Volume 27 · Part Two · Chapter 5 of 19
Analogue Gravity More Broadly
Sonic horizons, Bose–Einstein condensates, and what an analogue experiment can and cannot decide.
Unruh's observation
Sound waves in a moving fluid obey a wave equation that can be written as a massless field propagating in an effective curved metric built from the flow velocity and the speed of sound. Where the flow exceeds the sound speed, sound cannot escape upstream: an acoustic horizon. The mathematics of the horizon is the mathematics of a black hole horizon, and Hawking's derivation of horizon radiation goes through in the analogue with the same structure.
This has been carried out. Analogue Hawking radiation has been reported in Bose–Einstein condensates, with entanglement between the paired outgoing and infalling modes measured; correlated stimulated emission has been observed in water-tank and optical systems.
What such an experiment establishes
It establishes that the kinematics are sound. Hawking's derivation depends on the behaviour of field modes near a horizon, not on the Einstein equations, and the analogue confirms that this part of the argument works in a system where every ingredient is under laboratory control. That is a real result and it removes a real doubt — in particular the trans-Planckian worry, since the condensate has a known short-distance cutoff and the radiation survives it.
It does not establish anything about the dynamics of gravity. The effective metric in the analogue does not obey Einstein's field equations; it obeys the fluid equations. There is no analogue of the Einstein–Hilbert action, no back-reaction of Hawking radiation on a geometry, and therefore nothing to say about the information paradox, black-hole entropy, or evaporation endpoints. Analogue gravity tests one half of the theory and is regularly reported as if it tested both.
Sakharov's inversion
Sakharov's induced-gravity proposal runs the analogy the other way: perhaps the Einstein–Hilbert action is not fundamental at all but an effective elasticity of the vacuum, generated by quantum fluctuations of matter fields. The proposal is old, suggestive, and has never been made to yield a controlled calculation of Newton's constant. It belongs in the volume because it is the moment the analogy stops being a tool and becomes a hypothesis about what gravity is — and because it has not been cashed.
Equations borrowed
- Acoustic metric g^{eff}_μν built from background flow velocity and local sound speed
- Hawking's mode-mixing derivation at a horizon
- Sakharov's induced-gravity conjecture
Validity band
Kinematics of field propagation on a fixed effective metric. Says nothing about gravitational dynamics, back-reaction, or the Einstein equations.
Falsifier
Absence of the predicted Hawking-mode correlations in a well-characterised condensate horizon, where the effective metric is independently measured, would falsify the kinematic claim.
Where this chapter is weakest
The programme's weak point, and therefore the chapter's, is that its most-quoted implications concern precisely the half of gravity it cannot reach. The chapter should be read as narrowing a famous result rather than extending one.
The volume-wide audit of these weak points is collected in Where This Volume Is Weak.