Entanglement swapping and Bohmian mechanics

[Demystifier]

How important is it (in Bohmian terms) to include the measurement apparatus as a factor?

It is absolutely essential. Without that you cannot explain the effective collapse of the wave function, and even more importantly, you cannot explain how it is possible to measure any other observable except the position. Furthermore, without apparatus and environment you couldn't talk about the macroscopic description, without which there would be no time arrow, so you could'n properly understand the notions of cause and effect. Finally, there would be no explanation of the macroscopic world we all see and love.

 

[Demystifier]

From @Demystifier:

Furthermore, at the macroscopic level we also have a time arrow, due to which the past causes the future, so the correlation can also be interpreted causally as
$$ (M_A,A)_2 \rightarrow (B,M_{BC},C)_3 \leftarrow (M_D,D)_2$$
Thus we see that, at the macroscopic level, we can say that the results of measurements in the past cause the result of measurement in the future.

---

OK, I follow this. And presumably if the experimental ordering were reversed, we'd have:

$(M_A,A)_2 \leftarrow (B,M_{BC},C)_3 \rightarrow (M_D,D)_2$

And the results must be the same, correct? (I know this is a simple question.)

Almost correct, my only correction is that you also have to change the labels 2 and 3 in that case, namely
$(M_A,A)_3 \leftarrow (B,M_{BC},C)_2 \rightarrow (M_D,D)_3$
because $t_2$ is before $t_3$.

 

[Morbert]

1. It's literally the definition of cherry picking. Read and quote Ma's entire paragraph. Or Megidish.

2. I am quite comfortable with my understanding of Ma, Megisdish, Hensen, Weihs, etc. I am not stuck anywhere. It is slow going getting answers to some of my questions. Here's one for you:

You keep trying to move off the point, which will just result in mistakes compounding mistakes. It is not cherry picking to point out Ma says (2) is a rewriting of (1). Do you accept what Ma says plainly? Do you accept that (2) is a rewriting of (1)?

 

[Morbert]

Re/ Bohmian mechanics and entanglement swapping: I'm finding it conceptually straightforward but computationally fiddly. Considering spin instead of photons since that's more readily NRQM-friendly: The state takes a form like $$|\Psi_0\rangle
=
|\Phi_{\mathrm{spatial}}\rangle
|\Psi^-\rangle_{12}
|\Psi^-\rangle_{34}
\otimes
\left(
\frac{1}{\sqrt{3}}
\sum_{a=x,y,z}
|a\rangle_{q_A}
\right)
\otimes
\left(
\frac{1}{\sqrt{3}}
\sum_{b=x,y,z}
|b\rangle_{q_B}
\right)
\otimes
|A_0\rangle
|B_0\rangle
|V_0\rangle
$$where $q_A$ and $q_B$ are QRNGs modeling Alice's and Bob's choice of measurement axes, and $|A_0\rangle, |B_0\rangle,|V_0\rangle$ are the apparatuses. The Bohmian configuration is $$
Q_0
=
\left(
\mathbf{Q}_1,
\mathbf{Q}_2,
\mathbf{Q}_3,
\mathbf{Q}_4,
Q_{q_A},
Q_{q_B},
Q_A,
Q_B,
Q_V
\right)$$The Bohmian guidance equation will then give us trajectories and hence the data read off from the apparatuses including all observed correlations reported in these experiments.

The work seems to be in actually constructing the toy configuration space to model the essentials.

 

[javisot]

I agree that as a mathematical exercise

At the end of the day, what do "post" and "pre" mean in a context where there is no inherent order?

 

[javisot]

It is absolutely essential. Without that you cannot explain the effective collapse of the wave function, and even more importantly, you cannot explain how it is possible to measure any other observable except the position. Furthermore, without apparatus and environment you couldn't talk about the macroscopic description, without which there would be no time arrow, so you could'n properly understand the notions of cause and effect. Finally, there would be no explanation of the macroscopic world we all see and love.

It is a profound and intriguing idea, it is like using the macroscopic description as an arrow of time for QM.

 

[Roberto Pavani]

It is a profound and intriguing idea, it is like using the macroscopic description as an arrow of time for QM.

Still, Maxwell's equations do not require an arrow of time

 

[javisot]

Still, Maxwell's equations do not require an arrow of time

Or, as in GR, we can impose conditions that lead to a certain arrow of time, but in essence, the field equations are symmetric under time reversal.

 

[Lord Jestocost]

I am interested in an answer in terms of your own preferred interpretation. You don't need to tell me what interpretation it is (or you can - your call). I just want to know your opinion.

I guess you will get no satisfactory answer.

All interpretations of quantum theory (QT), Bohmian mechanics is no exemption, use Born’s rule for the calculation of probabilities for observable outcomes of physical experiments and use all other standard links between the mathematical formalism of QT and the physical phenomena. One can find the essential rules of QT in https://www.physicsforums.com/insights/the-7-basic-rules-of-quantum-mechanics/.

All interpretations of QT agree by construction with QT as far as its experimentally testable physical aspects are concerned and can thus deliver nothing new regarding physics or physical experiments. Therefore, using the title of a paper by Christopher A. Fuchs and Asher Peres: Quantum Theory Needs No ‘Interpretation’ (Christopher A. Fuchs and Asher Peres, Physics Today 53 (3), 70–71 (2000)).

To my mind, the relevant question regarding physics would thus merely be: Does one accept the fundamentally probabilistic world view of QT or not?

 

[Morbert]

I guess you will get no satisfactory answer.

A basic level of understanding of quantum theory is needed for any kind of advancement of the discussion. Fundamentally misunderstanding basic quantum theory has gummed up discussions before. There, @DrChinese denies an even more basic expansion |HH⟩ = (|Φ+⟩ + |Φ-⟩)/√2

 

[Demystifier]

It is a profound and intriguing idea, it is like using the macroscopic description as an arrow of time for QM.

The existence of the arrow of time is a matter of statistical physics, either classical or quantum. To see how that works in QM from a Bohmian point of view, see my https://arxiv.org/abs/2308.10500
especially Sec. 5.3.