Quantum Mechanics
The theoretical foundation of the concept of measurement in quantum mechanics is a contentious issue deeply connected to the many interpretations of quantum mechanics. A key topic is that of wave function collapse, for which some interpretations assert that measurement causes a discontinuous change into a non-quantum state, which no longer evolves. The superposition principle (ψ = Σanψn) of quantum physics says that for a wave function ψ, a measurement will give a state of the quantum system of one of the m possible eigenvalues fn, n=1,2...m, of the operator which is part of the eigenfunctions ψn, n=1,2,...n. Once we have measured the system, we know its current state and this stops it from being in one of its other states. This means that the type of measurement that we do on the system affects the end state of the system. An experimentally studied situation related to this is the quantum Zeno effect, in which a quantum state would decay if left alone but does not decay because of its continuous observation. The dynamics of a quantum system under continuous observation is described by a quantum stochastic master equation known as the Belavkin equation.
An important aspect of the concept of measurement has been clarified in some QM experiments where a single electron proved sufficient as an "observer" — there is no need for a conscious "observer".
A consequence of Bell's theorem is that measurement on one of two entangled particles can appear to have a nonlocal effect on the opposite particle. Additional problems related to decoherence arise when the observer too is modeled as a quantum system.
The uncertainty principle has been frequently confused with the observer effect, evidently even by its originator, Werner Heisenberg. The uncertainty principle in its standard form actually describes how precisely we may measure the position and momentum of a particle at the same time — if we increase the precision in measuring one quantity, we are forced to lose precision in measuring the other. An alternative version of the uncertainty principle, more in the spirit of an observer effect, fully accounts for the disturbance the observer has on a system and the error incurred, although this is not how the term "uncertainty principle" is most commonly used in practice.
Read more about this topic: Observer Effect (physics)
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