Three facts related to the collapse of quantum mechanical wavefunctions following measurements or observations are presented and explained. They are (1) in all stochastic theories, both classical and quantum mechanical, probability densities collapse following observations; (2) the laws of probability determine the probability density just after an observation in terms of that just before the observation and the result of the observation; (3) the wavefunction just after an observation can be found from that just before the observation by using the result of the observation, the laws of probability, and the assumption that immediate repetition of an observation yields the same result and does not change the wavefunction except for an arbitrary phase factor.
In this paper I present a thought experiment that gives different results depending on whether or not the wavefunction collapses. Since the wavefunction does not obey the Schrodinger equation during the collapse, conservation laws are violated. This is the reason why the results are different. Quantities that are conserved if the wavefunction does not collapse might change if it does. I also show that using the Born Rule to derive probabilities of states before a measurement given the state after it (rather than the other way round as it is usually used) leads to the conclusion that the memories that an observer has about making measurements of quantum systems have a significant probability of being false memories.
Abstract Measurement in quantum mechanics is a long-standing issue, and the measurement problem consists of essentially two parts: 1) no matter what the initial wavefunction of an object, the result of a measurement always results in the observation of a single eigenstate (i.e., “wavefunction collapse”), and 2) once the wavefunction collapses it remains collapsed. Though there have been a number of proposed solutions to the measurement problem, none to date is without debate. Here we discuss a solution to the measurement problem that avoids some others’ difficulties. We assume that for every eigenvector of an operator there is a set of unique discrete phases, and that the phase sets among eigenvectors are disjoint. With this hypothesis it is possible to show that wavefunction collapse is a consequence of destructive interference when a quantum object interacts with the large set of “quantum-measurement mapping operators” that must comprise a classical measuring device .