Could someone explain Luders Rule?

1. Dec 11, 2007

TimH

I'm reading The Structure and Interpretation of Quantum Mechanics by Hughes. He has a chapter where he develops an account of conditional probability in QM which he uses to explain the two-slit experiment and the EPR (singlet state) situation. Basically the idea is that this conditional probability function allows for talk of conditional probability in situations where the logic in non-Boolean (i.e. incompatible observables). Conditional probability is the probability of event A given that event B occurs. The rule he gives is in terms of density operators in Hilbert space and he refers to it as Luders rule (with umlauts over the u).

Anyway he argues that the rule has many very useful consequences in terms of explaining the "causal anomalies" of QM. I would really like to understand what this rule is really saying in practical terms (i.e. not just the math). Any help appreciated. Thanks.

2. Feb 12, 2017

Gabriel Maia

Let's say you have a system wich is comprised of a mixture of states. The way you describe this system is via a density matrix, which tells you how much of each state you have in the total system.

Now, if you measure some observable S, as a result, you will have one of the eigenstates si of the operator S, right? The Lüder's rule is telling you how the density matrix changes after this measurement. This matrix is not simply |si><si| as one might expect because the states building up the total system before the measurement need not be orthogonal, so more than one state can contribute to the result si.

3. Feb 12, 2017