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.

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