How the Universe Will End



How the Universe Will End

Scientists think they know how the universe began, but what happens at the

other end of the space—time continuum was a deep, dark mystery—until

now

BY MICHAEL D. LEMONICK

For those who live in a city or near

one, the night sky isn't much to look

at—just a few scattered stars in a

smoggy, washed-out, light-polluted

expanse. In rural Maine, though, or

the desert Southwest or the high

mountains of Hawaii, the view is quite

different. Even without a telescope,

you can see thousands of stars

twinkling in shades of blue, red and

yellow-white, with the broad Milky

Way cutting a ghostly swath from one

horizon to the other. No wonder our

ancient ancestors peered up into the

heavens with awe and reverence; it's

easy to imagine gods and mythical

heroes inhabiting such a luminous realm.

Yet for all the magnificence of the visible stars, astronomers know they are only the first

shimmering veil in a cosmos vast beyond imagination. Armed with ever more powerful

telescopes, these explorers of time and space have learned that the Milky Way is a

huge, whirling pinwheel made of 100 billion or more stars; that tens of billions of other

galaxies lie beyond its edges; and, most astonishing of all, that these galaxies are

rushing headlong away from one another in the aftermath of an explosive cataclysm

known as the Big Bang.

That event—the literal birth of time and space some 15 billion years ago—has been

understood, at least in its broadest outlines, since the 1960s. But in more than a third of

a century, the best minds in astronomy have failed to solve the mystery of what happens

at the other end of time. Will the galaxies continue to fly apart forever, their glow fading

until the cosmos is cold and dark? Or will the expansion slow to a halt, reverse direction

and send 10 octillion (10 trillion billion) stars crashing back together in a final,

apocalyptic Big Crunch, the mirror image of the universe's explosive birth? Despite

decades of observations with the most powerful telescopes at their disposal,

astronomers simply haven't been able to decide.

But a series of remarkable discoveries announced in quick succession starting this

spring has gone a long way toward settling the question once and for all. Scientists who

were betting on a Big Crunch liked to quote the poet Robert Frost: "Some say the world

will end in fire,/ some say in ice./ From what I've tasted of desire/ I hold with those who

favor fire." Those in the other camp preferred T.S. Eliot: "This is the way the world ends/

Not with a bang but a whimper." Now, using observations from the Sloan Digital Sky

Survey in New Mexico, the orbiting Hubble Space Telescope, the mammoth Keck

Telescope in Hawaii and sensitive radio detectors in Antarctica, the verdict is in: T.S.

Eliot wins.

For that reason alone, the latest news from space would be profoundly significant;

understanding where we came from and where we are headed have been obsessions of

thinking humans, probably for as long as we've walked the earth. But the particulars of

these discoveries shed light on even deeper mysteries of the cosmos, lending powerful

support to radical ideas once considered speculative at best. For one thing, the new

observations bolster the theory of inflation: the notion that the universe went through a

period of turbocharged expansion before it was a trillionth of a second old, flying apart

(in apparent, but not actual, contradiction of Albert Einstein's theories of relativity) faster

than the speed of light.

An equally bizarre implication is that the universe is pervaded with a strange sort of

"antigravity," a concept originally proposed by and later abandoned by Einstein as the

greatest blunder of his life. This force, which has lately been dubbed "dark energy," isn't

just keeping the expansion from slowing down, it's making the universe fly apart faster

and faster all the time, like a rocket ship with the throttle wide open.

It gets stranger still. Not only does dark energy swamp ordinary gravity but an invisible

substance known to scientists as "dark matter" also seems to outweigh the ordinary stuff

of stars, planets and people by a factor of 10 to 1. "Not only are we not at the center of

the universe," University of California, Santa Cruz, astrophysical theorist Joel Primack

has commented, "we aren't even made of the same stuff the universe is."

These mind-bending discoveries raise more questions than they answer. For example,

just because scientists know dark matter is there doesn't mean they understand what it

really is. Same goes for dark energy. "If you thought the universe was hard to

comprehend before," says University of Chicago astrophysicist Michael Turner, "then

you'd better take some smart pills, because it's only going to get worse."

ECHO OF THE BIG BANG

Things seemed a lot simpler back in 1965 when two astronomers at Bell Labs in

Holmdel, N.J., provided a resounding confirmation of the Big Bang theory, at the time

merely one of several ideas floating around on how the cosmos began. The discovery

happened purely by accident: Arno Penzias and Robert Wilson were trying to get an

annoying hiss out of a communications antenna, and after ruling out every other

explanation—including the residue of bird droppings—they decided the hiss was coming

from outer space.

Unbeknownst to the duo, physicists at nearby Princeton University were about to turn

their own antenna on the heavens to look for that same signal. Astronomers had known

since the 1920s that the galaxies were flying apart. But theorists had belatedly realized a

key implication: the whole cosmos must at one point have been much smaller and hotter.

About 300,000 years after the instant of the Big Bang, the entire visible universe would

have been a cloud of hot, incredibly dense gas, not much bigger than the Milky Way is

now, glowing white hot like a blast furnace or the surface of a star. Because this cosmic

glow had no place to go, it must still be there, albeit so attenuated that it took the form of

feeble microwaves. Penzias and Wilson later won the Nobel Prize for the accidental

discovery of this radio hiss from the dawn of time.

The discovery of the cosmic-microwave background radiation convinced scientists that

the universe really had sprung from an initial Big Bang some 15 billion years ago. They

immediately set out to learn more. For one thing, they began trying to probe this cosmic

afterglow for subtle variations in intensity. It's clear throughout ordinary telescopes that

matter isn't spread evenly through the modern universe. Galaxies tend to huddle

relatively close to one another, dozens or even hundreds of them in clumps known as

clusters and superclusters. In between, there is essentially nothing at all.

That lumpiness, reasoned theorists, must have evolved from some original lumpiness in

the primordial cloud of matter that gave rise to the background radiation. Slightly denser

knots of matter within the cloud—forerunners of today's superclusters should have been

slightly hotter than average. So scientists began looking for subtle hot spots.

FIRE OR ICE?

Others, meanwhile, attacked a different aspect of the problem. As the universe expands,

the combined gravity from all the matter within it tends to slow that expansion, much as

the earth's gravity tries to pull a rising rocket back to the ground. If the pull is strong

enough, the expansion will stop and reverse itself; if not, the cosmos will go on getting

bigger, literally forever. Which is it? One way to find out is to weigh the cosmos—to add

up all the stars and all the galaxies, calculate their gravity and compare that with the

expansion rate of the universe. If the cosmos is moving at escape velocity, no Big

Crunch.

Trouble is, nobody could figure out how much matter there actually was. The stars and

galaxies were easy; you could see them. But it was noted as early as the 1930s that

something lurked out there besides the glowing stars and gases that astronomers could

see. Galaxies in clusters were orbiting one another too fast; they should, by rights, be

flying off into space like untethered children flung from a fast-twirling merry-go-round.

Individual galaxies were spinning about their centers too quickly too; they should long

since have flown apart. The only possibility: some form of invisible dark matter was

holding things together, and while you could infer the mass of dark matter in and around

galaxies, nobody knew if it also filled the dark voids of space, where its effects would not

be detectable.

So astrophysicists tried another approach: determine whether the expansion was

slowing down, and by how much. That's what Brian Schmidt, a young astronomer at the

Mount Stromlo Observatory in Australia, set out to do in 1995. Along with a team of

colleagues, he wanted to measure the cosmic slowdown, known formally as the

"deceleration parameter." The idea was straightforward: look at the nearby universe and

measure how fast it is expanding. Then do the same for the distant universe, whose light

is just now reaching us, having been emitted when the cosmos was young. Then

compare the two.

Schmidt's group and a rival team led by Saul Perlmutter, of Lawrence Berkeley

Laboratory in California, used very similar techniques to make the measurements. They

looked for a kind of explosion called a Type Ia supernova, occurring when an aging star

destroys itself in a gigantic thermonuclear blast. Type Ia's are so bright that they can be

seen all the way across the universe and are uniform enough to have their distance

from Earth accurately calculated. That's key: since the whole universe is expanding at a

given rate at any one time, more distant galaxies are flying away from us faster than

nearby ones. So Schmidt's and Perlmutter's teams simply measured the distance to

these supernovas (deduced from their brightness) and their speed of recession

(deduced by the reddening of their light, a phenomenon affecting all moving bodies,

known to physicists as the Doppler shift). Combining these two pieces of information

gave them the expansion rate, both now and in the past.

DARK ENERGY

By 1998 both teams knew something very weird was happening. The cosmic expansion

should have been slowing down a lot or a little, depending on whether it contained a lot

of matter or a little—an effect that should have shown up as distant supernovas, looking

brighter than you would expect compared with closer ones. But, in fact, they were

dimmer—as if the expansion was speeding up. "I kept running the numbers through the

computer," recalls Adam Riess, a Space Telescope Science Institute astronomer

analyzing the data from Schmidt's group, "and the answers made no sense. I was sure

there was a bug in the program." Perlmutter's group, meanwhile, spent the better part of

the year trying to figure out what could be producing its own crazy results.

In the end, both teams adopted Sherlock Holmes' attitude: once you have eliminated the

impossible, whatever is left, no matter how improbable, has got to be true. The universe

was indeed speeding up, suggesting that some sort of powerful antigravity force was at

work, forcing the galaxies to fly apart even as ordinary gravity was trying to draw them

together. "It helped a lot," says Riess, "that Saul's group was getting the same answer

we were. When you have a strange result, you like to have company." Both groups

announced their findings almost simultaneously, and the accelerating universe was

named Discovery of the Year for 1998 by Science magazine.

For all its seeming strangeness, antigravity did have a history, one dating back to

Einstein's 1916 theory of general relativity. The theory's equations suggest that the

universe must be either expanding or contracting; it couldn't simply sit there. Yet the

astronomers of the day, armed with relatively feeble telescopes, insisted that it was

doing just that. Grumbling about having to mar the elegance of his beloved

mathematics, Einstein added an extra term to the equations of relativity. Called the

cosmological constant, it amounted to a force that opposed gravity and propped up the

universe.

A decade later, though, Edwin Hubble discovered that the universe was expanding after

all. Einstein immediately and with great relief discarded the cosmological constant,

declaring it to be the biggest blunder of his life. (If he had stuck to his guns, he might

have nabbed another Nobel.)

Even so, the idea of a cosmological constant wasn't entirely dead. The equations of

quantum physics independently suggested that the seemingly empty vacuum of space

should be seething with a form of energy that would act just like Einstein's disowned

antigravity. Problem was, this force would have been so powerful that it would have

blown the universe apart before atoms could form, let alone galaxies—which it clearly

did not. "The value particle physicists predict for the cosmological constant," admits

Chicago's Turner, "is the most embarrassing number in physics."

Aside from that detail, the Einstein connection made the idea of dark energy, or

antigravity, seem somewhat less nutty when Schmidt and Perlmutter weighed in. Of

course, some astrophysicists had lingering doubts. Maybe the observers didn't really

have the supernovas' brightness right; perhaps the light from faraway stellar explosions

was dimmed by some sort of dust. The unique properties of a cosmological constant,

moreover, would make the universe slow down early on, then accelerate. That's

because dark energy grows as a function of space. There wasn't much space in the

young, small universe, so back then the braking force of gravity would have reigned

supreme. More recently, the force of gravity fell off as the distance between galaxies

grew and that same increase made for more dark energy. Nobody had probed deeply

enough to find out what was really going on in the distant past.

Or rather, nobody had got enough data. Back in 1997, astronomers Mark Phillips of the

Space Telescope Science Institute and Ron Gilliland of the Carnegie Institute of

Washington had used the Hubble to spot a distant supernova designated SN 1997ff

and, with the help of Peter Nugent, a Lawrence Berkeley astronomer on Perlmutter's

team, had determined its speed of recession from Earth. Nugent couldn't figure out the

distance, though: determining the brightness of a Type Ia calls for not just one but

several measurements, spread over time.

On the rival team, Riess knew of the discovery, but he learned soon afterward that other

Hubble photos had also caught the supernova, completely by chance. So one day last

summer, he recalls, "I called up Peter and began fishing around for information. I guess I

wasn't especially cagey. He said almost right away, ÔAre you asking about 1997ff?'"

Rather than try to scoop each other, the friendly rivals decided to cooperate—and soon

realized they had stumbled onto something truly astonishing. The new supernova, some

50% closer to the beginning of the universe than any supernova known before, was far

brighter than had been predicted. That neatly eliminated the idea of dust, since a more

distant star should have been even more dust-dimmed than nearer ones. But the level

of brightness also signaled that this supernova was shining when the expansion of the

cosmos was still slowing down. "Usually," says Riess, "we see weird things and try to

make our models of the universe fit. This time we put up a hoop for the observations to

jump through in advance, and they did—which makes it a lot more convincing."

PROBING THE COSMIC FIREBALL

What makes it still more convincing is that an entirely different kind of observation—the

long-standing search for lumpiness in the cosmic background radiation—now suggests

independently that dark energy is real. The lumps themselves were first detected about

a decade ago, thanks to the Cosmic Background Explorer satellite. At the time,

astrophysicist and cobe spokesman George Smoot declared that "if you're religious, it's

like seeing God."

But it was more like seeing God through dirty Coke-bottle glasses: the satellite saw

lumps but couldn't determine much about them. In April, though, scientists offered up

much sharper images from a balloon-borne experiment called boomerang (Balloon

Observations of Millimetric Extragalactic Radiation and Geophysics), which lofted

instruments into the Antarctic stratosphere; from another named maxima (Millimeter

Anisotropy Experiment Imaging Array, which did the same over the U.S.); and from a

microwave telescope on the ground at the South Pole, called dasi (Degree Angular

Scale Interferometer).

All these measurements pretty much agreed with one another, confirming that the lumps

scientists saw were real, not some malfunction in the telescopes. And just two weeks

ago, astronomers from the Sloan Digital Sky Survey confirmed that this primordial

lumpiness has carried over into modern times. The five-year mission of the survey, to

make a 3-D map of the cosmos, is far from complete, but scientists reported at the

American Astronomical Society's spring meeting in Pasadena, Calif., that it is clearer

than ever that galaxies cluster together into huge clumps that reflect conditions that

existed soon after the Big Bang.

To the unaided eye, the images are meaningless. A statistical analysis, however, shows

that the early lumps—actually patches of slightly warmer or cooler radiation—don't come

at random but rather at certain fixed sizes. "It's as though you're studying dogs," says

University of Pennsylvania astrophysicist Max Tegmark, "and you find out that they come

in just three types: Labrador, toy poodle and Chihuahua."

That turns out to be enormously important. Knowing the characteristic sizes and also the

temperatures, to a millionth of a degree, of these warm and cool regions gives

theoretical physicists all sorts of information about the newborn cosmos. They were

already pretty sure, from the equations of nuclear physics and from measurements of

the relative amounts of hydrogen, helium and lithium in the universe, that protons,

neutrons and electrons (the building blocks of every atom in the cosmos) add up to only

about 5% of the so-called critical density—what it would take to bring the cosmic

expansion essentially to a halt by means of gravity.

But when you add Tegmark's "dogs," plus the more esoteric equations of sub-nuclear

physics, it turns out that an additional 30% of the needed matter most likely comes in the

form of mysterious particles that have been identified only in theory, never directly

observed—particles with quirky names like neutralino and axion. These are the

mysterious dark matter, or most of it anyway. The cosmic background radiation itself

began to shine when the universe was 300,000 years old, but the temperature

fluctuations were set in place when it was just a split-second old. "It's pretty cool," says

Tegmark, "to be able to look back that far."

THE FLAT UNIVERSE

The dogs also yield another key bit of information: they tell theorists how the universe is

curved, in the Einsteinian sense. There's no way to convey this concept to a

nonphysicist except by two-dimensional analogy (see How Does the Universe Curve?

diagram). The surface of a sphere has what's called positive curvature; if you go far

enough in one direction, you will never get to the edge but you will eventually return to

your starting point. An infinitely large sheet of paper is flat and, because it's infinite, also

edgeless. And a saddle that extends forever is considered edgeless and negatively

curved. It also turns out that any triangle you draw on the paper has angles that add up

to 180º, but the sphere's angles are always greater than 180º, and the saddle's always

less.

Same goes for the universe, but with one more dimension. According to Einstein, the

whole thing could be positively or negatively curved or flat (but don't try to imagine in

what direction it might be curved; it's quite impossible to visualize). "What the new

measurements tell us," says Turner, "is that the universe is in fact flat. Draw a triangle

that reaches all the way across the cosmos, and the angles will always add up to 180º."

According to Einstein, the universe's curvature is determined by the amount of matter

and energy it contains. The universe we evidently live in could have been flattened

purely by matter—but the new discoveries prove that ordinary matter and exotic

particles add up to only about 35% of what you would need. Ergo, the extra curvature

must come from some unseen energy—just about the amount, it turns out, suggested by

the supernova observations. "I was highly dubious about dark energy based only on

supernovas," says Princeton astrophysicist Edwin Turner (no relation to Michael, though

the two often refer to each other as "my evil twin"). "This makes me take dark energy

more seriously."

The flatness of the universe also means the theory of inflation has passed a key test.

Originally conceived around 1980 (in the course of elementary-particle, not

astronomical, research), the theory says the entire visible universe grew from a speck

far smaller than a proton to a nugget the size of a grapefruit, almost instantaneously,

when the whole thing was .000000000000000000000000000000000001 sec. old. This

turbo-expansion was driven by something like dark energy but a whole lot stronger.

What we call the universe, in short, came from almost nowhere in next to no time. Says

M.I.T.'s Alan Guth, a pioneer of inflation theory: "I call the universe the ultimate free

lunch." One of the consequences of inflation, predicted 20 years ago, was that the

universe must be flat—as it now turns out to be.

If these observations continue to hold up, astrophysicists can be pretty sure they have

assembled the full parts list for the cosmos at last: 5% ordinary matter, 35% exotic dark

matter and about 60% dark energy. They also have a pretty good idea of the universe's

future. All the matter put together doesn't have enough gravity to stop the expansion;

beyond that, the antigravity effect of dark energy is actually speeding up the expansion.

And because the amount of dark energy will grow as space gets bigger, its effect will

only increase.

THE FATE OF THE COSMOS

That means that the 100 billion or so galaxies we can now see though our telescopes

will zip out of range, one by one. Tens of billions of years from now, the Milky Way will be

the only galaxy we're directly aware of (other nearby galaxies, including the Large

Magellanic Cloud and the Andromeda galaxy, will have drifted into, and merged with, the

Milky Way).

By then the sun will have shrunk to a white dwarf, giving little light and even less heat to

whatever is left of Earth, and entered a long, lingering death that could last 100 trillion

years—or a thousand times longer than the cosmos has existed to date. The same will

happen to most other stars, although a few will end their lives as blazing supernovas.

Finally, though, all that will be left in the cosmos will be black holes, the burnt-out cinders

of stars and the dead husks of planets. The universe will be cold and black.

But that's not the end, according to University of Michigan astrophysicist Fred Adams.

An expert on the fate of the cosmos and co-author with Greg Laughlin of The Five Ages

of the Universe (Touchstone Books; 2000), Adams predicts that all this dead matter will

eventually collapse into black holes. By the time the universe is 1 trillion trillion trillion

trillion trillion trillion years old, the black holes themselves will disintegrate into stray

particles, which will bind loosely to form individual "atoms" larger than the size of today's

universe. Eventually, even these will decay, leaving a featureless, infinitely large void.

And that will be that—unless, of course, whatever inconceivable event that launched the

original Big Bang should recur, and the ultimate free lunch is served once more.

Astronomers and physicists are a cautious crew, and they insist that the mind-bending

discoveries about dark matter, dark energy and the flatness of space-time must be

confirmed before they are accepted without reservation. "We're really living

dangerously," says Chicago's Turner. "We've got this absurd, wonderful picture of the

universe, and now we've got to test it." There could be surprises to come: an

Einstein-style cosmological constant, for example, is the leading candidate for dark

energy, but it could in principle be something subtly different—a force that could even

change directions someday, to reinforce rather than oppose gravity.

In any case, new tests of these bizarre ideas will not be too long in coming. Next week a

satellite will launch from Cape Canaveral to make the most sensitive observations ever

of the cosmic background radiation. Supernova watchers, meanwhile, are lobbying nasa

for their own dedicated telescope so they won't have to queue up for time on the badly

oversubscribed Hubble. And lower-tech telescopes and microwave detectors, both on

the ground and lofted into the air aboard balloons, will continue to refine their own

measurements. If the latest results do hold up, some of the most important questions in

cosmology—how old the universe is, what it's made of and how it will end—will have

been answered, only about 70 years after they were first posed. By the time the final

chapter of cosmic history is written—further in the future than our minds can

grasp—humanity, and perhaps even biology, will long since have vanished. Yet it's

conceivable that consciousness will survive, perhaps in the form of a disembodied digital

intelligence. If so, then someone may still be around to note that the universe, once

ablaze with the light of uncountable stars, has become an unimaginably vast, cold, dark

and profoundly lonely place.

BIG BANG

About 15 billion years

ago, the universe

bursts into existence

in the Big Bang,

which gives birth to

space, time and all

the matter and energy

the universe will ever

hold

INFLATION ERA

The universe undergoes a

brief, explosive period of

inflation, growing from

smaller than an atom to the

size of a grapefruit. The

inflationary expansion stops

when the force driving it is

transformed into matter and

energy as we know them

RADIATION-DOMINATED ERA

Most of the energy is in the form of

electromagnetic radiation‹visible light, X

rays, radio waves and ultraviolet rays.

Quarks clump into protons and neutrons,

which later combine to make the nuclei

of all atoms. The lightest nuclei‹helium,

deuterium and lithium‹are forged in the

first three minutes of cosmic history

STELLIFEROUS ERA

Electrons combine with existing

nuclei to form atoms, mostly

hydrogen and helium. This raw

material condenses into the first

generation of stars during the

first billion years. The galaxies

also take shape during this

window of time. Our sun and

solar system were formed 4.6

billion years ago, and the first

life-forms appeared on Earth a

surprisingly short time

afterward. Modern humans

show up only 100,000 years

before the present. Earth

should remain habitable for

another few billion years

DEGENERATE ERA

This era extends to 10 trillion

trillion trillion years after the Big

Bang. Planets detach from

stars; stars and planets

evaporate from galaxies. Most

of the ordinary matter in the

universe is locked up in

degenerate stellar

remnants‹dead stars that have

withered into white dwarfs or

blown up and collapsed into

neutron stars and black holes.

Eventually, over spans of time

greatly exceeding the current

age of the universe, the

protons themselves decay

BLACK-HOLE ERA

This era extends to 10,000

trillion trillion trillion trillion

trillion trillion trillion trillion

years after the Big Bang.

After the epoch of proton

decay, the only large objects

remaining are black holes,

which eventually evaporate

into photons and other types

of radiation

DARK ERA

Now only waste products

remain: mostly photons,

neutrinos, electrons and

positrons, wandering through

a universe bigger than the

mind can conceive.

Occasionally, electrons and

positrons meet and form

"atoms" larger than the visible

universe is today. From here

into the infinite future, the

universe remains cold, dark

and dismal

The End of the Universe

John Baez

July 26, 2000

It's interesting to ponder the end of the universe. 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. They'll either become either black dwarfs, neutron stars, or black holes. 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.

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 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 1066 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 x 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 1066 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.

References

Many of the figures here are taken from table 10.2 in this book:

John D. Barrow and Frank J. Tipler, The Anthropic Cosmological Principle, Oxford U. Press, Oxford, 1988.

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 idea seems to be ruined by the presence of a nonzero cosmological constant and the resulting nonzero lower bound on the

temperature.

For more, try:

F. C. Adams and G. Laughlin, A dying universe: the long-term fate and evolution of astrophysical objects, Rev. Mod. Phys. 69

(1997), 337-372. (See also their Sky & Telescope article, Aug. 1998, and their book Five Ages of the Universe, 1999.)

L. M. Krauss and G. D. Starkman, Life, the universe, and nothing: life and death in an ever-expanding universe Astrophys. J.

(2000) 531, 22-30. (See also their Scientific American article, Nov. 1999.)

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:

Neal Dalal and Kim Griest, Black holes must die, preprint available as .

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.

The sun's not eternal. That's why there's the blues. - Allen Ginsberg

baez@math.ucr.edu

© 2000 John Baez

home

TIME April 10, 2000

How Will the Universe End? (with a bang or a whimper?)

by TIMOTHY FERRIS

The fate of the cosmos is not fiery cataclysm,

say the latest telescopic observations, but a

gradual descent into eternal, frigid darkness.

We Earthlings are newcomers to cosmology, the study of the universe as a whole, and there is no cosmological questions about which

we have more to learn than the riddle of where it's all ultimately headed. But we have glimpsed at least a few clues to cosmic destiny,

some of them hopeful and others bleak.

The good news is that we're not going to be evicted. The universe is likely to remain hospitable to life for at least an additional 100

billion years. That's 20 times as long as the earth has existed, and 5 million times as long as Homo sapiens has lasted so far. If we're

not around to shoot off fireworks on New Year's Eve of the year 100,000,000,000, it won't be the universe's fault.

The bad news is that nothing lasts forever. The universe may not disappear, but as time goes by it may get increasingly

uncomfortable, and eventually become unlivable. Calculating how and when this will happen is a genuinely dismal science, but not

without a certain grim fascination. The classic Big Bang theory, refined over the decades since the astronomer Edwin Hubble

discovered the expanding universe in 1929, suggests that cosmic destiny will be decided through a tug-of-war between two opposing

forces. One is the expansion of space, which for more than 1- billion years has been carrying galaxies ever farther apart from one

another. The other is the mutual gravitational force apart from one another. The other is the mutual gravitational force exerted by

those galaxies and all the other stuff in the universe: it acts as a brake, slowing down the expansion rate.

In this simple picture, if the gravitational force is strong enough to bring expansion to a halt, the universe is destined to collapse,

ultimately dissolving into a fireball- a Big Crunch that amounts to the Big Bang run in reverse. If it's not, and expansion wins out, then

the universe will eventually grow unpleasantly dark and cold. Starts produce energy by fusing light atomic nuclei, mainly hydrogen

and helium, into heavier ones. When the hydrogen and helium run low, old stars will sputter out without any new ones to take their

place, and the universe will gradually fade to black. Such were the gloomy alternatives the Robert Front wrote about after being

briefed on the theory of the cosmic endgame by the astronomer Harlow Shapley:

Some say the world will end in fire,

Some say in ice...

I think I know enough of hate

To know that for destruction ice

Is also great

And would suffice.

Either fate looks like curtains for life. If the end comes in fire, the Big crunch would melt down everything, even subatomic particles.

If, on the other hand, the universe winds up cold and dark, life might hang on for a long time - say, by extracting gravitational energy

from black holes. But trying to make a living once everything has subsided to pretty much the same temperature - a tad above

absolute zero - is like trying to run a water mill on dead-still pond.

Our ultimate fate, though, remains in doubt, in part because the jury is still out on whether the expansion or gravity will triumph in the

end. Most observations point toward the former, but many uncertainties persist. One is the galling "dark matter" issue. Studies of

how galaxies are moving around indicate that there's lots of extra gravity out there, suggesting that the stars and nebulae we can see

constitute only 1% to 10% of the matter in the universe. The rest is invisible; it emits no light. Nobody yet knows what this dark

matter is. One possibility is that it's made of WIMP - weakly interacting massive particles. Until the dark matter is identified and

tallied, predicting the future of the universe on the basis of what we can see will be as uncertain as trying to predict an election by

polling a few golfers down at the country club.

Meanwhile, ironists and fatalists draw austere satisfaction from the fire-or-ice scenario, which reflects the quintessential human

perception that nobody gets out of life alive. And that's just what makes me suspicious of it. The great lesson of scientific cosmology

is that the universe does not usually conform to our time-honored ways of thinking - that to understand it, we need to think in new

ways. Integral to modern cosmology are mind-bending 20th century concepts like Einstein's curved space, Heisenberg's uncertainty

principle and the realization that exotic subatomic particles sail through our bodies by the trillions without laying a glove on us, and I

see no reason to suppose that doors won't open onto even stranger notions in the century to come. So perhaps we can glimpse a few

shafts of light, shining under doors as yet unopened, that promise to refine our predictions of cosmic destiny.

One unknown has to do with inflation - the theory that the universe began as a bubble of empty space that initially expanded at a

velocity much faster than that of light. Cosmologists take inflation seriously because it resolves problems that bedeviled older versions

of the Big Bang, but inflation also has implications for the study of cosmic destiny. Among them is that the force that drove the

inflationary spasm, sometimes tagged with the Greek letter lambda after its designation in Einstein's general relativity equations, might

not have subsided altogether back when the inflationary hiccup ended. Instead, it might still be there, lurking in empty space and

urging expansion along, like an usher politely shooing playgoers back into the theater at intermission's end. Some observations of

exploding stars in distant galaxies suggest the presence of just such an ongoing inflationary impulse. If so, the tug-of-war over the

future of the universe involves not only expansion and gravitational braking but also the subtle turbocharging of lingering inflation,

which acts to keep the universe expanding indefinitely.

Perhaps the most intriguing unknown, however, concerns the cosmic role played by intelligent life itself. As the physicist Freeman

Dyson notes, "It is impossible to calculate in detail the long-range future of the universe without including the effects of life and

intelligence." Much of the earth has been transformed, for better and worse, by the presence here of an intelligent species capable of

manipulating its environment for its own benefit.

Similarly, advanced civilizations in the far future might be able to melt down stars and even entire galaxies to make gigantic campfires,

or otherwise tilt the long-term odds in the favor. Life in the waning cosmic twilight might jejune, but it could last a long time.

Consider the marshaled resources of all the natural and artificial intelligences in the observable universe over the next, say, trillion

years. Which would you bet on to prevail - that level of smarts or a claims, based on 19th century thermodynamics, that they're

doomed?

So let's stay tuned, heeding the words of Einstein, who wrote to a child anxious about the fate of the world, "As for the question of

the end of it I advise: Wait and see!"



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