# Re: Not quite magic physics [was Re: Quantum Computers]

Doug Jones (random@qnet.com)
Mon, 23 Aug 1999 11:00:39 -0700

hal@finney.org wrote:
> the Hawking lifetime of a black hole is (M/M_sun)^3 * 10^66 years.
> M_sun (mass of the sun) is about 2x10^30 kg. So this sets black hole
> lifetime at (M in kg)^3 * 10^-25 years or about (M in kg)^3 * 3x10^-18
> seconds.

So, one sol-second of mass, 4.2e9 kg, would give a lifetime of 2.2E11 seconds, or 7200 years. A useful size...

I couldn't figure out that glyph to the left of the "G" in equation 9, but extrapolating from your calculation below, I get T=1E23/M, so the 4 Mtonne hole is at "only" 2.3E13 K. Egad, the gammas must fizz out into positrons and electrons spontaneously... as Eugene Leitl pointed out, the beams used to make the hole would dissipate their energy in making particles out of the vacuum.

> To have a life time of, say, 3 seconds would require a mass of
> 10^6 kg, 1000 metric tons, which would be an energy of 10^23
> Joules, which is a lot, something like 10,000 years of our
> total current energy usage.

Well, yeah, but if you're playing with a dyson sphere, 1000 tonnes of energy is trivial- less than a microsecond's worth of throughput.

> The real problem though is to pack this energy into the required small
> size. Black hole radius is proportional to mass, a 1 kg black hole
> being about 10^-27 meters in radius, so the 10^6 kg would have to
> be packed into 10^-21 meters, much smaller than the nucleus of an
> atom.

...and the larger hole would be a whopping 4000 times bigger, at 4E-18 meters *still* much smaller than a nucleon.

> Also, black hole temperature is inversely proportional to mass,
> and according to the web page about the 10^6 kg black hole would
> be about 10^17 K, which is hot hot hot (although coming from a
> tiny area.).

At 3E-35 m2, that's about 3E-7 barns. That qualifies as tiny, all right.

I'll stick with the technology I know, at mere hundreds of megawatts per square meter.

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Doug Jones, Freelance Rocket Plumber
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