The ideas brought forth in this website got me going and I felt, I let my own thoughts unravel, unrestricted.
I read in the text, under the title 'How the environment eliminates interference effects',
"In the page on The Quantum Casino we have seen that when a measurement of an observable is performed, the quantum state appears to "jump" to a particular eigenstate (with the observable taking the associated eigenvalue). This apparent jumping puzzled physicists for many years because it was not understood how and why the usually linear time-evolution of the Schrödinger equation should suddenly decide to make a sudden jump."
A measurement of an observable been performed? Eigenstates and eigenvalues, as referring to states being part of a superposition? Simultaneously, with regard to the element of time, existing states? Superposed states? Or, would it make any difference if these superposed states are thought with regard to the element of space? States that occupy, in a sense overlapping, the same space? So, their simultaneous existence in the superposition can be attributed to the element of time? Existing or co-existing in the same space but at different times? Or, that thought can be turned around and assume the superposed states as existing at the same time but differ in the space that each superposed state occupies? A sort of time-like space and space-like time? Connected with the many worlds and many histories quantum interpretations? Quantum entities simultaneously existing in all worlds possible and at all times possible and by the measurement of an observable one of the superposed states decoheres? A particular eigenstate with its associated eigenvalue instantiates into a world state? unravelling
But what about the Schrödinger equation? Is that so significant? Bringing forth the thought that entered my mind often enough, that maths is a tool to stretch the human mind imagination. To break through a deadlock. And once this is done, to stay aside and let the imagination create. It is not the Schrödinger equation that decides to make a sudden jump. Its job is to set the stage for further thoughts to unravel. Trying to explain how the tool works would not provide new insights, new ways to conceive a phenomenon, new concepts. You can not explain a phenomenon with a tool. This over-reliance in maths and equations and rigorous solutions bears unyielding fruits. Moreover, as it is contained in the phrase 'the usually linear time-evolution', usually and not at all cases point towards the end of its usefulness in unraveling further the phenomenon.