Page 34 - Nature Of Space And Time
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more fundemental theory. This idea is anathema to most particle physicists who are a
very conservative lot and want to make everything like Yang-Mills theory. They agree that
the radiation from black holes seems to be thermal and independent of how the hole was
formed if the hole is large compared to the Planck length. But they would claim that when
the black hole loses mass and gets down to the Planck size, quantum general relativity will
break down and all bets will be o . However, I shall describe a thought experiment with
black holes in which information seems to be lost yet the curvature outside the horizons
always remains small.
It has been known for some time that one can create pairs of positively and negatively
charged particles in a strong electric eld. One way of looking at this is to note that in
at Euclidean space a particle of charge q such as an electron would move in a circle in a
uniform electric eld E. One can analytically continue this motion from the imaginary time
to real time t. One gets a pair of positively and negatively charged particles accelerating
away from each other pulled apart by the electric eld.
world line world line
of positron of electron
t = 0
Minkowski space
Electric Field
world line of electron
t = 0
Euclidean space
The process of pair creation is described by chopping the two diagrams in half along
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