For a long time, the big question was whether there was enough matter
in the universe to make it recollapse, or whether it would expand
forever. But in the late 1990's, astronomical observations began to
suggest that the expansion of the universe is actually speeding up!

Let's suppose this is true, and let's assume the most popular
explanation for it: namely, that there is a nonzero cosmological constant. A cosmological constant with
the right sign makes the energy density of the vacuum positive, but
makes its pressure negative - and 3 times as big. This makes the
universe tend to expand. Normal matter makes the universe tend to
recollapse. If the effect of the cosmological constant ever beats out
the effect of normal matter, the universe will keep expanding, making
the density of normal matter less... so the cosmological constant will
ultimately win hands down, and the universe will eventually expand at an
almost exponential rate.

Let's suppose this happens. What will be the ultimate fate
of the universe?

First let me set the stage. What happens in the short run, i.e.
the first 1023 years or so?

First, galaxies will keep colliding. These collisions seem to
destroy spiral galaxies — they fuse into bigger elliptical
galaxies. We can already see this happening here and there, and our
own Milky Way may collide with Andromeda in only 3 billion years or
so. If this happens, a bunch of new stars will be born from the shock
waves due to colliding interstellar gas, but eventually we will
inhabit a large elliptical galaxy. Unfortunately, elliptical galaxies
lack spiral arms, which seem to be a crucial part of the star
formation process, so star formation may cease even before the raw
materials run out.

Of course, even if this doesn't happen, the birth of new stars must
eventually cease, since there's a limited amount of hydrogen, helium,
and other stuff that can undergo fusion.

This means that all the stars will eventually burn out. The longest
lived are the red dwarf stars, the smallest stars capable of
supporting fusion today, with a mass about 0.08 times that of the Sun.
These will run out of hydrogen about 1013 years from now,
and slowly cool.

Stars become white dwarfs — and eventually black dwarfs when
they cool — if they have mass less than 1.4 solar masses. In
this case they can be held up by the degeneracy pressure caused by the
Pauli exclusion principle, which works even at zero temperature. If
they are heavier than this, they collapse: they become neutron stars
if they are between 1.4 and 2 solar masses, and they become black
holes if they are more massive.

In about 1014 years, all normal star formation
processes will have ceased, and the universe will have a
population of stars consisting of about 55% white dwarfs, 45% brown
dwarfs and a small number of neutron stars and black holes. Star
formation will continue at a very slow rate due to collisions between
brown and/or white dwarfs.

The black holes will suck up some of the other stars they encounter.
This is especially true for the big black holes at the galactic centers,
which power radio galaxies if they swallow stars at a sufficiently rapid
rate. But most of the stars, as well as interstellar gas and dust, will
eventually be hurled into intergalactic space. This happens to a star
whenever it accidentally reaches escape velocity through its random
encounters with other stars. It's a slow process, but computer
simulations show that about 90% of the mass of the galaxies will
eventually "boil off" this way — while the rest becomes a big black
hole.

(It may seem odd that first the galaxies form by gravitational
attraction of matter and then fall apart again by "boiling off", but
the point is, intergalactic matter is less dense now than it was when
galaxies first formed, thanks to the expansion of the universe. When
the galaxies first formed, there was lots of gas around. Now the
galaxies are essentially isolated — intergalactic space is
almost a vacuum. And you can show in the really long run,
any isolated system consisting of sufficiently many point particles
interacting gravitationally — even an apparently
"gravitationally bound" system — will "boil off" as individual
particles randomly happen to acquire enough kinetic energy to reach
escape velocity. Computer calculations already suggest that the solar
system will fall apart this way, barring other interventions. With
the galaxies it's even more certain to happen, since there are more
particles involved, so things are more chaotic.)

How long will all this take? Well, the white dwarfs will cool to black
dwarfs with a temperature of at most 5 Kelvin in about 1017
years, and the galaxies will boil away by about 1019 years.
Most planets will have already been knocked off their orbits by then,
but any that are still orbiting stars will spiral in thanks to gravitational
radiation in about 1020 years.

Then what? Well, in about 1023 years the dead stars will
actually boil off from the galactic clusters, not just the galaxies,
so the clusters will disintegrate. At this point the cosmic
background radiation will have cooled to about 10-13
Kelvin, and most things will be at about that temperature unless
proton decay or some other such process keeps them warmer.

Okay, so now we have a bunch of isolated black dwarfs, neutron stars,
and black holes together with atoms and molecules of gas, dust particles,
and of course planets and other crud, all very close to absolute zero.

As the universe expands these things eventually spread out to the point where
each one is completely alone in the vastness of space.

So what happens next?

Well, everybody loves to talk about how all matter eventually turns to
iron thanks to quantum tunnelling, since iron is the nucleus with the
least binding energy, but unlike the processes I've described so far,
this one actually takes quite a while. About 101500 years,
to be precise. (Well, not too precise!) So it's quite likely that
proton decay or something else will happen long before this gets a
chance to occur.

For example, everything except the black holes will have a tendency to
"sublimate" or "ionize", gradually losing atoms or even electrons and
protons, despite the low temperature. Just to be specific, let's
consider the ionization of hydrogen gas — although the argument is much
more general. If you take a box of hydrogen and keep making the box
bigger while keeping its temperature fixed, it will eventually ionize.
This happens no matter how low the temperature is, as long as it's
not exactly absolute zero — which is forbidden by the 3rd
law of thermodynamics, anyway.

This may seem odd, but the reason is simple: in thermal equilibrium
any sort of stuff minimizes its free energy, E - TS: the energy minus
the temperature times the entropy. This means there is a competition
between wanting to minimize its energy and wanting to maximize its
entropy. Maximizing entropy becomes more important at higher
temperatures; minimizing energy becomes more important at lower
temperatures — but both effects matter as long as the temperature
isn't zero or infinite.

Think about what this means for our box of hydrogen. On the one hand,
ionized hydrogen has more energy than hydrogen atoms or molecules.
This makes hydrogen want to stick together in atoms and molecules,
especially at low temperatures. But on the other hand, ionized
hydrogen has more entropy, since the electrons and protons are more
free to roam. And this entropy difference gets bigger and bigger as
we make the box bigger. So no matter how low the temperature is, as
long as it's above zero, the hydrogen will eventually ionize as we
keep expanding the box.

(In fact, this is related to the "boiling off" process that I mentioned
already: we can use thermodynamics to see that the stars will boil off
the galaxies as they approach thermal equilibrium, as long as the
density of galaxies is low enough.)

However, there's a complication: in the expanding universe, the
temperature is not constant — it decreases!

So the question is, which effect wins as the universe expands: the
decreasing density (which makes matter want to ionize) or the
decreasing temperature (which makes it want to stick together)?

In the short run this is a fairly complicated question, but in the
long run, things may simplify: if the universe is expanding
exponentially thanks to a nonzero cosmological constant, the density
of matter obviously goes to zero. But the temperature does not go to
zero. It approaches a particular nonzero value! So all forms of
matter made from protons, neutrons and electrons will eventually
ionize!

Why does the temperature approach a particular nonzero value, and
what is this value? Well, in a universe whose expansion keeps
accelerating, each pair of freely falling observers will eventually no
longer be able to see each other, because they get redshifted out of
sight. This effect is very much like the horizon of a black hole -
it's called a "cosmological horizon". And, like the horizon of a
black hole, a cosmological horizon emits thermal radiation at a
specific temperature. This radiation is called Hawking
radiation. Its temperature depends on the value of the
cosmological constant. If we make a rough guess at the cosmological
constant, the temperature we get is about 10-30 Kelvin.

This is very cold, but given a low enough density of matter, this
temperature is enough to eventually ionize all forms of matter made of
protons, neutrons and electrons! Even something big like a neutron
star should slowly, slowly dissipate. (The crust of a neutron star is
not made of neutronium: it's mainly made of iron.)

But what about the black holes?

Well, they probably evaporate due to Hawking radiation: a solar-mass
black hole should do so in 1067 years, and a really big one,
comparable to the mass of a galaxy, should take about 1099
years.

Actually, a black hole only shrinks by evaporation when it's in
an enviroment cooler than the temperature of its Hawking radiation —
otherwise, it grows by swallowing thermal radiation.
The Hawking temperature of a solar-mass black hole is about 6 ×
10-8 Kelvin, and in general, it's inversely proportional to
the black hole's mass. The universe should cool down below 10-8
Kelvin very soon compared to the 1067 years it takes for
a solar-mass black holes to evaporate. However, before that
time, such a black hole would grow by absorbing background radiation —
which makes its temperature decrease and help it grow more!

If a black hole ever grew to about 1022
solar masses, its Hawking temperature would go below 10-30
Kelvin, which would allow it to keep growing even when the universe has
cooled to its minimum temperature. Of course, 1022 solar
masses is huge — about the mass of the currently observable universe!
But it would take a nontrivial calculation to show that reasonable-sized
black holes have no chance of getting this big. I think it's true, but
I haven't done the calculation.

For now, let's assume it's true: all black holes will eventually
shrink away and disappear — none of them grow big enough to stick
around when it gets really cold.

As black holes evaporate, they will emit photons and other particles in
the process, so for a while there will be a bit of radiation like this
running around. That livens things up a little bit — but this process
will eventually cease.

What about the neutron stars? Well, if they don't ionize first,
ultimately they should quantum-tunnel into becoming black holes,
which then Hawking-radiate away.

Similarly, if the black dwarfs and planets and the like don't evaporate
and their protons don't decay, they may quantum-tunnel into becoming
solid iron — as I already mentioned, this takes about 101500
years. And then, if this iron doesn't evaporate and nothing else
happens, these balls of iron will eventually quantum-tunnel into
becoming black holes, which then Hawking-radiate away. This would take
about 10100000000000000000000000000 years — that's 26 zeros.

This is a much longer time than any I've mentioned so far, so
I wouldn't be surprised if some other effect we haven't thought
about happens first. Indeed, this whole discussion should be
taken with a grain of salt: future discoveries in physics could
drastically change the end of this story. It's also possible that
the intervention of intelligent life could change things — I've avoided
discussing that here. Cosmology has been full of surprises lately,
and there will probably be more to come.

But the overall picture seems to lean heavily towards a far future where
everything consists of isolated stable particles: electrons, neutrinos,
and protons (unless protons decay). If the scenario I'm describing
is correct, the density of these particles will go to zero, and eventually
each one will be cut off from all the rest
by a cosmological horizon, making them unable to interact. Of
course there will be photons as well, but these will eventually come
into thermal equilibrium forming blackbody radiation at the temperature
of the cosmological horizon — perhaps about 10-30 Kelvin or so.

This is why it's really a bad idea to keep putting things off for tomorrow.

However, Leonard Susskind has recently pointed out that in thermal
equilibrium at any nonzero temperature, any system exhibits random
fluctuations. The lower the temperature they smaller these are, but
they are always there. These fluctuations randomly explore the space
of all possible states of your system. So eventually, if you wait
long enough, these random fluctuations will carry the system to
whatever state you like. Well, that's a bit of an exaggeration: these
fluctuations can't violate conservation laws. But conservation of
energy doesn't count here, since at a nonzero temperature, a system is
really in a state of all possible energies. So it's possible, for
example, that a ice cube at the freezing point of water will melt or
even boil due to random fluctuations. The reason we never
see this happen is that such big fluctuations are incredibly rare.

Carrying this thought to a ridiculous extreme, what this means is that
even if the universe consists of more or less empty space at a
temperature of 10-30 kelvin, random fluctuations will
occaisionally create atoms, molecules... and even solar systems and
galaxies! The bigger the fluctuation, the more rarely it happens -
but eternity is a long time. So eventually there will arise, sheerly
by chance, a person just like you, with memories just like yours,
reading a webpage just like this.

In short: maybe the universe has already ended!

However, the time it takes for really big fluctuations like this to
occur is truly huge. It dwarfs all the time scales I've mentioned so
far. So, it's probably not worth worrying about this issue too much:
we don't know enough physics to make reliable predictions on such long
time scales.

The hypothesis of proton decay is less fashionable now than when this
book was written, since people have looked very hard for it and not
found it — pushing up the lower bound on the proton lifetime to
1032 years. Also, the nonzero mass of the neutrino was
discovered after this book was written, as was the apparent nonzero
cosmological constant. Nonetheless, it includes some dicussion of the
effects of a nonzero cosmological constant, and notes that in a
universe with ever-accelerating expansion due to a cosmological
constant, all computation must eventually cease due to a heat death,
as explained above.

Tipler subsequently wrote a book of speculations about the fate of
intelligent in the far future. He assumed there would be a big crunch,
which no longer seems to be true, so I do not use his ideas here.

Freeman Dyson has discussed the fate of intelligent life in the far
future assuming a perpetually expanding universe, but assuming the
cosmological constant is zero. In this situation the temperature of
the universe decreases ever closer to absolute zero, and Dyson figured
out that in principle, intelligent life could last forever and think
an infinite number of thoughts, although slower and slower:

This theory
seems to be ruined by the presence of a nonzero cosmological constant
and the resulting nonzero lower bound on the temperature.
However, Dyson's article is full of good thoughts on the far future.

The notion of a nonzero lower bound for the temperature of the universe
are discussed in Scientific American articles appearing in the April 1999
and November 1999 issues, the latter written by Krauss and Starkman.

The rough estimates of 10-30 Kelvin for the limiting
temperature of the universe and 1022 solar masses for
the smallest black hole that would never evaporate are derived here:

I don't think any of these sources mention the "ionization"
effect I discuss here. I would like to know the rate of this process,
but I'm busy, so if you can figure it out it, go ahead and let me know
the answer.

This article arose from a discussion among the
contributors to sci.physics.research, and I thank all these people for
their help in putting this together, especially Ted Bunn and Keith Ramsay.

I had a dream, which was not all a dream.
The bright sun was extinguishd, and the stars
Did wander darkling in the eternal space,
Rayless, and pathless, and the icy earth
Swung blind and blackening in the moonless air. — Lord Byron