The Spacetime Metric
Section 4Inertia, gravity and the vacuum

The analogue-gravity bench

Bench for the water tank, university for the fibre or the condensate. · 2 min read

What it proposes

Curved-spacetime physics genuinely emerges from ordinary matter in a laboratory. Push a fluid past its own speed of sound and waves inside cannot fight their way back out; the sound field then obeys exactly the wave equation of a massless field on a curved metric assembled from the fluid's density, flow speed and sound speed. That is not a metaphor and it is not a claim in dispute. It is the cheapest place in physics to learn metric engineering by hand — you build a metric, you measure what the metric does, and you iterate in an afternoon rather than a decade.

Who it is forPhotonics engineers · Cold-atom experimentalists · Warp-metric theorists

Why the library suggests it

Push the flow past the speed of sound in the medium and a horizon appears exactly where the two cross: upstream of it a wave still climbs out, past it the wave cannot.

The analogue horizon

Chill eight thousand rubidium atoms into a single quantum wave, then drive them over a step of laser light so that downstream they flow faster than their own speed of sound. A sound wave upstream of that crossing can still climb out. Past it, nothing can. Move the flow and watch the horizon appear, walk upstream, and finally swallow the whole channel.

Flow multiplier
Flow speed and sound speed along the channel, with the horizon where they crossTwo curves along a channel a few micrometres long. The sound speed starts at 0.52 millimetres per second and falls across the step to 0.31; the flow speed starts at 0.23 and rises to 0.90. Where they cross is the horizon. Above the curves, sound waves released at several positions are drawn as tracks: those upstream of the crossing climb out to the left, and those downstream are carried away to the right no matter how fast they swim. There is a horizon. Upstream of it a sound wave still climbs out; downstream the flow outruns sound and nothing escapes, however fast it swims. This is the case the measurement reports, at a multiplier of one.
  • Flow speed
  • Speed of sound in the condensate
The two ends of each curve are measured, not chosen: outside the horizon the condensate carries sound at 0.52 millimetres per second against a flow of 0.23, and inside it sound runs at 0.31 against a flow of 0.90. The smooth step joining them is the simplest profile with those ends, and its one free length is fixed by requiring the model to return the Hawking temperature the paper reports.Nothing moves on its own. The curves and the tracks change only when you move the slider.
Horizon position:
-0.48 micrometres
Gradient of the escape speed at the horizon:
288 per second
Hawking temperature this implies:
0.35 nanokelvin
The same temperature in the paper's own units:
0.12
Waves that still climb out:
3 / 7
Waves the flow carries away:
4 / 7

What the channel is doing: There is a horizon. Upstream of it a sound wave still climbs out; downstream the flow outruns sound and nothing escapes, however fast it swims. This is the case the measurement reports, at a multiplier of one.

At the measured flow this returns 0.35 nanokelvin, which is the temperature the experiment measured over 7,400 repetitions, with the spectrum matching the thermal prediction and no free parameters. (8,000)

What a fluid reproduces here is the kinematics: the metric that sound waves feel, horizon and all. Deriving Einstein's equations from the same fluid — the rule that says how a metric responds to energy — is the programme's open problem, and this instrument does not touch it.

Carlos Barceló, Stefano Liberati and Matt Visser survey the whole programme and its catalogue of analogues in condensates, superfluid helium, slow light, optical fibres and water tanks, and close on the argument that matters most here — that spacetime geometry may be emergent, the long-wavelength limit of a medium, exactly as fluid mechanics is the long-wavelength limit of molecules (Analogue Gravity, 2011, with the 2026 edition of Analogue Gravity published in 2026). Jeff Steinhauer swept a step of laser light along a rubidium condensate, measured a band of correlations linking points across the horizon, a Hawking temperature near 1.2 nanokelvin, and genuine quantum entanglement between the escaping particle and its partner (Observation of quantum Hawking radiation and its entanglement in an analogue black hole, 2016). And the newest result closes the energy books: in an optical fibre horizon made of light, one pair-creating term turns pump photons into a Hawking pair, and the kick back onto the pump grows as the square of the probe power while both carry the same temperature to within two per cent (Backreaction of stimulated Hawking radiation in an optical analogue, 2026). The programme this feeds is Volovik's — the vacuum sharing the topology of superfluid helium-3, with particles and gravity emerging as low-energy excitations (The Universe in a Helium Droplet, 2003).

The experiment or build

The under-used move is the engineering one rather than the physics one. Analogue systems are almost always run to observe an effect; nobody runs them to design a metric. Take the optical-fibre horizon, where the metric is set by a pulse shape you control completely, and program a target metric — a warp-like profile from the Warp Factory sweep of section 3 — into the pump pulse. Then measure what the analogue field does inside it. The settling measurement is the transit time and the emission spectrum of a probe through a programmed analogue metric, compared against the numerical prediction for that same metric, across a family of profiles. That is metric engineering with a real feedback loop, at a cost of one fibre laser.

Research context

The acoustic metric, the horizon and the Hawking emission are measured and reproduced across several platforms; the programmed-metric use of them has not been attempted.

Take it up

The measurement that settles it
The settling measurement is the transit time and the emission spectrum of a probe through a programmed analogue metric, compared against the numerical prediction for that same metric, across a family of profiles.
What it costs to start
Bench for the water tank, university for the fibre or the condensate.
The engineer it grows
It is the only place on Earth where somebody can practise metric engineering today with same-day feedback.

What it rests on

Where it sits in the curriculum

Superfluid Vacuum Theory: The Vacuum as a Quantum Fluid