The Unreasonable Efficiency of Black Holes

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.

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    Adam F

    What if you tripped when you throwing the cat? Have you thought of that? The cat will die of suffocation, and you are converting yourself into pure energy

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    Naiver Miigon

    Guys in Norway stop watching this vid now!! You are killing those lovely cats by consuming electricity!!😢

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    Geoff Nixon

    Excellent. Extinction Rebellion -> Feline Extinction "Revolution". Just submit this to Greta Thunberg for approval (you may have convert Norways to Swedens, however).

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    Stretop Overmind

    It is all very good and well, but how would you collect all that energy from that black hole and convert it into some usable form?

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    Matt S.

    Does that mean that every conversion of energy from one form to another causes the related matter to lose mass? So when I walk up stairs, I'm gaining a tiny bit of mass, and when I inevitably jump out the 50th story window, my shattered corpse on the pavement below will have less mass than when I exited the stairwell on the 50th floor?

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    Black Tim Howard

    This guy: antimatter is an impractical way to convert mass to energy
    Also this guy: just throw cats into a rotating black hole

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    yttrium

    So you're saying we should built a power plant that captures the energy radiated by objects falling into black holes?

    Sounds reasonable.

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    gamewizl

    I'll take one black whole … and some cats please.

    Ostensibly, the rotation rate of the black hole would also have some effect (beyond merely being rotating or not) – get a faster one.

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    Manisha Mhatre

    2 minutes silence for all cats that died during these events. May their souls rest in peace🙏🙇‍♂️🐱🐈🐱🐈🐱🐈

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    Shaggy2222

    How can a black hole with the mass of the earth be 2cm big? I mean, how could we possibly know? I thought we only just proved their existence, and the science behind them is still unknown? We don’t actually know what it is, just theories? I am just curious, would love an answer from someone, thanks

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    Arttu Kettunen

    Black holes convert 100% of their mass into energy over time (Hawking radiation), you just gotta wait until Sun goes boom, then wait that amount of time a couple bajillion times

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    ConvexEd

    but how do we harness this cat energy?
    (Of course, this would be more clear considering we would be a civ capable of going close to spinning black holes and throwing cats to them.)

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    Yukterez Net

    3:06 – relative to what would the infalling particle at the horizon have a kinetic energy of mc²/2? the local velocity relative to a stationary observer would be c so the kinetic energy relative to a local observer should go to infinity as the limit of r approaches the horizon. the redshifted kinetic energy at infinity would be the local kinetic energy divided by the lapse function, which gives 1mc² in the limit of r=rs, so how do you arrive at mc²/2?

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    Stu Lora

    3:30 When matter spirals down into a BH, it actually accelerates. What it looses is angular momentum. Counter-intuititive…. but that's what happens.

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    Ahmed Elian

    Hmmmmm wait…. Not all energy matter releases is from its mass, that's the case only in nuclear reactions and the like…. Usually the released energy is converted from OTHER FORMS OF ENERGY; e.g. kinetic (e.g. thermal), electrostatic (e.g. chemical bonds), potential energy (related to gravity)! What the hell are you talking about, man? Was I taught physics wrong in school?

    I wish I could dislike this misleading, very wrong video more than once!

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    mukundan nair

    But when he says the mass is converted to energy and radiated during the black hole spiral what does that mean? What kind of energy? How does the mass reduce?

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    drocles

    But what about the efficency of capturing the released energy, which for the black hole would entail a complete dyson sphere to capture the energy and send it to Norway….

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    I'M POSSIBLE

    4:58 If you blinked
    You missed the 42% written big on the screen!
    If your eyes are sharp
    Then you can see
    It is written there
    "42
    Coincidence? I think not"

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    Brandon Reed

    One thing to consider though is how long it takes to make that conversion. Time dilation would be an issue to consider.

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    Terji Djurhuus

    Norwegian minister of energy sees his video:

    "That's it guys, divert all of our funds into researching svarte hul & katter."

    Energy crisis solved.

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    tatsu

    well how do you gather energy from that falling object? surely whatever that process is would be extremely lossy as well if not more so than the other methods?

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    Renan_PS

    I made a catapult and threw 10 cats (I had 12) upwards, hopefully at least one of them will hit a black hole and then I won't have to pay no more energy bills for the rest of my life!!!! Why didn't no one thought about this before?

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    Leaf Maltieze

    Okay, but how do we harvest the power being released so close to a black hole? The energy might be there, but being able to use it is another thing entirely.

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    dryten

    what about micro kugelblitz black holes? due to hawking radiation working exponentially faster at smaller black hole masses, couldn't you just feed a tiny black hole a constant stream of matter and have it basically convert the mass directly into gamma rays? AND get some energy out of the falling as well, seems ideal

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