Dear Ken,
I appreciate your comments. However, I think only confusion and not clarity will result from trying to put the CH idea of a ‘framework choice’, specifying a quantum sample space, in the same bin with ‘hidden variables.’ Let me explain the difference.
A framework is chosen by a physicist constructing a stochastic quantum description; by contrast, hidden variables are regarded by their advocates as part of the ontology, the ‘beables’ to use Bell’s term. The closest analog to a framework in classical physics is a coarse graining of phase space in classical statistical mechanics: a division of phase space into cells of some size useful for discussing things like the microscopic origin of hydrodynamics. Just as for a coarse graining, the choice of a quantum framework is up to the physicist making up a quantum description, and the choice typically depends on the framework’s utility. It is not a physical property. See Sec. 4.3 in [1] for more details.
An important case comes up in the way CH deals with the well-known (or ‘first’ in my terminology) measurement problem. The big superposition |Psi> of the outcome pointer positions is, according to CH, perfectly fine, but if you put this into your framework you must pay attention to the single framework rule which prohibits combining incompatible quantum frameworks. Thus in the infamous example due to Schrodinger, one it is totally misleading to think of |Psi> as representing a dead-or-alive cate, because it is incompatible with any of a large number of cat-like properties (fur, etc.) represented by quantum projectors which do not commute with |Psi><Psi|. Conversely, any framework that allows a discussion of the cat as dead or alive cannot contain |Psi><Psi|. This is the same principle that prevents assigning to a spin half particle values of both S_x and S_z: the combination is nonsense. Similarly for the measurment outcome pointer. If you want to help Alice understand the outcome of her experiment, the “pointer basis” is much more useful than the state arising from unitary evolution, and the pointer basis is perfectly good CH quantum mechanics.
The same approach resolves the second measurement problem, relating the measurement outcome to the earlier property that was measured in a way that makes sense. If Alice’s apparatus is set to measure S_x and we are concerned about whether it is functioning properly, we should use a framework in which the S_x projectors make sense at the previous time. They do not commute with the singlet state (i.e., its projector). So if we insist on using the singlet state, that, too, is perfectly good CH quantum mechanics, but will be of no help in interpreting Alice’s result as a spin measurement, and it will not allow Alice to infer, on the basis of her outcome indicating S_x = -1/2, that Bob’s particle has the property S_x = +1/2 before he measures it–note again, that a proper framework, S_x for Bob’s particle must be used in order to arrive at this conclusion.
Thus in CH the same general principles are used for both predictions and retrodictions. Framework choice, absolutely essential in quantum physics and less essential in classical physics where the properties all commute, is neither causal nor retrocausal. Hidden variables theories, by contrast, start off by ignoring noncommutation, hoping or assuming that it is not true, and on this basis come up with all sorts of theorems that conflict with quantum mechanics, and when put to experimental tests the hidden variables always lose. If you’re interested in more details of how everything hangs together in a CH analysis of EPR-Bohm, I again recommend [2].
Bob Griffiths
[1] “The New Quantum Logic,” Found. Phys. 44 (June, 2014) pp. 610-640. arXiv:1311.2619.
{2} “EPR, Bell, and quantum locality”, Am. J. Phys., 79:954–965, 2011, arXiv:1007.4281.
Comments are closed, but trackbacks and pingbacks are open.