Physicists Demonstrate Relational Time in a Bose-Einstein Condensate Experiment
Researchers tracked internal entropy changes across expansion cycles to order quantum events without an external clock.
Physicists have realized an isolated cold-atom setup to quantitatively test relational models of time without relying on an external reference clock, according to an experimental study published in Physical Review Research 
doi.orgPhysical Review Researchdoi.orgOpen source ↗. The team, led by Giovanni Barontini from the University of Birmingham, used a Bose-Einstein condensate of approximately 24 thousand ultracold atoms held in a conservative trap partitioned by an optical barrier into an observed sector and an unobserved sector.
Motivated by relational-time approaches formulated in the Wheeler-DeWitt framework, the physicists sought to determine whether the evolution of a quantum system can be sequenced solely via its internal degrees of freedom doi.orgPhysical Review Researchdoi.orgOpen source ↗. In this framework, time does not exist as an independent fundamental coordinate, raising the question of how temporal succession emerges inside an isolated universe.
Entropic Time and Dynamic Cycles
To construct an internal clock, the researchers established an entropic time derived from an experimentally defined coarse-grained entropy doi.orgPhysical Review Researchdoi.orgOpen source ↗. During the experiment, the observed sector underwent repeated cycles of expansion and recollapse, structurally analogous to expansion and contraction phases in simplified cosmological models.
Measurements showed that the constructed entropic time robustly ordered sequential events across multiple cycles doi.orgPhysical Review Researchdoi.orgOpen source ↗. The progression of this relational measure depended on internal redistribution of states and could vary in pace or halt when internal modifications ceased, while retaining a forward direction without reference to external laboratory timing.
Effective Schrödinger Dynamics
The authors derived an effective Schrödinger equation parametrized entirely by this internal entropic time rather than standard external time doi.orgPhysical Review Researchdoi.orgOpen source ↗. This mathematical formulation was able to reproduce the measured physical evolution of the atomic cloud within the observed sector.
According to the authors, the results provide a controlled experimental benchmark for relational-time formalisms doi.orgPhysical Review Researchdoi.orgOpen source ↗. The setup demonstrates how quantum dynamics can be consistently ordered from within, offering empirical constraints for theoretical frameworks that attempt to reconcile quantum mechanics with timeless descriptions of gravitation.
