I Quantum theory - Nature Paper 18 Sept

[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.