Re: Question on quantum computing and many-worlds interpretations of Quantum Mechanics

  I agree that there might be theological issues to worry about in a
many-worlds interpretation of quantum mechanics.

  But I want to focus just on a scientific issue.

  Someone might have told you:

> The success of a quantum device therefore
> necessitates the existence of parallel universes ( multiverses ) in order
> for all the computations to be carried out in parallel.

  But that is false.
  Absolutely, positively, false.
  A successful quantum computer will not in any way necessitate the
existence of parallel universes or the Everett "many worlds"
interpretation of quantum mechanics.
  I'd stake my Ph.D. in atomic physics on it.

  There are many different interpretations of quantum mechanics. Four
general categories are (1) standard "Copenhagen" interpretations; (2)
Everett-type "many worlds" interpretations; (3) "non-local"
hidden-variable interpretations; (4) "local" hidden variable
interpretations (i.e. hidden variable interpretations which don't allow
changes in the wave function to propagate faster than the speed of light).
  The "Bell Inequality" is a famous theoretical prediction which describes
and experiment in which "local hidden variable" interpretations make a
different prediction for the outcome of an experiment than the other three
interpretations. The experiment has been done, and local hidden variable
interpretations have been shown to be inconsistent with data.

  There is, as of now, NO experimental or theoretical observational way to
distinguish between the other three interpretations (Copenhagen
interpretations, many-worlds interpretations, and non-local
hidden-variable interpretations). All three classes of interpretations
make identical predictions for how quantum computers should work.

  Quantum computers work by utilizing cleverly designed Hamiltonians in
_this_ universe, not by using anything from other universes. (In
classical or in quantum mechanics, a Hamiltonian is an equation or a
functional operator which describes the energy of the system in terms of
variables such as position, momentum, angular momentum, etc.)

  Here's an analogy. A few decades ago, people built some sophisticated
"analog computers" by combining resistors, capacitors, inductors, and
transitors in clever circuits. Analog computers are not as versitile as
digital computers. They cannot solve _any_ sort of mathematical problem
the way digitical computers can. But there there are certain classes of
problems (e.g. second-order differential equations) which analog computers
can solve much more quickly than digital computers. The electrons in
analog computers don't do anything special -- they just obey the same old
laws of motion that they always do in any circuit. But the circuit is
cleverly designed so that, when the electrons move according to their
regular old laws of motion, their behavior matches the solution to a
particular mathematical problem.

  In the same way, quantum computers are much less versitile than ordinary
digital computers. However, there are certain very restricted types of
problems on which they (like analog computers) out-perform digital
computers. Electrons in a quantum computer aren't doing anything weird
(or perhaps I should say, not doing anything weirder than they do all the
time in any ordinary atom or molecule). However, in a quantum
computer, the clever designers set up the system so that when the
electrons (or photons) obey the same old ordinary laws of motion that they
always do, their behavior matches the solution to a particular
mathematical problem.

  When someone builds a clever classical-physics device such that its
mechanical or electrical behavior matches the solution to a tricky
computation problem, we don't feel any need to invoke parallel universes.
Nor should we. Nor is there any such need when someone builds a clever
quantum-physics device such that its behavior matches the solution to a
tricky computational problem.

  Someday, physicists might find a way to distinguish experimentally
betwen Copenhagen, many-worlds, non-local hidden variable, and other
interpretations of quantum mechanics.
  But we haven't yet.

Loren Haarsma
Received on Thu Mar 2 20:40:30 2006