I Quantum theory - Nature Paper 18 Sept

[PeterDonis]

the Aravind-Mermin Pentagram

Is there a paper online that describes this scenario?

 

[akvadrako]

That doesn't matter too much, remember the Pusey-Leifer theorem is about seeing if a theory has an ontological symmetry that directly reflects OTS, this is defined as Ontological Time Symmetry, see p.8

The only thing I'm asking is if you agree Many-Worlds lacks such an ontological symmetry. The definition makes sense to me when applied to Many-Worlds and I would say it violates it at a global level.

First, to put it in my own words: for a theory to have Ontological TS (OnTS) it must be possible to swap the input/output while transforming the path, $(x,b,\lambda) \Leftrightarrow ( b, x, f(\lambda) )$, for every $(x, b, \lambda)$. This is based off the definition on page 8. The spirit seems to be that God “cannot tell the difference between a video played forwards and played in reverse”.

At least for finite systems, many worlds seems to have OnTS. The first reason is that due to being linear and the limited number of states available, every state $x$ which evolves to state $b$ will eventually return to $x$. Although that satisfies their definition of OnTS, it may not exactly fit the spirit because AFAIK the path from $x \rightarrow b$ may not be a mirror image of $b \rightarrow x$. However, there must be a point when it reaches a maximum # of branches and from then on they are more likely to merge, roughly mirroring the early forward evolution.

The second reason is that you can run your universal simulation on a quantum computer and invert all the gates. I’m not sure this is allowed, though it’s analogous to setting up an experiment backwards.

For infinite systems, it’s less clear and I need to guess a bit here. Wouldn’t it depend on the Hamiltonian? If the standard model is used, would the CPT symmetry suffice to satisfy OnTS, at least in spirit? If seems like for every $x \rightarrow b$, there is a mirror transform, $CP(b) \rightarrow CP(x)$, that’s indistinguishable in behavior.

If we are talking about our universe, then a big crunch situation would be similar to the finite dimensional version. Finally, if expansion continues forever then it seems like many worlds does violate OnTS, because any state has the tendency to spread out into new dimensions, even under a CPT reversal.

I'm not trying to make this overly complicated, but P&L's paper is full of aspects that don't apply in a straightforward manner to many worlds and they only devote a short paragraph to the issue. I think if they actually want to show that many worlds requires fine tuning, it would be a lot cleaner to just address that directly.

 

[DarMM]

Very good post, I'll need some time to think about it. These cosmological aspects of MWI are very interesting.

Just so you know where I'm going with this, Many Worlds in order to derive the existence of the classical worlds essentially needs to assume an environment/not-environment split with the environment having specific properties (see Zurek's work on Quantum Darwinism via einselection https://arxiv.org/abs/quant-ph/0105127).

Either this just happened to be in the initial conditions (fine-tuned) or it emerged (thermalisation). Ultimately Pusey and Leifer would be saying that restoring OTS in the branches is an additional thing this thermalisation needs to do.

However I see that this really needs a proper analysis.

Probably it's better to stick to the emergence of the "environment" early on in the universe's history as an example of where Many-Worlds would have different predictions.

 

[mfb]

Measurements happen inside the universe (deterministically, dependent upon preparations, parameter settings, and intentions of the experimenters), in a way not precisely specified by MWI. Hence its vagueness...

What is vague about "unitary evolution no matter what happens"?

 

[A. Neumaier]

What is vague about "unitary evolution no matter what happens"?

The unitary evolution itself is not vague. What is vague is the notion of measurement as event determined by the wave function - the only thing that is claimed to exist objectvely.

A criterion is missing that tells when and how the state of the universe indicates

• that, at any given place in the universe, a measurement is made,
• when the measurement result is deemed to be known, and
• how a particular observer's results are related to particular branches of the wave function at the appropriate moments.

Lacking this, all talk about measurement, observers, and results is just playing with buzzwords connected by vague, informative sounding statements.

 

[vanhees71]

Realistic is more clear in philosophy, and it means that there is some objective state. Realists believe there is something like that; anti-realists think everything is subjective. The MWI is realistic, because the wave function is real. In Bohmian QM, it's that plus a world-particle, to pick out the world you are in.

I don't think the word "realistic" means anything consistent to physicists.

Also, MWI is deterministic - it has only unitary evolution so that's obvious.

Well, I don't understand, what's clear with this definition since many philosophers (and maybe also a minority of physicists) consider QM as "non-realistic". On the other hand, it's clear that QM has a very clear definition of an objective state. It's even more explicit in defining what a state is than classical mechanics, where it is supposed to be implicitly clear from the formulation of the theory (the explicit statement on a fundamental level of classical mechanics, no matter whether Newtonian or relativistic, is that a state is represented by a point in phase space). In QM a state is represented by the statistical operator and operationally as an equivalence class of preparation procedures. That's an objective notion of state since a preparation procedure is clearly defined, and in my opinion it's utmost realistic, since this definition is in terms of real-world actions on the described system (e.g., at the LHC there's a preparation of protons with a pretty well determined momentum). The only difference between classical and quantum mechanics then is that the notion of the state in the latter is entirely probabilistic since a complete state determination (formally realized by the determination of the values of a complete set of compatible observables) doesn't imply the determination of the values of all possible observables on the system. That's also very "realistic" since this reflects our experience with testing QT for nearly 100 years with an amazing accuracy!

So, if you define, "realism" in this physicists's way, of course QT is realistic, even in the minimal statistical interpretation without additional esoterics a la MWI, where for me it is not clarified why we observe a unique outcome when measuring an undetermined observable; this is shared by all indeterministic interpretions; BM is different since it's a deterministic interpretation, where the probabilities are subjective, i.e., due to our incomplete knowledge of the particle's initial position as in classical statistical mechanics.

 

[stevendaryl]

In QM a state is represented by the statistical operator and operationally as an equivalence class of preparation procedures.

If you're using quantum mechanics to understand, say, the physics of cells in biology, or the physics of stars in astronomy, you're dealing with systems that were not "prepared" by anyone or anything. So do those systems not have a state?

 

[Lord Jestocost]

Well, I don't understand, what's clear with this definition since many philosophers (and maybe also a minority of physicists) consider QM as "non-realistic".

Regarding realists and anti-realists, Massimo Pigliucci describes the issue as follows (http://rationallyspeaking.blogspot.com/2012/08/surprise-naturalistic-metaphysics.html):

To put it very briefly, a realist is someone who thinks that scientific theories aim at describing the world as it is (of course, within the limits of human epistemic access to reality), while an anti-realist is someone who takes scientific theories to aim at empirical adequacy, not truth. So, for instance, for a realist there truly are electrons out there, while for an anti-realist “electrons” are a convenient theoretical construct to make sense of certain kinds of data from fundamental physics, but the term need not refer to actual “particles.” It goes without saying that most scientists are realists, but not all. Interestingly, some physicists working on quantum mechanics belong to what is informally known as the “shut up and calculate” school, which eschews “interpretations” of quantum mechanics in favor of a pragmatic deployment of the theory to solve computational problems.

 

[vanhees71]

If you're using quantum mechanics to understand, say, the physics of cells in biology, or the physics of stars in astronomy, you're dealing with systems that were not "prepared" by anyone or anything. So do those systems not have a state?

Then you have to figure out the state by measurements (on an ensemble of course ;-)).

 

[vanhees71]

Regarding realists and anti-realists, Massimo Pigliucci describes the issue as follows (http://rationallyspeaking.blogspot.com/2012/08/surprise-naturalistic-metaphysics.html):

To put it very briefly, a realist is someone who thinks that scientific theories aim at describing the world as it is (of course, within the limits of human epistemic access to reality), while an anti-realist is someone who takes scientific theories to aim at empirical adequacy, not truth. So, for instance, for a realist there truly are electrons out there, while for an anti-realist “electrons” are a convenient theoretical construct to make sense of certain kinds of data from fundamental physics, but the term need not refer to actual “particles.” It goes without saying that most scientists are realists, but not all. Interestingly, some physicists working on quantum mechanics belong to what is informally known as the “shut up and calculate” school, which eschews “interpretations” of quantum mechanics in favor of a pragmatic deployment of the theory to solve computational problems.

What am I then? Of course I believe in electrons as one thing existing in the "world as it is" and at the same time believe that physical theories are there to describe objectively observable facts about this "world as it is". That's the only criterion distinguishing scientific theories (scientific narratives if you wish) from fairy tales (including philosophical speculations of all kind). Also in a sense I think the right attitude is indeed the "shut up and calculate" attitude, but this has to taken with a grain of salt since of course you need also some heuristic intuition to be creative in finding new models to describe things, but these creations are only science if they are objectively testable by experiment and then either become a valid description of "the world as it is" or are put into the garbage can of failed trials to understand more about this "world as it is".

 

[stevendaryl]

Then you have to figure out the state by measurements (on an ensemble of course ;-)).

But the issue is: does it have a state before you measure it, or not? If not, then your view of "state" is not realistic, but is epistemological.

 

[akvadrako]

Well, I don't understand, what's clear with this definition since many philosophers (and maybe also a minority of physicists) consider QM as "non-realistic".

Do you think that:

1. There is an objective quantum state for the whole universe? (one we don't know, of course)
2. There is no non-unitary evolution (collapse) ?

That's the entirety of MWI. Those who say QM is non-realistic disagree with the first part.

Edit: If you consider the point of a scientific theory to make predictions for experiments, then MWI is not complete; that's A. Neumaier's objection. But the situation is better than string theory because we can use some weak additional assumptions to show the predictions are equal to standard QM, at least for practical experiments.

 

[A. Neumaier]

That's the entirety of MWI.

No.

All interpretative stuff - which is what makes up the MWI (I=interpretation!) - is missing in these two statements. Your two statements say nothing at all about how the state relates to reality in general and to measurement and probabilities in particular.

Though it may well be the only consensus among all variants of MWI.

 

[akvadrako]

No.

All interpretative stuff - which is what makes up the MWI (I=interpretation!) - is missing in these two statements. Your two statements say nothing at all about how the state relates to reality in general and to measurement and probabilities in particular.

Though it may well be the only consensus among all variants of MWI.

Then what would you call the theory (scientific or just mathematical) described by my two points? Would the term "unitary QM" be more clear?

 

[A. Neumaier]

Then what would you call the theory (scientific or just mathematical) described by my two points? Would the term "unitary QM" be more clear?

Yes, that's observer-free, unitary quantum mechanics.

By the way, it is the background upon which my (single world) thermal interpretation of quantum mechanics operates.

 

[vanhees71]

Do you think that:

1. There is an objective quantum state for the whole universe? (one we don't know, of course)
2. There is no non-unitary evolution (collapse) ?

That's the entirety of MWI. Those who say QM is non-realistic disagree with the first part.

Edit: If you consider the point of a scientific theory to make predictions for experiments, then MWI is not complete; that's A. Neumaier's objection. But the situation is better than string theory because we can use some weak additional assumptions to show the predictions are equal to standard QM, at least for practical experiments.

Ad 1. The notion "quantum state for the whole universe" is a non-physical fiction since there's no way to observe the "whole universe", not even in principle since only a tiny part of the whole universe is principally observable, i.e., within our horizon according to the standard model of cosmology. This holds for any theory, not only QT.

Ad 2. For closed systems (!) there's no non-unitary evolution. As soon as one measures something, the observed system isn't closed anymore, because it's interacting with the measurement device (and usually additionally to "the environment", i.e., anything else except the observed system and the measurement apparatus).

 

[stevendaryl]

Ad 1. The notion "quantum state for the whole universe" is a non-physical fiction since there's no way to observe the "whole universe"

That view is what I consider anti-realist. To believe that something exists only if it is possible to observe it is almost the opposite of realism.

 

[Stephen Tashi]

Do you think that:

In the MWI, what is meant by "you"? , or "I", or "me"?

As I understand MWI, "I" am something real at an instant in time, but in an instant later, that "I" has branched off into descendants of that "I" who are distinct things.

In fact, from the viewpoint of an instantaneous "I", what is the point of using a wave function to limit the possible branches that can "really" happen? Why not say that all imaginable futures happen? (I suppose that would be the many-many-worlds interpretation.)

The notion that a predictive theory has utility depends on the fact (or illusion) that "I" have a persistence in time and will experience the consequences of a prediction.

 

[A. Neumaier]

For closed systems (!) there's no non-unitary evolution.

But the only closed system is the universe, since any smaller system necessarily interacts with its environment. Thus small closed systems are a ''non-physical fiction'', to use your words.

there's no way to observe the "whole universe",

No. Whenever we observe part of the universe, we observe one of the properties of the whole universe.

This is completely analogous to observing the value of an observable of a tiny physical system, which gives us only some property of the tiny system.

Since you are willing to assign observability and hence a physical state to the tiny system because you can measure some of its properties, it would only be consistent if you also grant observability and hence a physical state to the whole universe.

 

[vanhees71]

That view is what I consider anti-realist. To believe that something exists only if it is possible to observe it is almost the opposite of realism.

Then I'm an anti-realist ;-).

 

[vanhees71]

But the only closed system is the universe, since any smaller system necessarily interacts with its environment. Thus small closed systems are a ''non-physical fiction'', to use your words.No. Whenever we observe part of the universe, we observe one of the properties of the whole universe.

This is completely analogous to observing the value of an observable of a tiny physical system, which gives us only some property of the tiny system.

Since you are willing to assign observability and hence a physical state to the tiny system because you can measure some of its properties, it would only be consistent if you also grant observability and hence a physical state to the whole universe.

We can NOT observe the properties of the whole universe, at least not if GR and the cosmological standard model are not completely wrong.

Of course you are right in saying that strictly speaking there are no exactly closed systems. However there are close enough approximations. If this weren't the case it's hardly conceivable that physics in its present form could ever work. E.g., ESA or NASA can fly to a comet with sufficient accuracy pre-calculating its about 10-year journey through the solar system, using all kinds of tricks like swing-by manoevres to reach that goal. That's only possible, because the solar system is at the accuracy sufficient to fulfill this non-trivial task with sufficient accuracy "closed", i.e., all there is to be taken into account to plan and successfully conduct this space travel of the probe.

 

[A. Neumaier]

We can NOT observe the properties of the whole universe,

We know certain observable properties of the whole universe, for example its approximate age, the approximate density with which its galaxies are distributed (at least sufficiently close to ours) or that it contains a solar system with a planet called Earth on which physicists perform measurements. Or would you claim that neither is a property of the whole universe?

But then would you claim that observing the age of a person, the color of a person's hair, or the genetic composition of one of the hairs is not observing something about the whole person?

strictly speaking there are no exactly closed systems. However there are close enough approximations. If this weren't the case it's hardly conceivable that physics in its present form could ever work. E.g., ESA or NASA can fly to a comet with sufficient accuracy pre-calculating its about 10-year journey through the solar system, using all kinds of tricks like swing-by manoevres to reach that goal. That's only possible, because the solar system is at the accuracy sufficient to fulfill this non-trivial task with sufficient accuracy "closed", i.e., all there is to be taken into account to plan and successfully conduct this space travel of the probe.

But we also observe the spacecraft during its flight, proving that a system that is effectively (but not truly) closed is still observable. But then you cannot argue the following:

As soon as one measures something, the observed system isn't closed anymore, because it's interacting with the measurement device

Moreover, realistic optical quantum systems are always lossy, i.e., have a nonunitary evolution, even without any measurement. This even holds for your favorable example of realistic systems, namely bunches of particles in an accelerator. Great care is needed to ensure that the losses there are small, but even then they are not negligible. And quantum systems in the kinetic (Kadanoff-Baym) or hydrodynamic (1PI) approximation used for most detailed calculations are dissipative, too, due to the collision terms. The underlying closed system is in the latter case a system extending to spatial infinity, i.e., (a local approximatin of) the whole universe!

 

[DarMM]

Well, I don't understand, what's clear with this definition since many philosophers (and maybe also a minority of physicists) consider QM as "non-realistic". On the other hand, it's clear that QM has a very clear definition of an objective state. It's even more explicit in defining what a state is than classical mechanics, where it is supposed to be implicitly clear from the formulation of the theory (the explicit statement on a fundamental level of classical mechanics, no matter whether Newtonian or relativistic, is that a state is represented by a point in phase space). In QM a state is represented by the statistical operator and operationally as an equivalence class of preparation procedures. That's an objective notion of state since a preparation procedure is clearly defined, and in my opinion it's utmost realistic, since this definition is in terms of real-world actions on the described system (e.g., at the LHC there's a preparation of protons with a pretty well determined momentum).

However this isn't what many of us grow up thinking of and it isn't how one thinks of things in classical mechanics. Thinking of a quantum mechanical object as literally being "those measurement statistics of observables on the system given an equivalence class of methods of preparation" is very far from how people think of say a tree. So far that it has earned the name "AntiRealist", because it is entirely about how it reacts to my devices not a "narrative" about what it is like in and of itself like one has in Classical Mechanics.

Whether it should be called AntiRealist is debatable (probably not as you are not saying it isn't real or something), but it's definitely unlike the normal conception of objects. Participatory Realist is the more modern term in Quantum Foundations, as you basically consider the quantum object only in terms of its participation in interactions with our macroscopic realm and consider discussions outside that, i.e. even the mere idea of what the universe is when not observable, as meaningless.

@stevendaryl points out the right sentence here:

The notion "quantum state for the whole universe" is a non-physical fiction since there's no way to observe the "whole universe"

This isn't the case in classical mechanics, e.g. there are things the theory says are real that I can't measure, e.g. the entire velocity profile of the Triangulum galaxy down to the centimeter level. Things are posited to exist even if observation on them isn't possible. So for example, "the number of black holes in the universe" is sensible, even if I can never know it.

Several interpretations of QM would say the same (e.g. Bohmian Mechanics, MWI, Type I $\psi$-epistemic interpretations), the universe has a state, it's just I can't learn it given physical constraints.

However to say it has no state because you can't observe it eliminates QM from discussing things as they are, independent of measurement. It becomes about the statistics of observations alone and not about the reality of what is going on with these systems, hence the historical name for it.

 

[vanhees71]

We know certain observable properties of the whole universe, for example its approximate age, the approximate density with which its galaxies are distributed (at least sufficiently close to ours) or that it contains a solar system with a planet called Earth on which physicists perform measurements. Or would you claim that neither is a property of the whole universe?

But then would you claim that observing the age of a person, the color of a person's hair, or the genetic composition of one of the hairs is not observing something about the whole person?But we also observe the spacecraft during its flight, proving that a system that is effectively (but not truly) closed is still observable. But then you cannot argue the following:

Moreover, realistic optical quantum systems are always lossy, i.e., have a nonunitary evolution, even without any measurement. This even holds for your favorable example of realistic systems, namely bunches of particles in an accelerator. Great care is needed to ensure that the losses there are small, but even then they are not negligible. And quantum systems in the kinetic (Kadanoff-Baym) or hydrodynamic (1PI) approximation used for most detailed calculations are dissipative, too, due to the collision terms. The underlying closed system is in the latter case a system extending to spatial infinity, i.e., (a local approximatin of) the whole universe!

Well, we extrapolate from our pretty local observations about the universe to the whole universe by assuming the cosmological principle. So far this works pretty well, but strictly speaking, we can't ever experimentally really test it.

Of course you are right in saying that all ”closed systems” are idealizations.

 

[akvadrako]

In the MWI, what is meant by "you"? , or "I", or "me"?

In modern Copenhagen and QBism, "I" is taken for granted and the hard part is figuring out what objective universe is compatible with multiple interacting "I"s.

In MWI, the objective universe is taken for granted and we try to figure out what "I" must be to approximate our experience. That's an important part of the program. A few ideas that try to derive standard QM at the subjective level are:

1. assuming "I" is a kind of rational agent and applying decision theory (Deutsch-Wallce)
2. assuming "I" is a roughly a point on the wavefunction (dBB / many interacting worlds)
3. assuming "I" is part of a stable classical history (entangled histories)
4. ...

 

[.Scott]

<Moderator's note: Merged into this thread.>

With my limited understanding and practice with QM, I am tackling an article published in "Nature Communications" this past September regarding an analysis of a particular QM system.
Here is a link to that article:
https://www.nature.com/articles/s41467-018-05739-8

If you haven't read the article, the gist is that the result of a coin toss that favors tails drives the generation of a particle that is either |down> (for heads) or |up+down> (for tails). Given different QM calculations made from different sets of information, sometimes the original result of the coin toss can be demonstrated to be definitely heads and definitely tails at the same time. The point is that certain other basic, well-accepted assumptions are made and one of those has to be abandoned.

I have not finished my rereading/rerereading of this article, but I believe I see a problem right away - and I would like comments.

The problem I have is that the coin toss is being viewed as a QM event - but I don't think that it is being treated correctly. Basically, if you start with ($\frac{1}{3}$|heads> + $\frac{2}{3}$|tails>), as a model for a coin toss, then the very first thing you need to do is to take that state and copy it so that agent $\bar{F}$ will remember it. In fact, the notion of a coin toss is that the coin is sitting there for anyone to observe - available for arbitrary copying.

But agent $F$ isn't considering this "copy" operation in her calculations.

So here is my question:
When working with QM states (in the way that is done in this experiment), don't you need to consider when a state is "copied"? In the case of this coin toss, I don't believe there ever is a quantum state ($\frac{1}{3}$|heads> + $\frac{2}{3}$|tails>). Instead, there are other quantum states that resolve to a $\frac{1}{3}$ : $\frac{2}{3}$ ratio of a larger system (the coin). So if someone wants to consider the entire coin-toss/particle emission operation as a QM system, they would need to go back to QM conditions that led to the coin toss result.

 

[timmdeeg]

You seem to mean this discussion:

https://www.physicsforums.com/threads/quantum-theory-nature-paper-18-sept.955748/

 

[.Scott]

Would there be anything wrong with that if "dead" and "alive" were replaced by "spin up" and "spin down"? I guess not.

I would guess so. In fact, I believe this is the crux of the issue. In one case (the cat), you have a regular probability based on a lack of information. In the other case (spin) you have probabilities based on HUP. I think of it as the information carrying capacity of the particle(s).

When you are dealing with probabilities that describe a superposition of states, it is appropriate to use the wave equations. When you are dealing with unknown states, you use common statistics.

One of the things you don't need to deal with in classical unknown states is copying the information. In a coin toss, the result is available for anyone to non-destructively read. So as many copies as are needed can be made.

It is possible for QM states to "decide" a coin toss. When that happens and you want to consider the system to be a QM system, then you need to model those initial, decisive QM states - and that's not going to give you those relatively simple $\sqrt{p_{heads}}$ and $\sqrt{p_{tails}}$ terms.

To make the "coin toss" simple, consider a needle balanced on its tip. Because of HUP, it will soon fall. And you could call any fall that is mostly Northerly to be heads and anything basically Southerly to be tails. Or, for the thought experiment in question, you could break it up into 120 and 240 degree sections.

What this needle does is amplify a small HUP-style uncertainty in the location of the point of the needle relative its center of gravity. Not only is that state "read", the result is copied a many-fold. Leaving a life-size piece of evidence behind. Attempting to deal with the probability of North or South (or heads or tails) at this level is an error - because the initial quantum states have been copied and amplified. So the QM equations that model it must include those "copy operations".

 

[bhobba]

Then I'm an anti-realist ;-).

I do not thunk so - but that would take us into a deep discussion of the Ensemble Interpretation.

Thanks
Bill

 

[stevendaryl]

The problem I have is that the coin toss is being viewed as a QM event - but I don't think that it is being treated correctly. Basically, if you start with ($\frac{1}{3}$|heads> + $\frac{2}{3}$|tails>), as a model for a coin toss, then the very first thing you need to do is to take that state and copy it so that agent $\bar{F}$ will remember it. In fact, the notion of a coin toss is that the coin is sitting there for anyone to observe - available for arbitrary copying.

It's probably misleading to call it a "coin toss" it's a hypothetical quantum device that can have two different states: $|heads\rangle$ or $|tails\rangle$. Somehow, it can be initialized to be in the state: $|init\rangle = \sqrt{\frac{1}{3}} |heads\rangle + \sqrt{\frac{2}{3}} |tails\rangle$. It's assumed that everybody knows that this is the initial state. There is no copying of the state, it's just common knowledge. (You need the square-roots, because it's the square of the coefficients that give the probabilities.)

 

[stevendaryl]

I do not thunk so - but that would take us into a deep discussion of the Ensemble Interpretation.

I have never understood how the ensemble interpretation helps in understanding quantum mechanics. In classical statistical mechanics, I think it does help. You imagine a collection of systems that are macroscopically indistinguishable (same values for the macroscopic variables such as number of particles, volume, total energy, total momentum, total angular momentum, etc). But the systems differ in microsopic detail (the positions and momenta of the individual particles within the system).

But in quantum mechanics, if you don't have any "hidden variables", then a collection of systems, each of which is described by the same wave function, have nothing to distinguish them. So saying that a fraction f will be found to have some particular property seems to me to be neither more nor less meaningful than saying that a specific system has probability f of having that property. Nothing is gained by considering many, many identical systems. Or I don't see what is gained, anyway.

The only benefit that I can see --- and maybe this is the point --- is that while a pair of properties such "the z component of the spin of an electron" and "the x component of spin of that electron" can't meaningfully be said to have values at the same time, collective properties such as "the average of the z-component of the spin for the collection of electrons" and "the average of the x-component of the spin for the collection of electrons" almost commute. If the number of systems in the ensemble is $N$, then letting:

$S_z \equiv \frac{1}{N} \sum_j s_{jz}$
$S_x \equiv \frac{1}{N} \sum_j s_{jx}$

(where $s_{jx}$ and $s_{jz}$ mean the x and z components of spin for electron number $j$),

$lim_{N \rightarrow \infty} [S_z, S_x] = 0$

So the collective properties are approximately commuting, and so there is no difficulty in letting them all have simultaneous values. Then quantum mechanics becomes a realistic theory about these collective properties. However, it's hard for me to see how "average of $s_z$" can be a meaningful, objective property of the world if $s_z$ for each case isn't.

 

[zonde]

I have never understood how the ensemble interpretation helps in understanding quantum mechanics.

Ensemble interpretation is a generic hidden variable theory at least from perspective of Ballentine.
You can look up chapter "9.3 The Interpretation of a State Vector" in Ballentine's book. There he contrasts two classes of interpretations:
A) A pure state provides a complete and exhaustive description of an individual system.
B) A pure state describes the statistical properties of an ensemble of similarly prepared systems.
And then he says: " Interpretation B has been consistently adopted throughout this book,"

 

[bhobba]

Ensemble interpretation is a generic hidden variable theory at least from perspective of Ballentine.

That was true of the original 1970 paper from memory - access to the paper seems to have disappeared from the internet otherwise I could dig up the relevant bits. Remember though the original champion of the Ensemble Interpretation was Einstein who strongly believed QM was correct but incomplete. Its no wonder Ballentine may have gone down that path in his original paper on it But later versions were as for espoused for example in his textbook are agnostic to it - especially my version - the ignorance ensemble which is explained in this paper I often link to:
http://philsci-archive.pitt.edu/5439/1/Decoherence_Essay_arXiv_version.pdf

See bottom page 39.

Thanks
Bill

 

[zonde]

That was true of the original 1970 paper from memory - access to the paper seems to have disappeared from the internet otherwise I could dig up the relevant bits. Remember though the original champion of the Ensemble Interpretation was Einstein who strongly believed QM was correct but incomplete. Its no wonder Ballentine may have gone down that path in his original paper on it But later versions were as for espoused for example in his textbook are agnostic to it

I haven't seen any quotes that would show that he has changed his mind. The quotes I gave are from his 1988 book.
I found this paper https://arxiv.org/abs/1402.5689. There he says:
However, ψ-epistemic models and ψ-ontic-supplemented models remain as viable candidates. In all of those models, the cat may be either alive or dead, but the quantum state does not provide us with the information as to which is the case.
And later he writes:
(For the record, my own writings on this subject are firmly in the classes of ensemble and objective. So far, I maintain an open mind regarding ontic versus epistemic.)
Obviously ontic for him is ψ-ontic-supplemented which allows even for coherent cat to be dead or alive. So for him it's still HVs in 2014.