Work and World

The Unreasonable Efficiency Of Black Holes

E=mc^2, the most famous equation in the world,
describes the fact that anything with mass possesses a huge amount of energy, in principle
– like, a 5kg cat has enough energy in its mass to power the entire country of Norway
for a year – if only the energy could somehow be fully extracted from the cat. But it turns out that efficiently extracting
energy from mass is a very hard thing to do. Anti-matter is, of course, the most efficient
way of extracting energy from mass since, if you collide a cat with a cat made of anti-matter,
100% of the mass of the cat and anti-cat will be converted into energy (powering Norway
for 2 years). But the universe has almost no naturally-occurring
anti-matter, so it’s not a practical choice for generating energy, since you’d first
have to use a lot of energy to make a large mass of antimatter. Since we can’t use antimatter, there are basically
three options left to us: chemical reactions, nuclear reactions, and gravitational reactions
– aka stuff getting pulled together by gravity, like matter falling into black holes. Chemical reactions, for example, are so bad
at extracting energy from mass that we don’t even think about what they’re doing as converting
mass to energy (even though it is). As an illustration, reacting a balloon of
hydrogen and oxygen gases creates a nice big explosion, but the end-products of the reaction
only weigh half a nanogram less than the initial reactants , which amounts to a measly 0.00000001%
efficiency of converting mass into energy. At that rate, you’d need ten billion cats
to power Norway for a year. Nuclear reactions are a lot more efficient,
but still pretty bad on an absolute scale: splitting uranium-235 into krypton and barium
converts only about 0.08% of the uranium’s mass into energy, and fusing hydrogen into
helium like in the sun converts about 0.7% of the hydrogen’s mass into energy. At that rate you’d need 150 cats to power
Norway for a year. This where black holes come in – they’re
about as good as it gets in our universe for extracting energy from mass. Which may sound weird, because, as you’ve
probably heard, nothing can escape black holes – once inside. But the efficiency of black holes comes from
what stuff does while falling towards them, before passing the no-turning-back point of
the event horizon. Anything that falls in a gravitational field
speeds up, gaining kinetic energy, and if it then crashes into something it can convert
that kinetic energy into heat. That heat can then radiate away as infrared
radiation, slightly decreasing the mass of the object. For planets and stars, this conversion of
mass into energy is pretty pathetic: an object falling to the surface of the earth releases
only about one billionth of its mass as energy. That’s basically as bad as a chemical reaction! But black holes have something special going
for them: they are stupendouslysmall. A black hole with the mass of the earth would
be about 2 cm across, providing way farther for an object to fall – and since gravity
gets stronger and stronger the closer you are to an object, objects falling into black
holes get accelerated to ridiculous speeds. Specifically, an object falling all the way
to the event horizon of a black hole will have kinetic energy equivalent to converting
roughly half of its half of its E=mc2 mass energy mass. However, if the object continues to fall into
the black hole, all of that energy will be stuck inside the black hole. The way to actually convert mass into energy
that goes out into the universe is to have the object slowly spiral into the black hole,
crashing into other stuff, heating up, radiating that energy away thereby losing mass and speed,
slowing down more, spiraling to a yet lower orbit, and so on, all the way down to the
innermost possible orbit. And this is exactly what accretion disks around
black holes do! So how good are they at converting mass to
energy? Well, for a non-rotating black hole, the innermost
possible circular orbit is actually 3 times farther out than the event horizon, and in
order to spiral in to that point an object has to convert around 6% of its mass into
energy radiated away to the outside universe. After that point if it loses any more energy
it’ll plunge down into the black hole, after which no more energy can be extracted. But at this 6% rate, you’d only need to
throw 17 cats into a black hole to power Norway for a year. Compared to the 0.00000001% efficiency of
chemical reactions and the 0.7% efficiency of nuclear reactions, 6% for a non-rotating
black hole may seem pretty good. But rotating black holes are even better,
because of how they bend spacetime. They literally “drag” things orbiting
them in the direction of their rotation, which means the innermost possible orbit can be
much closer to the black hole (as long as you’re rotating along with the black hole). The details depend on how fast the black hole
is rotating, but for a very quickly rotating black hole the innermost possible orbit coincides
with the event horizon! And the event horizon itself is half as big
as for a non-rotating black hole. Combined together, this means that matter
falling into rotating black holes can convert as much as 42% of its mass into energy. Or equivalently, you’d only need 2 and a
half inspiralling cats to power Norway for a year. So, if you really want to convert the mass
of an object into energy, don’t bother with chemical reactions, or nuclear fission, or
nuclear fusion: throw it into a rapidly rotating black hole. If you’re wondering how I calculated the
efficiencies of converting mass to energy, you can just divide the energy any reaction
releases by the mass energy of the things involved – for example, when radium radioactively
decays into radon and helium it releases 6.6 MeV of energy, and the mass energy of a single
neutron or proton is about 940MeV, so I’ll leave it to you to figure out how efficient
alpha decay is at converting mass to energy! Or you can learn more about nuclear fission
and fusion by finishing this quiz on Brilliant.org, which is this video’s sponsor and is full
of interactive quizzes and mini courses on physics and math. If you really want to understand physics deeply,
you have to work through calculations and solve problems yourself, and Brilliant offers
an interactive online way to do just that. You can check out their course on black holes
for free using the link in the description, and if you decide to sign up for premium access
to all of their courses, you can get 20% off by going to Brilliant.org/minutephysics. Again, that’s Brilliant.org/minutephysics
which lets Brilliant know you came from here.
Video source: https://www.youtube.com/watch?v=t-O-Qdh7VvQ

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