A brief History of Time: From Big Bang to Black Holes

The information paradox

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One reason for my excitement over LIGO’s gravitational wave detections is
that the area theorem is directly linked to a major controversy surrounding
black holes known as the information paradox. Information is a sacred thing
in physics; if we are able to describe the entire state of the universe today
with a certain amount of information (the positions and speeds of all the
particles, for example), we expect to need the same amount of information
to describe the entire state of the universe tomorrow. This assumption
underlies our ability to make scientific predictions, and is quietly built into
Newton’s and Einstein’s work; it’s even part of quantum mechanics. One
might therefore hope it will remain true when we formulate a final theory of
quantum gravity.
When a black hole is formed, information about individual objects that
have fallen in (their shapes, sizes, and chemical compositions, for example)
becomes obscured. The only information about what formed it, is its total
mass, its spin and its possible electric charge. This is the so-called ‘no-hair’
theorem.This is not too much of a problem, since the objects can just be
regarded as hidden away rather than entirely lost. But if, as I showed in a
letter published in Nature in 1974, quantum mechanics allows black holes
to lose their mass and disappear (p.119), there is a difficulty. After the black
hole is gone, what has then happened to the information?
When I wrote A Brief History of Time, I believed that the information
concerning what had fallen into the black hole was truly lost, perhaps
residing in a separate universe hived off from our own. In 1997 I even bet
Caltech physics professor John Preskill an encyclopedia of his choice that I
was right.
It was only later, in 2004, that I realized I had been wrong, after
considering what happens to black holes after an infinite amount of time
has passed. The amount of information at the start and the end was the
same! When I conceded, John asked for an encyclopedia of baseball which
I duly gave him. (My attempt to persuade him that cricket is more
interesting was unsuccessful.)
My change of opinion started by considering one of the most remarkable
discoveries to arise from string theory: there appears to be an exact
correspondence between the behavior of gravity and an obscure branch of
physics known as conformal field theory. The details of the link don’t
matter for our purposes. All one needs to know is that anything described
by conformal field theory – now including black holes – demonstrably

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preserves information. Very recently, it was realized that the ‘no-hair’
theorem was formulated in a way that was too restrictive. There is also
supertranslation and superrotation hair. It seems that the information about
material that formed the black hole remains preserved on the horizon as
supertranslation and superrotation hair. We do not yet know if this is
enough information to save the principles of quantum mechanics. Neither
do we yet know how the information might emerge from the black hole.
Even harder questions can be asked then about the fundamental nature of
the singularities of spacetime that general relativity predicts must exist
inside black holes.
Of course, this abstract argument doesn’t tell us exactly how the lost
information manages to leak back out of a black hole in practice.
One must be clear that, when the information finally makes its way out of
the black-hole-like region, it will emerge in a very hard-to-interpret format.
It is like burning a book. Information is not technically lost, if one keeps the
ashes and the smoke – which makes me think again about the baseball
encyclopedia I gave John Preskill.
I should perhaps have given him its burnt remains instead.
Outlook
In the twenty years since the last revision of this book, progress in
cosmology has been rapid. Some of the developments, such as the detection
of gravitational waves and the steady improvement in our understanding of
the early universe, were anticipated; others, like dark energy and the
accelerating universe, less so.
Perhaps the most striking trend is one that many find uncomfortable: the
no boundary proposal and eternal inflation point increasingly strongly to the
idea that our universe is just one of many. Copernicus first suggested in the
sixteenth century that we are not placed at the center of even our own
universe (p. 4); yet we are still struggling to accept just how vanishingly
small a fragment of reality our familiar world represents. It may not be
much longer before the evidence for a multiverse becomes overwhelming.
Despite the vastness of the multiverse, there is a sense in which we
remain significant: we can still be proud to be part of a species that is
working all this out. With that in mind, the coming years should be just as
exciting as the last twenty.

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GLOSSARY