Renowned
cosmologist Professor Stephen Hawking passed away in the early hours of March
14, news that has saddened us all. His scientific output was truly incredible
and his work in engaging the wider public in the complexities of the universe
will continue to inspire. His most famous formula, describing the entropy of a
black hole, might even adorn his tombstone.

He declared
his wishes for this in 2002, during a workshop on the future of theoretical
physics and cosmology held to mark his 60th birthday. The formula is the
centerpiece of our understanding of black holes and a crowning achievement for
Hawking, who worked on it with his colleague Jacob Bekenstein. It connects
important thermodynamical quantities such as entropy, represented by the
capital S, to physical properties of the black hole, namely its area, A.

The
remaining letters are constants of the universe; k is the Boltzmann constant, c
is the speed of light, h-bar is the reduced Planck constant, and G is the
universal gravitation constant. Entropy is described in school physics
textbooks as a measure of disorder within a macroscopic system. But it can also
be defined as the amount of information that you can pack into an object.

And this is
the crucial importance of the formula. The entropy of a black hole is
proportional to its surface area, not its volume. The surface of the black hole
is its event horizon, beyond which, nothing can escape. Understanding the
thermodynamics of black holes required the Cambridge physicist to apply quantum
mechanics to these incredibly dense objects, and this led to the proposal of
Hawking radiation. Black holes had entropy and a temperature.

Hawking
himself extended this work to a more general and far-reaching interpretation.
The whole universe could be seen as having a “cosmological event horizon”
suggesting that the universe as a whole has an entropy value and a specific
temperature. This idea was the base for the formulation of the holographic
principle, suggesting that all the information encoded in the universe can be
interpreted from the properties of a lower dimensional boundary.

There is
also another interesting parallel that makes Professor Hawking's wish even more
poignant. The first proposer of entropy was Austrian physicist Ludwig Boltzmann
and his tombstone bears the inscription of his own entropy formula. It seems
right that Hawking should have his own, too.

Hawking had
just recorded a cameo for a new radio version of Douglas Adams' Hitchhikers
Guide to the Galaxy, so as that other late, great visionary once wrote (sort
of): So long, Professor Hawkings, and thanks for all the fish.

É absolutamente fantástico Stephen Hawking ter feito esta ligação entre entropia de um buraco negro e informação. Também inferiu que os buracos negros perdem massa, através da evaporação de Hawking e podem desparecer, mas ao fim de uma infinidade de milénios.

ReplyDeleteE é impressionante o que a fórmula mostra: essa entropia é indescritivelmente gigantesca, pois é proporcional à área do buraco negro (que não costuma ter dimensões de um balãozinho...) X o cubo da velocidade da luz no vácuo que, além disso, ainda fica muito maior por ser dividida por um número extraordinariamente pequeno: 4x a constante de Dirac (cerca de 1,05 elevado a -34 J s, ou, usando outras unidades: 6,6 x 10 elevado a -16 eV s ), que ainda é multiplicado por um outro muito pequeno: G = 6,67 x 10 elevado a menos 11 m3 /kg s2

Curioso como a constante de Dirac, h barra, ou constante de Planck reduzida aparece, também, no princípio de incerteza de Heisenberg -- , que serviu para Hawking estudar, com Bekenstein e Zel'dovich a radiação de corpos negros, levando à presente fórmula da entropia dos buracos negros).