Undergrad Questions about ensemble interpretation of QM

[soothsayer]

I've been reading up on the ensemble interpretation (aka statistical interpretation) of QM and it's making a bit more sense to me that it did on the onset, but I still have some questions about how it is consistent with experimental observations of various QM experiments, especially "single-particle" experiments.

My understanding is that the basic tenant of the ensemble interpretation (EI) is that the wavefunction is not a real physical entity, nor a property that describes a single particle/quantum state, but rather applies only to an "ensemble" of identically prepared systems. This explains why the interference pattern from the double-slit experiment can only be seen after many repetitions, for example (you cannot determine which pattern you are looking at from just a single result). By what mechanism does EI consider that individual particles obey the wavefunction of their respective "ensembles"? How does EI incorporate the impact of making measurements, if the wavefunction "collapse" is thought to be purely mathematical? By what mechanism does this occur, if not some sort of pilot wave theory? If the wavefunction cannot be applied to individual particles, what explains the quantum uncertainty of their position, momentum, etc? What does it mean for a particle to be in a superposition of various eigenstates?

Is there any reading you would recommend to help supplement my understanding of what ensemble interpretation advocates are trying to argue about the nature of the particle and the wavefunction in QM?

Thanks!

 

[strangerep]

Is there any reading you would recommend [...]

See my signature line below.

How does EI incorporate the impact of making measurements,

That's in ch9. (But if you search this forum for my older posts that mention Ballentine and apparatus, you'll find a brief summary.)

If the wavefunction cannot be applied to individual particles, what explains the quantum uncertainty of their position, momentum, etc?

This is best understood in terms of how one might (try to) prepare a single particle of exact position and momentum.

 

[vanhees71]

There's not much to add to @strangerep 's answer.

I want just say that in my opinion, what's called "collapse" is simply the epistemic update of the description due to gained knowledge from a measurement. It's like knowing on Saturday evening which numbers came out from the drawing of the numbers in the lotery. Before, unfortunately I couldn't know them but only guess a probability for getting a lot of money out of the gamble (an this makes me rather save my money ;-))). Afterwards I know these numbers. All of a sudden the probability description "collapsed" to firm knowledge about the outcome of this "(random) experiment".

 

[DarMM]

My understanding is that the basic tenant of the ensemble interpretation (EI) is that the wavefunction is not a real physical entity

This is common to all Copenhagen-like views. Everything I say here applies to all Copenhagen views except for one very small bit.

By what mechanism does EI consider that individual particles obey the wavefunction of their respective "ensembles"?

The wavefunction describe the statistics of observations on them. QM doesn't give a mechanism beyond this.

How does EI incorporate the impact of making measurements, if the wavefunction "collapse" is thought to be purely mathematical? By what mechanism does this occur

@vanhees71 describes this very well.

What does it mean for a particle to be in a superposition of various eigenstates?

It's just a form of statistics not commonly found in classical probability. I'd have a look though at this paper:
https://arxiv.org/abs/quant-ph/0401052There you get superpositions even in a classical theory. Again just as an alternate form of statistics. What really differentiates classical and quantum probability is something called contextuality. This model doesn't replicate contextuality. In fact that's the point of the model to show what features are truly quantum.

The only real difference between the ensemble interpretation and other Copenhagen views is purely a difference in what you think about probability.

Probability theory tells us that if a coin has a 60% chance of landing heads (biased coin) then:
(a) If it happens once and you can buy a ticket that will give you $1 if you win, then the rational thing to do is to pay $0.60
(b) An ensemble of flipped coins in the limit as the ensemble gets larger will have a ratio of 0.6 between heads and the total coin flips.

Some people take (a) to be the more fundamental meaning, known as Bayesians. Others take (b) to be the more fundamental meaning, known as Frequentists. Others don't care as such.

Transferred over to quantum theory this is QBism (Quantum Bayesianism), the Ensemble Interpretation and Copenhagen.

Again though it is only on this minor "philosophy of probability" point that they disagree, not really anything specific to QM.