4 ms·

I think what you're describing is the infamous Measurement Problem: 1. Hamiltonian evolution is linear 2. Measurements produce nonlinear projections onto eige

I think what you're describing is the infamous Measurement Problem: 1. Hamiltonian evolution is linear 2. Measurements produce nonlinear projections onto eigenvectors in accordance with the Born rule Note that this projection is a function of the initial state - but a probabilistic function, so therefore not reversible. There isn't really a satisfying answer to this question yet. Decoherence explains how the system evolves to a mixture of eigenstates but not the collapse into a single one, nor the Born rule.

danbruc 8y ago
Note that this projection is a function of the initial state - but a probabilistic function, so therefore not reversible. I understand what you want to say, but I think it is not correct to call it a function. The term »probabilistic function« does appear in Google results but it seems not to be a common one. I also spent a few minutes looking for a mathematical formalization of a random number generator as a function with no inputs returning a random number adhering to a given probability distribution but could not find anything. Mathematicians seem to be pretty good at avoiding problematic definitions and according to Wikipedia some do this deliberately. The best formalization I could find would be a function from the initial state to a random variable but I was unable to figure out in a couple of minutes how I would mathematically formalize the step from a random variable to a concrete result of a single trail. Decoherence explains how the system evolves to a mixture of eigenstates but not the collapse into a single one [...] I never managed to really wrap my head around decoherence, I always only had a quite fuzzy picture of it. But now it is starting to click, it's about the transition from superposition states to probabilistic mixtures, the transition from uncertainty due to superposition to uncertainty due to ignorance.

danbruc 8y ago

Note that this projection is a function of the initial state - but a probabilistic function, so therefore not reversible. I understand what you want to say, but I think it is not correct to call it a function. The term »probabilistic function« does appear in Google results but it seems not to be a common one. I also spent a few minutes looking for a mathematical formalization of a random number generator as a function with no inputs returning a random number adhering to a given probability distribution but could not find anything. Mathematicians seem to be pretty good at avoiding problematic definitions and according to Wikipedia some do this deliberately. The best formalization I could find would be a function from the initial state to a random variable but I was unable to figure out in a couple of minutes how I would mathematically formalize the step from a random variable to a concrete result of a single trail. Decoherence explains how the system evolves to a mixture of eigenstates but not the collapse into a single one [...] I never managed to really wrap my head around decoherence, I always only had a quite fuzzy picture of it. But now it is starting to click, it's about the transition from superposition states to probabilistic mixtures, the transition from uncertainty due to superposition to uncertainty due to ignorance.