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The term beable was proposed in (Bell 75) as a replacement in quantum physics of the traditional term observable. While the latter is typically given a precise mathematical meaning which does express the way in which the physical system may be, the word “observable” alludes to the complicated and subtle issue of something (a quantum measurement device) or even somebody (a concious experimentor) “observing” these ways of the system to be. The point of the term “beable” is to help conceptually cleanly separate the being of quantum systems from whatever it means to observe them.

In (Bell 75), to further justify this, recourse is made to Niels Bohr‘s expressed view that whatever quantum physics really is, it must be possible to communicate statements about it in terms of classical logic. Hence beables mostly refer to sets of commuting operators, classical contexts. This same argument was much later used to motivate Bohr toposes. In this context, the Kochen-Specker theorem proves the absence of certain global sections (Proposition 1). Halvorson and Clifton define a beable subalgebra (p9) with respect to a given state ρ\rho. We first consider the important special case of the definite algebra D ρD_\rho for a state ρ\rho. This is the subalgebra on which ρ\rho is dispersion free. This gives, for each commutative subalgebra of CD ρC\subset D_\rho, a choice of an element of its spectrum. These choices are compatible. Hence, we obtain not a global section, but only local section. The general notion of beable subalgebra only requires ρ\rho to be a mixture of dispersion-free states.

In practice of theoretical physics most everytime one writes “observable” it should, by this logic, rather be “beable”. While this might be reasonable, as a convention of conversation it has not been picked up.

quantum probability theoryobservables and states


The original discussion of beables in the context of causal locality in AQFT is in

and further in

A survey is in

A more technical development can be found here:

Discussion in the context of interpretation of quantum mechanics includes

  • Yuichiro Kitajima, Interpretations of Quantum Mechanics in Terms of Beable Algebras, (pdf)

Last revised on February 8, 2020 at 06:04:15. See the history of this page for a list of all contributions to it.