biorthogonal

Van Fraassen's possible decompositions are restricted to one singled out by a mathematical criterion (related to the so-called biorthogonal decomposition theorem), and a dynamical picture is explicitly sought

...anything but love... 2009

One might well ask: Why begin with the biorthogonal decomposition (or more generally, the spectral decomposition) in the first place?

Modal Interpretations of Quantum Mechanics Dickson, Michael 2007

Richard Healey (1989) was also among the first to make use of the biorthogonal decomposition theorem, taking Kochen's ideas in a somewhat different direction.

Modal Interpretations of Quantum Mechanics Dickson, Michael 2007

We could arrive at properties for A by applying the biorthogonal decomposition theorem to the two-component system

Modal Interpretations of Quantum Mechanics Dickson, Michael 2007

Healey's intuition about the way a modal interpretation based on the biorthogonal decomposition theorem would be applied to, say, an EPR experiment is to implement the idea that an EPR pair possesses a 'holistic' property; this can then explain why the apparatus on one side of the experiment acquires a property that is correlated to the result on the other side.

Modal Interpretations of Quantum Mechanics Dickson, Michael 2007

Earlier we suggested that the spectral-decomposition (and the biorthogonal-decomposition) modal interpretations solve the measurement problem in a particularly direct way: at the end of a von Neumann measurement, the compound system (apparatus plus measured system) is in a state such that the possible properties picked out by these modal interpretations are exactly the pointer states of the apparatus.

Modal Interpretations of Quantum Mechanics Dickson, Michael 2007

We now see in the biorthogonal decomposition theorem a way to provide a rule that is restrictive: define as the possible value states (for each component system of a composite system) the elements of the basis picked out by the theorem.

Modal Interpretations of Quantum Mechanics Dickson, Michael 2007

Dieks first notes that the density operator (reduced state) of a single component of a two-component system has for its spectral resolution exactly the projections spanned by the basis elements picked out by the biorthogonal decomposition theorem, in the case when the decomposition is unique.

Modal Interpretations of Quantum Mechanics Dickson, Michael 2007

This new proposal matches the old one in cases where the old one applies, and generalizes by fixing the definite-valued quantities in terms of multi-dimensional projectors when the biorthogonal decomposition is degenerate.

Modal Interpretations of Quantum Mechanics Dickson, Michael 2007

Should one ascribe the property P&Q to A&B, or should A&B have some property that it gets from applying the biorthogonal decomposition to

Modal Interpretations of Quantum Mechanics Dickson, Michael 2007