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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