Three Roads To Quantum Gravity

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THREE ROADS TO QUANTUM GRAVITY
any given observer can only see a fixed amount of information
given by the N-bound.
In this circumstance, the traditional formulations of quantum
theory fail because they assume that an observer can,
given enough time, see anything that happens in the universe.
It seems to me that there is then no alternative but to
adopt the program I described in Chapter 3, which was proposed
by Fotini Markopoulou—to reformulate physics in
terms of only what observers inside the universe can actually
see. As a result, Markopoulou’s proposal has been getting
more attention from people on both sides of the string theory/
loop quantum gravity divide.
So far there is no proposal for how to reformulate string
theory in such terms. One possible step toward such a formulation
is Andrew Strominger’s new proposal, which applies
the holographic principle to spacetimes, with a positive
cosmological constant.
At the same time, loop quantum gravity is clearly compatible
with such a reformulation of quantum theory—it is already
background-independent and expressed in a language
in which the causal structure exists all the way down to the
Planck scale.
In fact, Bank’s N-bound is easy to derive in loop quantum
gravity, using the same methods that led to the description of
the quantum states on black hole horizons. Moreover, in
loop quantum gravity there is a complete description of a
quantum universe filled with nothing but a positive cosmological
constant. This is given by a certain mathematical expression,
discovered by the Japanese physicist Hideo Kodama.
Using Kodama’s result, we are able to answer
previously unsolvable questions, such as exactly how the solutions
of Einstein’s general relativity theory emerge from
the quantum theory. Thus, at least in our present stage of
knowledge, while string theory has trouble incorporating the
apparently observed positive value of the cosmological constant,
loop quantum gravity seems to prefer that case.
Beyond this, there has continued to be steady progress in
loop quantum gravity. The work of two young physicists,