Three Roads To Quantum Gravity

AREA AND INFORMATION
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physics are expressed as limitations on what we can know.
Einstein's principle of relativity (which was an extension of a
principle of Galileo's) says that we cannot do any experiment
that would distinguish being at rest from moving at a constant
velocity. Heisenberg's uncertainty principle tells us that we
cannot know both the position and momentum of a particle to
arbitrary accuracy. This new limitation tells us there is an
absolute bound to the information available to us about what
is contained on the other side of a horizon. It is known as
Bekenstein's bound, as it was discussed in papers Jacob
Bekenstein wrote in the 1970s shortly after he discovered the
entropy of black holes.
It is curious that, despite everyone who has worked on
quantum gravity having been aware of this result, few seem to
have taken it seriously for the twenty years following the
publication of Bekenstein's papers. Although the arguments
he used were simple, Jacob Bekenstein was far ahead of his
time. The idea that there is an absolute limit to information
which requires each region of space to contain at most a
certain ®nite amount of information was just too shocking for
us to assimilate at the time. There is no way to reconcile this
with the view that space is continuous, for that implies that
each ®nite volume can contain an in®nite amount of information.
Before Bekenstein's bound could be taken seriously,
people had to discover other, independent reasons why space
should have a discrete, atomic structure. To do this we had to
learn to do physics at the scale of the smallest possible things.