Uncertainty versus indeterminism: formulation?

[nomadreid]

Although the difference between the ontological uncertainty of quantum physics (as reflected in such things as Bell's inequalities) and the epistemic uncertainty of mathematical systems (as reflected in such things as Gödel's Incompleteness Theorems) is clear to me, I find it tricky to formulate the difference in terms of the standard triangle Theory-Model (Interpretation)-Lattice of Truth Values, with perhaps some sort of Kripke-like hierarchies. Can anyone push me in the right direction? I don't need explanations of the two uncertainties separately, but in contrast. If you have a source, please only on-line free sources, as I do not have access to a decent academic library and am tired of paying for articles. Oh, and don't even think about mentioning Penrose.

 

[bhobba]

I can't quite grasp what your issue is. That said there is, even among professionals, sometimes a misconception of the uncertainty principle. Many have a view similar to Heisenberg and his microscope thought experiment. That it was wrong was pointed out by Bohr, but for some reason it didn't propagate through to all physicists and texts.

I will state it precisely and if you could then rephrase your question it may be easier to answer. The uncertainly principle places no limit on how accurately you can measure position or momentum - you can measure them as accurately as you like. Suppose we have two large ensembles of quantum systems all prepared in exactly the same state. The uncertainty principle says that if one measures position accurately (and it can be as accurately as you like) in one ensemble, and if one measures momentum accurately (again as accurately as you like) in the other ensemble, the product of the standard deviations of the position results and momentum results is as per the Heisenberg uncertainty principle.

Thanks
Bill

 

[nomadreid]

Thanks, bhobba. I do understand the Uncertainty Principle in the same manner as you stated it (one of the nicest formulations I have seen is on page 89 of the classic "Quantum Computation and Quantum Information" by Nielsen and Chuang). What I am attempting to do is to bridge the gap between ordinary physics and the area of Mathematical Logic known as Model Theory --- so this question should probably only be proposed to logicians, as most physicists are probably unfamiliar with Model Theory. Put another way: how would a Model Theorist reformulate the Uncertainty Principle? Since this question does not fit into the usual forums, I put it into the workshop, but perhaps the question does not have a place in Physics Forums.

 

[bhobba]

Since this question does not fit into the usual forums, I put it into the workshop, but perhaps the question does not have a place in Physics Forums.

It has a place alright - its just we may not have anyone knowledgeable enough to answer it. I know something of non-standard analysis, ultra-filters and all that, but I have no idea how to answer your question. Maybe someone else does.

Thanks
Bill