Phys. Rev. Research 8, L022047 · G. Barontini · University of Birmingham · 11 June 2026
24,000 rubidium atoms, one laser barrier — and a clock that ticks only when entropy moves between what you watch and what you ignore.
In canonical quantum gravity the whole universe obeys the Wheeler–DeWitt equation, Ĥψ = 0. A closed universe has nothing outside it — so the equation contains no time parameter at all, and no built-in arrow pointing from past to future. Yet we plainly experience time flowing. One family of answers: time is relational — it emerges when you split the universe into pieces and let one piece serve as a clock for another.
Barontini built the smallest testable version: a Bose–Einstein condensate of ~2.4 × 10⁴ rubidium-87 atoms in an isolated optical trap. Over the 120 ms experiment it loses no atoms and no measurable energy — effectively a closed system with a time-independent Hamiltonian, the same predicament as a Wheeler–DeWitt universe.
A laser sheet just 8 µm thin (675 nm light, shaped by a digital micromirror device) splits it in two: a bright sector that is observed, and a dark sector that is deliberately ignored. The condensate sloshes; atoms spill over the barrier. Each time the bright sector fills it undergoes a “big bang”, expands to maximum size, recollapses, and drains in a “big crunch”. The barrier height V sets how much can cross.
Now forbid yourself the lab clock. Can the bright sector's history be ordered using only quantities measured inside it? The paper's answer is an entropic time:
τ = (σ / kB) ∫ (dS / dφ) |dφ|τ advances in proportion to the entropy S exchanged between the sectors (φ is the condensate's centre of mass, playing the role of a scalar “clock field”). Crucially, the entropy of the whole mini-universe stays constant — only the act of splitting it, and ignoring one half, makes an entropy current visible. No flow, no tick.
τ orders events in the same sequence as lab time — but flows at a completely different rate. It runs fast while atoms flood across during a bang or crunch. Between a crunch and the next bang, zero entropic time elapses: nothing is exchanged, so nothing “happens”. Raising the barrier throttles the exchange and time flows ever slower — until at V ≈ 1 the bright sector reaches its “heat death”: a stationary state where the entropic clock stops entirely while lab clocks march on.
Barontini then rewrote quantum mechanics against this internal clock — a Schrödinger equation in τ, with an entropy-dependent energy pump Λ(τ) — and its numerical solutions reproduce the measured evolution of the condensate. Ordinary unitary quantum mechanics reappears exactly in the limit of zero entropy flow.
This is the first controlled experiment where relational constructions of time — proposed for quantum cosmology since Page & Wootters (1983) — can be tested quantitatively against data. Time, and its arrow, behave here as bookkeeping of what the observed part of a universe gives up knowing about the unobserved part. The platform opens follow-ups the paper sketches: competing internal clocks, quantum-bounce vs singularity at the bang/crunch, Loschmidt-echo reversibility tests, even analog black holes inside the bright sector.