Quantum theory is plenty strange, but one of the strangest discoveries is the realization that there’s a limit to how much you can measure at any one time. This was famously described by Werner Heisenberg, with his uncertainty principle: how you can never know both the position and motion of a particle at the same time.

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The most mysterious aspect of quantum mechanics is we are not sure what we mean by reality. Quantum mechanics is about as much a physical logic as it is a theory. We have curious problems of what we mean by reality, for there exist in QM complementary sets of observables, say A and B, where physical systems can be described by A or B as an exclusive or, and where the two are incommensurate or contradictory. A classic case is observables corresponding to position and momentum. The complementary observables obey a noncommutative algebra

[x, p] = i?,

where ? is the fundamental unit of action. A measurement may give information about a system as A or B, but not both, and so prior to such measurements we have a hard time saying there is anything ontological about the quantum system. Prior to a measurement a quantum system can only be said to be epistemic, but a measurement is what gives ontology. Piles of papers have been written on quantum interpretations, where any interpretation is just a formal equivalence between sets of rules for operating on experimental data. This makes quantum interpretations ineffective, or not something which can be determined by empirical testing. I think that quantum gravity makes the situation far worse, for on top of there being a complementarity of observables mathematically represented by noncommutative operators, there is a duality between causal descriptions (S-matrices) separated by event horizons (quantum horizons) where this extends into nonassociativity.

LC