Conceptual underpinning(s) of the QM projection postulate

[eloheim]

I find explanations like Zurek's slightly circular, in the following way: The argument that the environment selects certain preferred "pointer states" is a "large numbers" type argument. Decoherence is overwhelmingly likely to occur, but you need a pre-existing notion of probability to have a notion of "overwhelmingly likely". So if decoherence is used to justify the appearance of collapse, and therefore Born probabilities, then the whole thing seems sort of circular.

I know this is six months old but in the paper cited, Zurek goes to great length to make his conclusions (derivation of the Born rule) dependent upon only his "Envariance" and not presuppose decoherence in any way (because reduced density matrices and traces depend upon it already).

 

[nanosiborg]

I know this is six months old but in the paper cited, Zurek goes to great length to make his conclusions (derivation of the Born rule) dependent upon only his "Envariance" and not presuppose decoherence in any way (because reduced density matrices and traces depend upon it already).

But the OP is asking about the conceptual basis of the projection postulate. So, how is the conceptual basis of the Born rule related to the conceptual basis of the projection postulate?

How about this? Consider qm as a wave mechanical view of fundamental reality. That is, light, electricity, magnetism are all due to wave mechanical interactions in a medium or media of unknown structure. And then let's also consider the wave mechanics of waves in air and water. Ok, so there's the extant experimental literature regarding this stuff, and it tells us that the probability of triggering a detector is proportional to the intensity of the incident wavefront. No matter what the medium. Even if it's unknown. And intensity is proportional to amplitude. Hence, the Born rule. But what about the projection postulate? Well, it follows from the same classical wave mechanics (applied to whatever) that the Born rule does. They go hand in hand.

You can't have the Born rule without the projection postulate, and you can't have the projection postulate without the Born rule. And they're both entailed by a wave mechanical approach to dealing with disturbances in any medium. It just happens that the media that qm deals with are, uh, imaginary media ... but media nonetheless. Is there any reason to think that disturbances in these imaginary media (of unknown structure) behave in accordance with different wave dynamics than disturbances in media of known structure? Well, no. Of course not. There's just no basis for assuming that. Instead, it's assumed that quantum phenomena behave according to the same fundamental dynamics that macroscopic waves in macroscopic media do. And, so far, this has proven to be a very productive conceptual analogy.