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Is Quantum Mechanics An Island In Theoryspace? SCOTT AARONSON
 

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 2-norm by some
other p-norm, then there are no nontrivial norm-preserving 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 PP-complete problems (as
well as superluminal signalling). And third, if we restrict amplitudes to be real, we
run into a difficulty much simpler than the usual one based on parameter-counting
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 self-explanatory, but if not: "theoryspace" is the space of logically
conceivable physical theories, with two theories close to each other if they differ in few respects. An
"island" in theoryspace is a natural and interesting theory, whose neighbors are all somehow perverse or
degenerate.a

  

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

 

Collections: Physics; Computer Technologies and Information Sciences