e equals mc-squared the most famous
equation in the world describes the fact
that anything with mass possesses a huge
amount of energy in principle like a 5
kilogram 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 antimatter is
the most efficient way of extracting
energy from mass since if you collide a
cat with a cat made of antimatter a
hundred percent of the mass of the cat
an anti cat will be converted into
energy powering Norway for two years but
the universe has almost no naturally
occurring antimatter 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
like matter falling into black holes to
start chemical reactions 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
point zero zero zero zero zero zero zero
zero one percent efficiency of
converting mass into energy at that rate
you'd need 10 billion cats to power
Norway for a year nuclear reactions are
a lot more efficient but still pretty
mediocre on an absolute scale splitting
uranium-235 into Krypton and barium
converts only about point zero eight
percent of the uranium's mass into
energy and fusing hydrogen into helium
like in the Sun converts about 0.7
percent of the hydrogen's mass into
energy at that rate you'd need 150 cats
to power Norway for a year this is 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 and explains why we don't think
of falling to the ground as a way of
converting mass into energy it's a
really bad way but black holes have
something special going for them they
are stupendously small a black hole with
the mass of the earth would be about two
centimeters 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
roughly half of its e equals mc-squared
mass energy 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 on the way
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
three times farther out than the event
horizon and in order to spiral into 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
and no more energy can be extracted but
at this 6% mass energy conversion rate
you'd only need to throw 17 cats into a
black hole to power Norway for a year
compared to the point zero zero zero
zero zero zero zero zero one percent
efficiency of chemical reactions and the
point 1/2 point seven percent efficiency
of nuclear reactions 6 percent for a
non-rotating
Cole may seem pretty good but rotating
black holes are even better because of
how they been to space-time they
literally drag the things orbiting them
along with them in the direction of
their rotation which means the innermost
possible orbit can be much closer to 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
instead of being three times farther
away 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 forty-two percent
of its mass into energy or equivalently
you'd only need two and a half in
spiraling cats to power Norway for a
year so if you really want to take
advantage of e equals mc-squared and
convert the mass of an object into
energy
don't bother with chemical reactions or
nuclear fission or nuclear fusion just
throw it into a black hole if you're
wondering how I calculated the
efficiencies of converting mass to
energy you can just take the energy any
reaction releases and divide by the mass
times C squared of the things involved
for example when radium radioactively
decays into radon and helium it releases
six and a half MeV of energy and the
mass energy of a single neutron or
proton is about 940 MeV 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
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math if you really wanna 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
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using the link in the description and if
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