Why protective measurement is important to understand psi?

[MichPod]

Why protective measurement is important to understand whether the wave function is the ontic property of a single particle and not of the ensabmle of similarly prepared particles?

I need some help with understanding the following topic (which is currently above my level so I may easily miss some simple important points).

There are some recent articles (Why protective measurement establishes the reality of the wave functionShan Gao, 2018) which claim that being able to measure average values of many observables for a single particle in protective measurement (and by that calculating the wave function) somehow proves that the wave function is the property of a single particle (and not of the ensamble of particles).

In my view, when we somehow "protect" the measurement, i.e. maintain the wave function of the particle non-changed, and produce a set of measurements, we actually are doing something which may be equivalent to producing a set of measurements on the ensamble of different particles. For what I see, to ensure a protective measurement, we need to know some characteristics of the wave function ahead to "protect" it with Zeno effect or otherwise. We cannot just take an arbitrary particle with not known wave function and proceed with protective measurements of it. So it may be said that a protective measurement "imposes" the original wave function firstly by already knowing quite much of what it may be. So I fail to see much difference (theoretical one) between conducting a set of protected measurements of a single particle vs a set of regular measurements on a pure ensamble of particles which have a same wave function.

I have no doubt that realizing a set of protective measurements on a single particle may be a serious experimental challenge, but I fail to see how being able to do them proves anyting new on the nature of the wave function.

 

[bhobba]

I do not know much about protective measurements and used the following to get an idea:
http://tabish.freeshell.org/physics/pm/

From my reading it is a form of weak measurement:
https://arxiv.org/abs/1702.04021

Weak measurements can produce results that seem to indicate some of the basic results of QM are invalid eg the simultaneous measurement of momentum and position at the same time. However such claims are only superficial and even peer reviewed papers get it wrong. Weak measurements can not, by their very nature, tell us anything the formalism can not. And the formalism is clear - you can't tell the difference between interpretations such as 'wave function is the ontic property of a single particle and not of the ensemble of similarly prepared particles'. Although I consider that a mildly badly worded question that shows a bit of a misunderstanding in the ensemble interpretation of Ballentine, Einstein and others - however that is another issue and another thread - What is The Ensemble Interpretation? Just as an overview of the issue the ensemble interpretation does not preclude the wave-function being 'ontic' (what ever that means - the definition is - relating to entities and the facts about them; relating to real as opposed to phenomenal existence). In relation to physics I can't really make much sense of such things - except in a very broad way - and when using it you face the issue of - what is reality. I think of reality as what our theories tell us so from my viewpoint it's a pretty meaningless . However in some cases its clear eg BM. In BM a real particle, real in the sense of classical physics, is guided by a pilot wave. That would be in my view an ontically real interpretation. However the Ensemble interpretation is perfectly compatible with BM - in fact some thought the original 1970 paper on it was really BM is disguise. But to each their own.

Thanks
Bill