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- Thread starter Feeble Wonk
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Alternatively, there are also pairs of observables that are complementary, but not conjugate. As an example, it is not possible to prepare a spin-1/2 particle in a state where you will be able to predict the measurement outcomes of all its spin components with accuracy.

As an interesting side note, the list of all kinds of sets of complementary observables is not complete yet, even for simple systems. For example, for quantum systems of dimension 6 (say, a pair of particles; one spin-1/2 and one spin-1) it is an unsolved problem to find a complete set of complementary observables (also called "mutually unbiased" observables).

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Vanadium 50

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Fair enough. I was aware of the various forms position/momenta complimentarity. But I'd recently read a passage where Lee Smolin referred to aspects of time and space having a similar complementary relationship, and it got me thinking about the general concept.

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atyy

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A quantum theory is specified by (1) Hilbert space (2) Observables (3) Hamiltonian.

In specifying (2) Observables, a very important part is their commutation relations, which is how "complementary observables" are formalized in the mathematics.

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Atyy is absolutely right - I might even drop the "in a sense". Once you define the commutator algebra, you have defined the theory. That's both its power, and the reason you can't write it all down.

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atyy

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Yes, I put "in a sense" in at the last moment, knowing that this is PF and there will be all sorts of tricky questions, like whether an anti-commutation relation is also "complementary" :)Atyy is absolutely right - I might even drop the "in a sense". Once you define the commutator algebra, you have defined the theory. That's both its power, and the reason you can't write it all down.

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