Physicist: You hear about nuclear devices taking advantage of “E=mc2” to turn matter into energy, so nuclear power seems like it might be a good way to go. But it so happens that everything that releases energy loses mass in the process. The statement that nuclear devices turn mass into energy, while true, is giving them more credit than they deserve. Even a wind-up clock loses mass as it winds down (just not much). Any kind of energy that you can tie up in matter; chemical, nuclear, electrical, whatever, genuinely increases the weight of the object in question. A charged 9-volt battery, for example, literally weighs about a tenth of a nano-gram more than an absolutely identical uncharged battery. But it’s hard to notice an increase of one part in 500 billion.
What this question is about is a process like: step 1) take a brick, step 2) turn it into energy and no brick.
In order to convert matter into energy requires us to get past a few conservation laws. These are the conservation laws that keep us from turning into energy just whenever. For example, there’s a conservation law that says that the total number of protons + neutrons has to stay the same forever, and there doesn’t seem to be an easy way around that.
But there may be a cheat! A difficult way, if it’s possible at all, to circumvent the conservation laws may be to create a tiny black hole, feed it matter, and collect its “Hawking radiation“. Black holes aren’t very particular about what kind of energy or matter they absorb, and the Hawking radiation they produce is mostly just light. So, problem solved! Make a black hole, feed it any kind of matter, and collect the energy it generates. But, there’s a whole lot involved in that that’s impossible, or nearly impossible. Despite all of the hoopla surrounding CERN, creating artificial black holes is pretty difficult. Even if they had managed to create a black hole, the kind that we’d need would have to be just a whole lot bigger.
Hawking’s whole thing is that a black hole, through some pretty fancy quantumy tricks, radiates energy as though it were hot and that the temperature that it acts like it has is greater the smaller the black hole is. The black holes that exist today are huge and extremely cold (much colder than even the back ground radiation of the universe). But, as a black hole radiates energy it loses mass and shrinks, which makes it “warmer”, which makes it radiate hotter, and so on. So, oddly enough, if you want to get a black hole to radiate more energy you need it to be smaller.
Powering humanity takes about 17 trillion watts, which would require a black hole no more massive than 4.6 million metric tons and no larger than 0.0000000000000000014 meters (14 attometers) across. Black holes are hella dense. The bad news there is that a black hole that small can’t “eat”, because it’s already smaller than any particle (electrons, the smallest particle, are 400 times larger), so nothing will fit into its “mouth”. Technically, for quantum-ish reasons, it’s more accurate to say that it’s unlikely that the black hole would be able to eat an available particle.
A “feedable” black hole, assuming you could get the particle guns perfectly lined up to fire matter into it (even as it’s basically exploding) would need to be at least, say, proton-sized. That puts a cap on it’s power output at a measly 200 mega-watts, give or take. You can’t even power a flux capacitor with that.
Quick aside: This stuff here about “feedability” and whether or not particles can fit into a black hole are non-issues. Black holes “burn” long enough that they do not continuously need new matter. This was a mistake born out of misunderguestimation. There’s a correction at the bottom of this page under “my bad!”.
So, maybe, in the far off future we could (somehow) create thousands of tiny black holes and harness them for power. Harvesting energy from micro-black holes is a tricky business and they’d have to be kept off-world, somewhere in space. Unlike other power sources, they can’t be turned off, and on a strictly practical note, when something weighs a few millions of tons and is smaller than the point of the world’s sharpest pin, it’s difficult to hold on to. It would fall through the floor of your power station faster than you could say “hey, who left this black hole over here?” so orbit or higher is really the way to go.
Long story short, there are easier, safer ways to get power than matter annihilation and black holes. Although it’s still a much better option than coal.
By the by, while the physics behind them is horrifying the equations governing Hawking radiation are pretty clean. The power output, P, for a black hole of mass M (in watts and kilograms) is . Or, using the black hole’s radius (in meters), .
My bad!: A concerned reader pointed out that you don’t need to keep feeding a micro black hole to get power out of it. They stay hot for so long that you can set it and forget it. All the same, you still need to get a tremendous amount of material into an impossibly small region to get the ball rolling.
In the case of a 4.6 million ton black hole capable of powering Earth, you can expect it to keep going strong for over 250 thousand years. In fact, it’s power output would increase substantially with time. The danger is that civilization may forget to move their black hole power sources far away before they burn out. In the last minute of a black hole’s life it destroys about 1 megaton of matter, which translates to about 1.5 billion “Little Boy” bombs, with about a fourth of that being radiated in the last second. Not the sort of thing that should be parked in orbit.
The black hole’s last few decades aren’t particularly pleasant either.
By the way, if you feel the need to run through this sort of thing yourself, the mass of a black hole at a given time, t, is , where Mo is the initial mass. It’s easy enough to figure out how much energy that translates too: .