Quantum theory - Nature Paper 18 Sept

[.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.