Summary: Is Quantum Mechanics An Island In Theoryspace?
SCOTT AARONSON
University of California, Berkeley CA USA
aaronson@cs.berkeley.edu
This paper investigates what happens if we change quantum mechanics in several
ways. The main results are as follows. First, if we replace the 2­norm by some
other p­norm, then there are no nontrivial norm­preserving linear maps. Second, if
we relax the demand that norm be preserved, we end up with a theory that allows
rapid solution of hard computational problems known as PP­complete problems (as
well as superluminal signalling). And third, if we restrict amplitudes to be real, we
run into a di#culty much simpler than the usual one based on parameter­counting
of mixed states.
1 Introduction
``It is striking that it has so far not been possible to find a logically consistent theory that is close
to quantum mechanics, other than quantum mechanics itself.'' ---Steven Weinberg, Dreams of a
Final Theory 13
The title of this paper should be self­explanatory, but if not: ``theoryspace'' is the space of logically
conceivable physical theories, with two theories close to each other if they di#er in few respects. An
``island'' in theoryspace is a natural and interesting theory, whose neighbors are all somehow perverse or
degenerate. a The Standard Model isn't an island, because we don't know any compelling (non­anthropic)

Source: Aaronson, Scott - Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology (MIT)

Collections: Physics; Computer Technologies and Information Sciences