Three Roads To Quantum Gravity

POSTSCRIPT 217
light, which is the speed of the least energetic photons. What
these developments imply is that Einstein’s insights must be
deepened to take into account the quantum structure of
space and time, just as Einstein deepened Descartes’s and
Galileo’s insights about the relativity of motion. It may be
time for us to add another layer of insight into our understanding
of what motion is.
Exactly how relativity is to be modified is a subject of hot
debate at the moment. Some people argue that special relativity
theory must be modified to account for the atomic
structure of spacetime predicted by loop quantum gravity.
According to loop quantum gravity, all observers see the
discrete structure of space below the planck length. This
seems to contradict relativity, which tells us that lengths
are measured differently by different observers—the famous
length contraction effect. One resolution is that special relativity
can be modified so that there is one length scale, or
one energy scale, that all observers agree on. Thus, while all
other lengths will be measured differently by different observers,
for the special case of the Planck length all observers
will agree. There is still complete relativity of motion, as
posited by Galileo and Einstein. But one consequence is
that the speed of light can pick up a small dependence on
energy.
I heard about the possibility of such a new twist on relativity
from several people at once: Giovanni Amelino-
Camelia, Jurek Kowalski-Glikman, and Joao Magueijo. At
first I told them this was the craziest thing I’d ever heard, but
Joao, who was my colleague in London at the time, was patient
enough to keep coming back many times, until I finally
got it. Since then I’ve seen other people go through this
process. It is interesting to observe one of Thomas Kuhn’s famous
paradigm shifts in action.
Another hot topic is whether the possible variation of the
speed of light with energy has consequences for our understanding
of the history of the universe. Suppose that the
speed of light increases with energy. (This is not the only
possibility, but it is so far allowed by the observations we