Abstract

We present a relational framework in which temporal structure is not fundamental but emerges from correlations within a globally stationary quantum state. Each subsystem includes an internal clock, and conditional states evolve effectively with respect to these internal readings. The construction naturally extends to relativistic motion, gravitational redshift, and cosmological expansion, leading to a unified emergent-time functional valid across diverse physical regimes. The theory reproduces classical time dilation, predicts correlation-dependent deviations from standard evolution, and suggests that non-interacting or massless particles exhibit negligible internal time. These consequences open directions for conceptual and experimental investigations in the foundations of temporal physics, from multi-clock quantum systems to precision metrology and cosmological settings. In particular, the framework suggests measurable deviation from standard quantum evolution for highly entangled systems and predicts negligible internal time for massless particles.

Figures (4)

• Figure 1: Schematic of the emergent-time framework. A stationary global clock sector entangles with three local clock subsystems (A, B, C), generating distinct relational time parameters for each observer.
• Figure 2: Figure: Relationship between entanglement and local coherence in an emergent Schrödinger dynamics framework. The horizontal axis represents the entanglement between the clock and the subsystem, while the vertical axis shows the local coherence of the subsystem. According to the standard model, local coherence decreases exponentially with increasing entanglement. This plot illustrates the monotonic decay of local coherence as entanglement grows.
• Figure 3: Figure: Schematic representation of the global configuration-space hyper-cube and emergent observer-dependent time slices. The full hyper-cube encodes all possible configurations of the universe in a stationary entangled state. Each observer accesses only a conditional one-dimensional slice selected by their internal clock state, which is perceived as a continuous temporal evolution. Differences in time-flow arise from entanglement structure and relativistic time dilation.
• Figure 4: Figure: Conceptual illustration of relational emergent time. Local subsystem $S_i$ are entangled with a global clock state, while differences in spacetime geometry and motion modify the effective rate correlation evolution. As a result, each observer experiences a distinct emergent temporal flow, reproducing relativistic time dilation within a quantum-relational framework.