Historical research guide · 0889 · 2011

Measurement of Stimulated Hawking Emission in an Analogue System

Silke Weinfurtner · Edmund W. Tedford · Matthew C. J. Penrice · William G. Unruh · Gregory A. Lawrence

In one minute

Hawking predicted that a black hole emits a thermal glow at its horizon. The holes we know of are far too cold to measure, so Bill Unruh proposed in 1981 that the same mathematics governs waves on flowing water, and that the effect could be put in a laboratory. Silke Weinfurtner, Edmund Tedford, Matthew Penrice, Unruh and Gregory Lawrence did it in a six-metre water channel at the University of British Columbia. A shaped obstacle on the floor speeds the flow above it enough to stop long surface waves travelling upstream — a white-hole horizon, the time-reverse of a black hole. Waves sent toward it are blocked and converted into a pair of short, deep-water waves, one carrying positive and one negative norm. The team measured the ratio of the two across nine frequencies and found it thermal, exactly the Boltzmann form Hawking’s calculation predicts, at an effective temperature of about five million-millionths of a degree. The effect survived turbulence and viscosity, which is the point: it looks generic.

Connection

This is chapter five’s cleanest laboratory result — an effective horizon built out of ordinary water, behaving as the curved-spacetime mathematics says it must. It matters for chapter two because the emission is a pair-creation process at a horizon, the vacuum answering the geometry it sits in; and it strengthens the whole analogue-gravity programme by showing the Hawking process does not depend on Planck-scale physics that no laboratory can reach.

From the source

Long surface waves on an open channel flow of varying depth obey, in the shallow-water limit, the wave equation of a field on a curved spacetime background, so a counter-current strong enough to block upstream propagation is the analogue of a white hole horizon.Sec. II, following Eq. (5); after Schützhold and Unruh, Phys. Rev. D 66, 044019 (2002)
A streamlined obstacle 1.55 metres long in a 6.2 metre flume creates the blocking region, and a single ingoing shallow-water wave is converted there into a pair of outgoing deep-water waves — one on the positive norm branch of the dispersion relation and one on the negative norm branch.Sec. III; Sec. IV, Fig. 4a and Fig. 4c–d
Across nine ingoing frequencies between 0.02 and 0.67 hertz the ratio of the negative norm to the positive norm outgoing wave follows the Boltzmann form predicted for the Hawking process, with a linear fit whose inverse slope is 0.11 hertz and whose offset is close to zero, corresponding to a temperature of about five times ten to the minus twelve kelvin.Sec. IV, Fig. 5b and the paragraph describing it; Eq. (1)
The conversion is not a non-linear artefact of the apparatus: repeating every run with ingoing amplitudes fifty per cent larger scaled the converted wave amplitudes linearly, and off the dispersion curves the background noise stayed below a tenth of a millimetre.Sec. IV, paragraph beginning ‘To test whether or not the negative norm wave creation was due to non-linearities’; Fig. 3b
The thermal ratio holds in a system containing turbulence, viscosity, flow separation risk and non-linearities, and with a dispersion relation quite unlike the one Hawking assumed — which the authors read as evidence that the effect depends only on the low-frequency, long-wavelength physics and not on quantum gravity or Planck-scale behaviour.Sec. V, ‘Summary’, first paragraph
What this experiment measures is stimulated emission at a white hole analogue; the spontaneous quantum emission is the measurement still wanted, and the authors name Bose–Einstein condensates and optical fibre systems as the places to look for it. They also note the blocking point in their flow is not a phase velocity horizon, which leaves the temperature predicted from surface gravity uncertain even though the thermal form is clear.Sec. IV, final paragraph; Sec. V, second paragraph

The way in

https://doi.org/10.1103/PhysRevLett.106.021302

Historical source-access record. This guide links to the original; it does not reproduce the paper text.

Published as Physical Review Letters 106, 021302 (2011) under the APS default licence. The author version is free to read on arXiv as 1008.1911, posted 11 August 2010 with a second version on 18 August 2010, and that record carries the arXiv non-exclusive distribution licence version 1.0 — not a Creative Commons licence, checked on the arXiv abstract page on 2026-09-08, and no Creative Commons statement appears in the text either. So this sheet carries the summary, the claims and the authors’ own abstract and sends the reader to the source. The claims below were written from the arXiv text and the locators use its section and figure numbering. Weinfurtner, Penrice and Unruh write from the Department of Physics and Astronomy at the University of British Columbia, Tedford and Lawrence from its Department of Civil Engineering, whose flume the experiment used; the work was supported by the Natural Sciences and Engineering Research Council, the Canadian Institute for Advanced Research, the Canada Research Chairs programme and a Marie Curie Fellowship. Companion sheets in this library carry the rest of this line of work: Barceló, Liberati and Visser’s review Analogue Gravity at /library/stm-9d9474c4b5; Steinhauer’s quantum measurement in a Bose–Einstein condensate at /library/stm-a3449e5f7e and the thermal-temperature measurement at /library/stm-95010a1182; and the optical-fibre backreaction measurement at /library/stm-b13dca2c59.

How to cite it

Silke Weinfurtner, Edmund W. Tedford, Matthew C. J. Penrice, William G. Unruh, Gregory A. Lawrence (2011) Measurement of Stimulated Hawking Emission in an Analogue System doi:10.1103/PhysRevLett.106.021302

Where it sits in the curriculum

The vacuum as a quantum fluid