The explanations given to the collapse of wavefunction seem rather complicated. For example, in wikipedia, it’s claimed that
In general, quantum systems exist in superpositions of those basis states that most closely correspond to classical descriptions, and, in the absence of measurement, evolve according to the Schrödinger equation. However, when a measurement is made, the wave function collapses—from an observer’s perspective—to just one of the basis states, and the property being measured uniquely acquires the eigenvalue of that particular state. After the collapse, the system again evolves according to the Schrödinger equation.
In literature, even more “unreasonable” descriptions suggesting that the position of a particle become suddenly certain at the moment of measurement. Some even treat it as the change in the system caused by measuring instruments that are “into contact”.
So here are my questions:
- I think that outcomes of “collapsing” are just different outcomes of a stochastic process. The value of observables is certain at any time, but changing randomly, so even if we perform some measurement, we can only obtain a probability distrubution of the observable. That’s where the uncertainty rised. Plus, the measurements do NOT change the state of the system and make it certain. Is this intepretation appropriate?
- Are there any mathematical fomulation for each of the explanations of “Collapse” given above in the paragraph written in bold face? I mean, if one claim that measurement changes the system, he needs to give a mathematical model to describe how it changes. For example, does quantum decoherence play a role in giving more clear description?
My ideas may be rude and I know I may recieve downvote if I am stupid. However, such question have bothered me for a long while and I really want a perfect mathematical explanation for this, so please understand me and do not downvote.
And I really want a mathematical explanation. I am not intending to make this question opinion based or philosophical.
