In this analogy, spacetime is the bathtub. The black hole
is the drain. Matter and energy are the water. The shape of
the tub is the curvature of spacetime by gravity. Dark energy
is some exotic and invisible water flowing into our bathtub
through the black whole whose collapse fourteen billion years
ago was the impetus for our big bang. Here's how an extremely
drunk Ford explains it to Arthur in
The Restaurant At The End Of The Universe:
"All right," said Ford, "imagine this. Right.
You get this bath. Right. A large round bath. And it's made
of ebony...And it's conical."
"Conical?" said Arthur. "What sort of..."
"Shhh!" said Ford. "It's conical. So what
you do is, you see, you fill it with fine white sand, all
right? Or sugar. Fine what sand, and/or sugar. Anything.
Doesn't matter. Sugar's fine. And when it's full, you pull
the plug out...are you listening?"
"I'm listening."
"You pull the plug out, and it all just twirls away,
twirls away you see, out of the plughole."
"I see."
"You don't see. You don't see at all. I haven't got
to the clever bit yet. You want to hear the clever bit?"
"Tell me the clever bit."
"I'll tell you the clever bit."
Ford thought for a moment, trying to remember what the
clever bit was.
"The clever bit," he said, "is this. You
film it happening."
"Clever," agreed Arthur.
"You get a movie camera, and you film it happening."
"Clever."
"That's not the clever bit. This is the clever bit.
I remember now that this is the clever bit. The clever bit
is that you then thread the film in the projector...backward!"
"Backward?"
"Yes. Threading it backward is definitely the clever
bit. So then, you just sit and watch it, and everything
just appears to spiral upward out of the plughole and fill
the bath. See?"
"And that's how the Universe began, is it?" asked
Arthur.
"No," said Ford. "But it's a marvelous way
to relax."
The bathtub analogy isn't perfect. Spacetime isn't rigid
like porcelain; it's stretchy like rubber. A better analogy
might be a balloon animal. Spacetime is a single 'sausage
link' worth of rubber in an enormous and complex balloon creature.
Matter and energy are the air molecules in our region of the
balloon, including the dark energy exerting ever-greater outward
pressure on the balloon's 'sides'. A black hole is a twist
in the balloon leading to another link in the giant rubber
hypersausage.
Lee Smolin has suggested that a
black hole's collapse in one region of the higher-dimensional
bulk starts a big bang in its own new region of bulk.
My naïve imagination goes like this: In stars, collapsing
inwards produces violent reactions outwards. If the violence
can be contained within our spacetime, we get supernovas.
If the violence ruptures spacetime, by making a singularity
for example, the explosion happens in another region of the
bulk, setting off another big bang, putting another twist
in the balloon animal.
The balloon animal analogy isn't perfect either. A balloon
animal in 3D space customarily only has two 'links' in a given
stretch of balloon, while spacetime can have as many 'links'
as it wants. There are hundreds of billions of galaxies out
there that we know of, many if not most of which probably
have gargantuan black holes at their centers. On top of that
are the countless smaller black holes scattered around. Also,
Brian Greene thinks that electrons might be micro black holes.
So that's a whole lot of twists to the balloon animal.
So in all likelihood, there are many other universes out
there. Sadly, though, most of the other universes are likely
to be boring. Lee S thinks that each big bang event produces
a slightly different set of laws of physics from its 'parent'
universe: different starting distributions of matter and antimatter,
different value of basic physical constants, and so on. As
it turns out, few of the possible outcomes result in the formation
of stars and galaxies as we know them. If a universe has too
much matter, then it collapses quickly back on itself into
a pointlike singularity before anything can really happen.
If it has too little matter, then the bang disperses everything
before gravity can clump it together into structures, so you
wind up with a homogenous gas of, say, a single proton every
trillion cubic miles. Different starting ratios of matter
to antimatter give you universes full of light and nothing
else, or a bunch of black holes and nothing else, or other
similarly barren cosmic landscapes. To get the complex structures,
the 'interestingness' our universe, things have to be in that
Goldilocks state: just right.
Here's a model of the primordial gas filling universe after
our Big Bang collapsing under its own gravity,
from the Millenium Simulation.
