Quantum Logic?

Most recent answer: 07/12/2014

Q:
I'm a mathematician and I want to know the relationship between the observer effect in quantum mechanics and the uncertainty principle. Apparently, people claims that the double slit experiment implies that the logic of quantum mechanics does not form a distributive lattice. However in other references they claim that the uncertainty principle is the assumption that causes the non distributivity. So what is the relationship between these two fenomena and how they imply the differences between logics in the classical and quantum setting? Thanks in advance.
- Fernando (age 20)
Brazil
A:

I'm not a big fan of "quantum logic", but here's a little introduction. In the two slit experiment with slits A and B and arrival sites say X and Y one might think that the condition ( (A OR B) AND (X OR Y)) distributes into ((A AND X) OR (A AND Y) OR (B AND X) OR (B AND Y)). Now if you try to assign probabilities to each of those outcomes there's no way to get them to add up to match experimental results. So it's tempting to say that the distributive law of OR and AND only works as an approximate result for large-scale classical events.

These days even the people who once eloquently advocated quantum logic (e.g. Hilary Putnam) have generally lost interest in it. The main reason is that quantum logic doesn't help with the central mysteries: how the predictions of local realism break down (search this site for "Bell Inequalities"), and how a random experience arises from an underlying deterministic equation. Instead we think that the problems lie not with logic but with the attempt to project a quantum reality onto some classical possibilities. The physical state as the quantum object goes through the slits is (some of A plus some of B). 

So what is the relation between the "observer effect" and the "uncertainty principle"? We've addressed that exact question in follow-up #5 here: https://van.physics.illinois.edu/qa/listing.php?id=1228.

Mike W.


(published on 07/12/2014)