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CYMM writes:

Do you have any links to tweaking the

individual axioms of axiomatic QM?

I'm especially interested in tweaking

the axioms involving the integral of

the intensity of Psi.... you know

the Born stuff and such...

Lucien Hardy

Quantum Theory From Five Reasonable Axioms

http://xxx.lanl.gov/abs/quant-ph/0101012

The usual formulation of quantum theory is based

on rather obscure axioms (employing complex Hilbert

spaces, Hermitean operators, and the trace rule for

calculating probabilities). In this paper it is shown

that quantum theory can be derived from five very

reasonable axioms. The first four of these are

obviously consistent with both quantum theory and

classical probability theory. Axiom 5 (which requires

that there exists continuous and reversible

transformations between pure states) rules out

classical probability theory. If Axiom 5 is

substituted by another axiom, Axiom 5C, then we

obtain classical probability theory instead.

This work provides insight into the reasons quantum

theory is the way it is. For example, it explains

the need for complex numbers and where the trace

formula comes from. We also gain insight into

the relationship between quantum theory and

classical probability theory.

Ariel Caticha

Consistency, Amplitudes and Probabilities

in Quantum Theory

http://xxx.lanl.gov/abs/quant-ph/9804012

Quantum theory is formulated as the only consistent

way to manipulate probability amplitudes. The crucial

ingredient is a consistency constraint: if there are

two different ways to compute an amplitude the two

answers must agree. This constraint is expressed

in the form of functional equations the solution

of which leads to the usual sum and product rules

for amplitudes. A consequence is that the Schrodinger

equation must be linear: non-linear variants of quantum

mechanics are inconsistent. The physical interpretation

of the theory is given in terms of a single natural rule.

This rule, which does not itself involve probabilities,

is used to obtain a proof of Born's statistical postulate.

Thus, consistency leads to indeterminism.

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