I spent over 20 years trying to make such a picture work. You are right that there should be some unified picture in terms of the wavefunction. I finally found a way to describe it this way but it required including the correlation of ejected photons in dividing the space up into effectively separated regions of the many body wavefunction tied to individual sites of "collapse". I work out the details of such a picture here Article Quantum Measurement and Classical States

I was mildly under the influence of cheap Tequila when i wrote that. Of course, you would have to include photons, phonons, or whatever to conserve energy and momentum. I'll take a look at your article.

Some say tequila and physics don't mix. Fightin' words I say.

I save the good Tequila for when i go backpacking.

Actually, i suppose a transition from one state to another, for example, the emission of a photon from a higher atomic state to a lower one, could be considered a collapse of the wave function. However, this does not seem to be the situation in which the collapse of a wave function is generally discussed. Mostly, it seems to involve the transition of a non-local wave function to a localized one.

The many worlds interpretation has the advantage of no loss or deviation of energy and conserved quantities during the measurement but it is still rather ad hoc in how it is selected. I also annoyed me that the *time* of the measurement was never considered. A wavefunction can impinge on different parts of the screen at different times. I made a point of including all that. The slicing of the space into distinct pieces by measurement always appealed to me but I couldn't get it to work out until I included the photon's dof i.e. quantum optics/ lowest order QED. This seems keep the measurement spaces sufficiently separated for very long times. The transition from nonlocal to local never occurs. It is an artifact of how the high dimensional many body psi is partitioned into the different "worlds" or "slices".

I read your piece on this space slicing, but i really did not understand it. Is it sort of like the many-worlds idea except that spacetime breaks up into some sort of parallel pieces rather than entirely new universes splicing off for every measurement so that all possibilities occur? I have to admit i don't understand the many-worlds idea either. I've never read much about it for that matter. Recall i've been busy carrying a heavy teaching load for over two decades.

People have gotten flummoxed about the nature of QM by the formal algebraic approaches used. The wavefunction of an H-atom is 6D. Quantum chemists and QMC people tend to know this but do not examine the full implications. Extrapolate the problem to a mole of particles. What people have gotten used to is the kind of Bloch-Heisenberg models of solids with periodic lattices and assumed they understood the wavefunction of a solid. This is NOT true. Such a solid is a very particular state that is far from the true eigenstates when you include CM motion and rotation.

This is the hard work. Once you get this and grok the massive freedom of such a high dimensional space and how particular the wavefunctions that correspond to classical-seeming objects are, the slicing picture becomes more reasonable. The wavefunction is subdivided into long lasting independent subregions that we perceive and living in a history of quantum measurements.

Sorry, i'm still not quite getting you. I've done solid state calculations using the Born-Oppenheimer approximation (slowly moving nuclei compared to electrons) and have read about many others (years ago in grad school). The agreement with experiment is not perfect, but there are a lot of factors other than what you mention such as exchange and correlation effects. Density functional theory then used an average potential hoping to mimic these effects. One problem with DFT was the inclusion of self-interaction. One paper i published was a quantum calculation of a cluster of lithium atoms with a correction for self-interaction. Of course, DFT had to assume a very cold substance and experiments relating to its results had to be cryogenic.

I don't really know where that line of research is today. (Furthermore, i've never done any "groking" to my knowledge. :-) Back then, at least, i don't remember much assuming that we understood the wavefunction. Group theory gives you the Bloch functions for perfect lattices at 0 K, and then you can solve some sort of Schroedinger equation, but no one to my knowledge thought, "well, that's that!" Energy levels obtained were generally much better than other things, such as total energy. I was dismayed when i found out my postdoc study was to calculate the energy difference between a perfect crystal and one with an impurity. A fool's errand, i thought, and i left first chance i got.

But, again, i'm having conceptual difficulties trying to think about slices of wavefunctions with classical properties. To me they can no longer be wavefunctions. But maybe i'm trying to envision something you are not proposing.

I know why this is hard. I spent many years doing those calculations and I am certainly not saying they are not valuable. I'm saying they don't correspond to the true many body eigenstates of the system, even the ground state. They are, however, highly durable over time and useful for investigating solids.

As a starting point, what is the wavefunction of a phonon? What are the symmetries of a ground state of N-atoms? These are the subtle points that took me 20 years and helped me see how the many body wavefunction of a solid was richer than those calculations and provide essential insight into the nature of measurement.

I just want to point out that my proposal for the collapse of the wavefunction does not resolve the measurement problem. I do believe quantum mechanics is not complete when it comes to this. It is not just a choice is made on a causative basis, but the process involved in the probabilistic outcome.

I like the line of thinking you have. What I would argue is that you should include the emitted photon degrees of freedom associated with binding. This will let the various measurement states to have some coordinate separation in the Hilbert space, and, since the photons are massless and don't interact, the states will live in effectively separated "worlds."

I think one aspect of this that is overlooked is the role of the second law of thermodynamics. I've read and heard so many times that nature seeks the lowest energy state. That is patently untrue as energy is conserved. An atom emitting a photon does go to a lower energy state, but the total energy of the system, atom plus photon, remains the same. Rather, there are a lot more final states (free photon plus ground state atom) than initial states (excited atom). So, it's just a manifestation of a system tending to greater disorder. In other words, nature isn't lazy, just messy.