### Instability, Isolation, and the Tridecompositional Uniqueness
Theorem.

#### quant-ph/0412013

** Abstract ** The tridecompositional uniqueness theorem of Elby and Bub
(1994) shows that a wavefunction in a triple tensor product Hilbert space has
at most one decomposition into a sum of product wavefunctions with each set of
component wavefunctions linearly independent. I demonstrate that, in many
circumstances, the unique component wavefunctions and the coefficients in the
expansion are both hopelessly unstable, both under small changes in global
wavefunction and under small changes in global tensor product structure. In
my opinion, this means that the theorem cannot underlie law-like solutions to
the problems of the interpretation of quantum theory. I also provide examples
of circumstances in which there are open sets of wavefunctions containing no
states with various decompositions.

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#### Matthew J. Donald

#### The Cavendish Laboratory, JJ Thomson Avenue, Cambridge CB3 0HE, Great
Britain.

#### e-mail :
mjd1014@cam.ac.uk

#### home page:
http://people.bss.phy.cam.ac.uk/~mjd1014