# nLab beable

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## Surveys, textbooks and lecture notes

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• Axiomatizations

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• Tools

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• Structural phenomena

• Types of quantum field thories

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• examples

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# Contents

## Idea

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 $\rho$. We first consider the important special case of the definite algebra $D_\rho$ for a state $\rho$. This is the subalgebra on which $\rho$ is dispersion free. This gives, for each commutative subalgebra of $C\subset D_\rho$, 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 $\rho$ 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.

## References

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 January 8, 2014 at 22:36:17. See the history of this page for a list of all contributions to it.