Seattle,
the city where I live, teach, and do physics research, is the home of Paul
Allen's new Science Fiction Museum (SFM), located in the Experience Music
Project building at Seattle Center, in the shadow of the Space Needle.The SFM is well worth a visit, offering a fascinating display of
collected TV and movie props (e.g., Captain Kirk's Chair from Star
Trek), SF memorabilia, and treasured books and manuscripts from the
classic works of science fiction.In
early December, 2005, Stephen Hawking was on a fund-raising tour in celebration
of the 800th anniversary of the founding of Cambridge
University, where he holds the same Chair once occupied by Isaac Newton.Hawking paid a visit to the West Coast during this tour, and he took the
opportunity to make a virtual appearance (by closed-circuit TV) to a gathering
at the SFM (including my wife and me) in order to present to the SF Museum the
manuscript of a 1976 physics paper which, as he put it, had just entered the
realm of science fiction (because it turns out to be wrong).
Hawking's
1976 paper, "Breakdown of predictability in gravitational collapse",
describes a physics paradox, the apparent loss of information in black holes.Basically, information can be considered to be a form of entropy, and as
such is subject to the 2nd Law of Thermodynamics.In classical physics it is expected that information can be scrambled,
but not really destroyed.As Hawking
puts it, if you burned an encyclopedia, you could in principle recover the
information it contained from a detailed study of the resulting light, smoke and
ashes.
However,
suppose you dropped the same encyclopedia down a small black hole, and the black
hole subsequently "evaporated" through the emission of Hawking radiation.In that situation, where did the information go?The evaporating black hole emits radiation with a "thermal" spectrum
of frequencies (i.e., the same spectrum as that the radiation would have if
radiated from a hot object), and it therefore contains no information passed to
it from the interior of the black hole.Ultimately,
a black hole will evaporate away all
of its mass-energy and disappear, so the information that had previously passed
into the black hole has apparently vanished without a trace.This is the information paradox described in Hawking's 1976 paper.
The
initial publication of this work created quite a stir in the theoretical physics
community.Whole physics conferences
were devoted to the subject, at which theorists gave several days of talks and
speculated on whether or not information could vanish intoa black hole.At the time,
Hawking suggested that the interior of the black hole might spawn one or more
"baby universes" containing the missing information, and that it might
therefore be possible to use a black hole as a vehicle for travel from our
universe to other universes.
Some
distinguished theorists doubted Hawking's conclusion that information could
vanish without a trace.In
particular, in1997, Hawking and CalTech theorist Kip Thorne made a bet about the
predicted information loss with CalTech physicist John Preskill, who works in
quantum computation.Here's the
text of their wager:
Whereas
Stephen Hawking and Kip Thorne firmly believe that information swallowed by a
black hole is forever hidden from the outside universe, and can never be
revealed even as the black hole evaporates and completely disappears,
And
whereas John Preskill firmly believes that a mechanism for the information to be
released by the evaporating black hole must and will be found in the correct
theory of quantum gravity,
Therefore
Preskill offers, and Hawking/Thorne accept, a wager that:
When
an initial pure quantum state undergoes gravitational collapse to form a black
hole, the final state at the end of black hole evaporation will always be a pure
quantum state.
The
loser(s) will reward the winner(s) with an encyclopedia of the winner's choice,
from which information can be recovered at will.
Stephen
W.Hawking, Kip S.Thorne, John P. Preskill
Pasadena,
California
6
February 1997
Hawking's
new paper on this subject, "Information loss in Black Holes", was released
as a revised preprint on September 15, 2005.It constitutes a de-facto
retraction of the 1976 paper.In it,
Hawking builds on work from string theory, which has shown a "duality" (a
1:1 mapping) between conformal field theory (in which information is definitely
conserved because of a property called unitarity) and string theory (which
should include quantum gravity) in "anti de Sitter space" (symmetric space
with constant negative curvature) at very large distances from gravitating
objects.This connection is
interpreted as telling us that if we could only do quantum gravity properly, we
would find that no information is lost in black holes.
In
his calculations, Hawking pulls several techniques from his bag of tricks, using
scattering theory, imaginary time, and semi-classical constraints.Rather than entering the strong-field mess created by quantum gravity, he
considers an observer standing off aloofly at infinity, sending a flood of
particles and radiation into the heart of the system (where they may or may not
form a black hole that evaporates) and observing the particles and radiation
that come back to him.In tracking
the particles and radiation, Hawking replaces the time variable T by iT, where i
is the square root of -1, thereby changing normal 3+1 dimensional space-time
into "timeless" 4 dimensional space.In
principle, he should then sum over all
of the paths that all of the particles might take in this 4-D space, sum the
results, and transform back to 3+1 dimensional space-time.Instead, he sums only those paths that are close to semi-classical
solutions of the same system, while assuming that contributions from the other
more complicated paths can be neglected.
Hawking
focuses on two scenarios: (1) the input particles have formed a static black
hole, and (2) no black hole is formed, and he demonstrates that it is not
possible to determine from the returning particles and radiation which of these
scenarios actually happened.He
further shows that information is not lost in scenario 2 (not surprising), and
that in scenario 1 has differences that decay away exponentially as the
particles return to the observer at infinity.
His
conclusion from these mathematical gymnastics is that (a) no information is
lost, and (b) that the price of this result is that it is not possible for the
observer at infinity to tell whether a black hole is formed or not.In the conclusion of the paper, he suggests that the information
"tunnels" out of the black hole and appears as subtle correlations between
the photons of the emitted Hawking radiation.Hawking's point seems to be that if there is an uncertainty about
whether or not the black hole exists, this uncertainty leaves room for the
survival of the information.This
might be considered to be a new uncertainty principle, applicable to the unknown
formalism of quantum gravity.
Hawking
considers that he has now resolved the paradox, and that he has lost the bet.On July 21, 2004 at the 17th International Conference on
General Relativity and Gravitation, held in
Dublin
,
Ireland
, Hawking presented a copy of the Encyclopedia
of Baseball to John Preskill in payment of his end of the wager.To my knowledge, Kip Thorne has not yet conceded his end of the wager.
How
has the physics community received Hawking's new paper?It's difficult for me to tell.Following
the initial release of the preprint there have been 16 new papers referring to
the work.None of them is
particularly critical of Hawking's work, but neither do they directly build on
that work.There have also been two
blog-type extended internet comments posted by physicists.Neither is devastatingly critical, but both raise unanswered questions
about what Hawking actually did.I
would conclude that Hawking may have answered his own questions about
information loss in black holes, but he has not satisfied the physics community
as a whole.In particular, the
actual form taken by the emerging information remains very vague and ephemeral,
even if Hawking's mathematics, taken at face value, insists that the
information is actually there.
What
are the SF implications of this work?First, the widely used SF gimmick of entering another universe through a
black hole seems to have had the rug pulled out from under it.Further, the spawning of baby universes by black holes, which has been
used in some SF, seems to have received a dose of strong contraceptive.
It's
perhaps nice to know that the fundamental laws of physics like the 2nd
Law of Thermodynamics work even for black holes, and that information cannot be
irretrievably lost.But so far, not
much of SF depends on either of those ideas.
John G. Cramer's 2016 nonfiction book (Amazon gives it 5 stars) describing his transactional
interpretation of quantum mechanics, The Quantum Handshake -
Entanglement, Nonlocality, and Transactions, (Springer, January-2016) is
available online as a hardcover or eBook at: http://www.springer.com/gp/book/9783319246406
or https://www.amazon.com/dp/3319246402.
Alternate View Columns Online: Electronic reprints of 212 or more
"The Alternate View" columns by John G. Cramer published in Analog
between 1984 and the present are currently available online at: http://www.npl.washington.edu/av
.
References:
Hawking's 1976 paper:
"Breakdown of predictability
in gravitational collapse", S. W. Hawking, Physical Review D14, 2460-2473 (1976).
