Why is the Wave Function Central to Quantum Theory's Physical Interpretation?

[rkastner]

As I understand it the wave function itself does not carry any physical interpration. Rather it is the square of it's absolute value. But that forces the question: Why construct a theory with the basic equation being about the time evolution of the wave function, when you could (I guess just as well) set up an equation for the time evolution of the absolute value of it squared. It just seems weird to me that we make this middle step, where we calculate something which actually carries no importance for the physical system.

Great question, and that's why I advocate a realist interpretation of the wave function (more generally, projection of the state vector on the measured observable eigenspace). In fact the state vector does describe something real and that's why the theory needs it to correctly describe reality. The state vector describes a physical possibility. This interpretation can give a natural account of the Born Rule as the square of the wf. It is the transactional interpretation, with a new 'possibilist' approach. See my new book, which you can get for a 20% discount here:

http://www.cambridge.org/us/knowledg...US&code=L2TIQM

Also see my website, transactionalinterpretation.org, for introductory and preview material.

 

[akhmeteli]

Actually, my interpretation is a blockworld approach so there is no MP. We use a path integral where the future boundary conditions are input, so there is no wave function collapse, i.e., one computes the amplitude for an entire process to include outcomes. Accordingly, MP is a faux problem associated with incorrectly trying to understand a spatiotemporal phenomenon in terms of time-evolved entities.

So, if I understand you correctly, you do not accept wave function collapse of standard quantum theory. Then we do agree on this point.

You don't have wave function collapse in the path integral approach because the experimental outcome is a boundary condition, i.e., there is nothing being "time evolved," so there is nothing to "collapse." One is thinking spatiotemporally (4D) rather than dynamically ((3+1)D). By assuming 4Dism is the correct fundamental description and that not all 4D situations permit a (3+1)D story, MP and violation of the Bell inequality are no longer "mysterious," i.e., those are just situations where a 4D quantum result doesn't permit a (3+1)D time-evolved story.

I took a quick look at your interpretation. What's important to me, it looks like QFT is just a continuous approximation to a fundamental discrete theory in your interpretation, so you don't seem to consider standard quantum theory a precise theory. That's where we might agree.