Programmable Black Hole Computers

One usually thinks of a black hole as an omnivorous object swallowing energy and spitting some of it back in the form of Hawking evaporation radiation, consisting of particles created in pairs out of the vacuum near the edge of the black hole. In principle, a tiny black hole can be formed in a way that encodes instructions for performing calculations. Correspondingly, the answers could be read out from the escaping Hawking radiation.

Why use a black hole at all? Because of the presumed tremendous density of information and potential processing speed implicit in the extreme black hole environment. Seth Lloyd of MIT has previously addressed himself to calculating the conceivable limits on the computing power of such a black hole computer (Nature, 31 August 2000) and arrives at a maximum processing speed of about 10⁵¹ operations/sec for a 1-kg black hole.

Now Jack Ng of the University of North Carolina yjng@physics.unc.edu, 919-962-7208) extends this study by asking whether the very foaminess of spacetime, thought to arise at the level of 10^-35 m, provides an alternative way to limit theoretical computation. Ng not only finds that it does but that the foaminess of spacetime leads to an uncertainty in timekeeping (the more accurate the clock, the shorter its lifetime) which in turn leads to a bound on information processing (speed and memory simultaneously) analogous to the Heisenberg bound on simultaneous measurement of momentum and position.

These limits are so generous that they normally pose little problem for ordinary physical measurements, but in the case of black hole computer the limits would apply immediately. Ng adds, apropos of detecting gravity waves with LIGO and other interferometric devices, that in addition to accounting for various forms of noise, such as seismic disturbances or thermal noise in the detectors, the faint gurgle of spacetime foam will eventually have to be included as an additional and unavoidable source of noise in the measurement of very short displacements (the movement of mirrors owing to the flexings of spacetime brought about by passing gravity waves).

If Ng is right, the noise sensitivity achievable by the prospective advanced phase of LIGO will only need a further hundredfold enhancement in order to detect the quantum foam, which is to say the very fabric of spacetime. Thus the Planck scale, so far only a hypothetical extreme regime, might eventually become a realm that can be approached and measured. (Physical Review Letters, 2 April 2001; text at Physics News Select.)