How Math Explains the World.pdf

(Marcin) #1

Over the course of the next decade or so, astrophysical measurements
should reveal the future of the universe: whether it is destined to expand
forever or whether it will eventually recollapse in what has been termed
the big crunch. Black holes will merge with other black holes until there
may be only one giant black hole with all the matter in the universe, col-
lapsing ever in on itself.
This was the conventional view of black holes until Stephen Hawking
showed in the 1970s that black holes are not as black as initially thought.
Quantum-mechanical processes allow matter to escape from the black
hole in a process known as Hawking radiation.^11 Just as water in a glass
slowly evaporates as its individual molecules acquire enough velocity to
escape the bounds of the glass, the matter within a black hole evaporates
over time. Surprisingly, though, the rate at which the matter disappears
depends strongly on the size of the black hole. A black hole the size of the
Sun will take on the order of 10^67 years to evaporate. Considering that the
age of the universe itself is approximately 10^14 years, solar mass black
holes will be hanging around until the far, far, far distant future. Should
the universe collapse into a black hole via the big crunch, it may take
close to forever for it to evaporate, but evaporate it will.


The Universe and Princess Leia
Hawking’s work also led the way to the surprising result that the entropy
of a black hole is proportional to its surface area, rather than its volume.
What makes this result surprising is that we have already seen that en-
tropy is a measure of disorder, and we would certainly expect volume to
be capable of displaying more disorder than the vessel that contains the
disorder.
As a result, some physicists have speculated that all the order and disor-
der we see in our universe is merely a projection of order and disorder on
a multidimensional boundary that in some sense encloses our universe
the way the surface of a basketball encloses the region inside it. This is
something akin to the way a hologram works. A hologram is a clever de-
vice that projects the illusion of a three-dimensional object from the in-
formation inscribed on a two-dimensional one.
There is a scene early in Episode 4 of Star Wars (that’s the first one
filmed back in the mid-1970s) in which Luke Skywalker and his droids
discover an old holographic projection device. They crank it up and a
holographic image of Princess Leia appears. The image is a little fuzzy,
but it is nonetheless three-dimensional, and the holographic Princess
Leia certainly possesses a considerable amount of passion as she makes

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