(April 29, 2012 at 5:15 am)Phil Wrote: Besides my joke poster above and a mathematical one, show me a true collapse of a wave function. BTW, the wave function of the system is the wave function of the universe (more aptly named the universal wave function). There really is no sharply defined way to define the wave function of a subsystem (partial system). See the work of Hawking and Hartle on the Wheeler–DeWitt equation.The wave function can be used to describe any system including the system of the entire universe. There is a defined way to describe subsystems and they are used all the time from in electronics systems to the electron configurations in chemistry. Using the Schrodinger equation you can describe the position and energy of the electrons in a hydrogen atom and by manipulating the differential equation an infinite amount of other things. Quantum Mechanics is what lead to modern Chemistry btw.
But, ...now using the Copenhagen interpretation, until the position or energy of the electron is measured the wave does not "collapse". This is the entire basis for this model and is the first one you learn in any modern physics course. Not until something is measured will the waveform collapse hence there has to be an awareness doing the measuring.
I don't know what you mean by true collapse. According to the uncertainty principle the waveform will never fully collapse. You could measure the position for example but what you actually measure is just another waveform with a more defined position and a fluctuating energy. The more times you measure the position the more defined it will be but you will never get a waveform that has truly collapsed. So you can't get a wave function to ever fully collapse into a defined state, only a slightly more defined state. There will always be a slight amount of uncertainty whether the moon exists or doesn't.
From what I have read on the Wheeler–DeWitt equation, it is basically the Schrodinger equation used in three or four dimensions, meaning it could be used to describe the universe. I did read a little about Hawkings work on it but don't have time at the moment....
