Entanglement and FTL signaling in professional scientific literature

[PeterDonis]

There is no variable from the entangled state (other than I guess a selection of type of conservation rule) that is a part of the quantum expectation value.

Yes, there is: the relative amplitudes of the terms in the entangled state. The only reason this doesn't appear in Bell's papers is that Bell assumed a particular entangled state (the singlet state) for which the ratio of amplitudes (or more precisely its squared modulus) is $1$ so it drops out of the formulas. But if we consider all possible entangled states of two qubits, the relative amplitudes of the terms in the particular entangled state we prepare will certainly contribute to the expectation value.

 

[vanhees71]

The "microcausality constraint" is that spacelike separated measurements must commute. That doesn't rule out a "mutual influence" altogether; it just means that any such "influence" cannot depend on the order in which the measurements occur. Some might say that rules out any "influence" at all, but others might disagree.

It rules out causal connections between space-like separated events, because the time evolution in the Heisenberg picture is described by the equation of motion,
$$\partial_t \hat{O}(x)=\frac{1}{\mathrm{i}} [\hat{O(x)},\hat{H}],$$
where
$$\hat{H}=\int_{\mathbb{R}^3} \mathrm{d}^3 y \hat{\mathcal{H}}(t_y,\vec{y}).$$
Plugging this in the said equation of motion together with the microcausality constraint, which by construction holds particularly for the commutators of any local observable and the Hamilton density, the only contribution in the time evolution can come from arguments $x$ and $y$ that are light-like or time-like separated. Thus the commutation at space-like distances rules out causal actions over space-like separated events.

It's of course also true that the measurement results, including the correlations between local measurements at time-like separated measurement events, are not "time ordered" in any sense. You can always find an inertial frame, where the measurements are completed simultaneously. The temporal order of space-like separated events is frame-dependent, and that's why they cannot be causally connected by definition, and that's why one assumes the microcausality constraint and last but not least that's why it's called microcausality contraint.

 

[PeterDonis]

the only contribution in the time evolution can come from arguments and that are light-like or time-like separated

What "time evolution" are we talking about? It looks to me like this concept in QFT as you are describing it is frame-dependent.

 

[DrChinese]

Yes, there is: the relative amplitudes of the terms in the entangled state. The only reason this doesn't appear in Bell's papers is that Bell assumed a particular entangled state (the singlet state) for which the ratio of amplitudes (or more precisely its squared modulus) is $1$ so it drops out of the formulas. But if we consider all possible entangled states of two qubits, the relative amplitudes of the terms in the particular entangled state we prepare will certainly contribute to the expectation value.

Who cares if you *can* add variables in, that's a red herring. Bell tests don't do that! Reference:

https://arxiv.org/abs/quant-ph/9810080

"In a rather general form the CHSH inequality reads S(α, α′ , β, β′ ) = |E(α, β) − E(α ′ , β)| + +|E(α, β′ ) + E(α ′ , β′ )| ≤ 2. Quantum theory predicts a sinusoidal dependence for the coincidence rate C_qm++(α, β) ∝ sin2 (β − α) on the difference angle of the analyzer directions in Alice’s and Bob’s experiments."

I don't see anything other than settings for Alice and Bob. According to theory, and as far as can be determined from all experiments ever run: every individual entangled pair used in a Bell test is 100% identical in all respects to every other pair. This is canon. You'd have to agree with this, and as such, we are right back to where I started. Only Alice and Bob's settings matter. (And yes of course, you must be operating on entangled pairs - I am not questioning that particular point.)

 

[PeterDonis]

Who cares if you *can* add variables in, that's a red herring.

I'm not talking about "adding variables". An entangled state of two qubits will have at least two terms, and those terms will have relative amplitudes that have physical meaning. Those "variables" are already there. There's no need to "add" anything.

Bell tests don't do that!

Bell test experiments and theoretical discussions, including the paper you reference, are all done using only a very limited number of all of the possible entangled states of the qubits involved. Those states, as I've already said, are constructed so the amplitudes of all the terms (or more precisely their squared moduli) are equal, so their ratios are $1$ and drop out of the formulas. That doesn't mean those "variables" aren't there; it just means the experiments and theoretical discussions are focused on particular states where those "variables" drop out of the formulas.

I don't see anything other than settings for Alice and Bob.

Of course not, because you're looking at the formula for states where all of the amplitudes of the terms are equal so their ratios drop out of the formulas.

If you want to see what happens when the amplitudes of the terms are not equal, try doing a similar analysis to the one that predicts violations of the CHSH inequality, but for this state:

$$
\ket{\Psi} = \sqrt{\frac{1}{3}} \ket{H}_1 \ket{V}_2 + \sqrt{\frac{2}{3}} e^{i \varphi} \ket{V}_1 \ket{H}_2
$$

 

[DrChinese]

Of course not, because you're looking at the formula for states where all of the amplitudes of the terms are equal so their ratios drop out of the formulas.

If you want to see what happens when the amplitudes of the terms are not equal, try doing a similar analysis to the one that predicts violations of the CHSH inequality, but for this state:

$$
\ket{\Psi} = \sqrt{\frac{1}{3}} \ket{H}_1 \ket{V}_2 + \sqrt{\frac{2}{3}} e^{i \varphi} \ket{V}_1 \ket{H}_2
$$

Yes, you COULD run an experiment where there is a mismatch between the terms and the outcomes are not balanced (more likely to be V than H or vice versa). So what? This has absolutely nothing to do with what is being discussed in this thread - nor anything to do with attempting to isolate what contributes to the theoretical quantum expectation value. What you are doing is going in the opposite direction from actual tests: we wish to factor out things like outside noise, source or detector inefficiency, distinguishability, any contribution other than the purest of entangled states; so we have the opportunity to locate any hypothetical deeper explanation for observed statistics.

As we do that, the settings of Alice and Bob are all that remain as inputs. Nothing else seems to matter, and we get that from theory as well as experiment. Again: every individual entangled pair used in a Bell test is 100% identical in all respects to every other pair (as far as we know, and as far as QM predicts). There is no suspected difference that satisfactorily accounts for, contributes to, or otherwise explains the outcomes of one trial run versus any other. Alice's individual results appear completely random, as do Bob's. And yet when Alice and Bob compare results when observing at identical settings, their results are perfectly synchronized. I have no idea why you would debate this point. This is all standard, we should be in complete agreement.

 

[PeterDonis]

This has absolutely nothing to do with what is being discussed in this thread

I think this is a matter of opinion. You are of course free to ignore what I'm posting if you think this.

nor anything to do with attempting to isolate what contributes to the theoretical quantum expectation value

This is obviously false since if we do consider other entangled states, the relative amplitudes of the terms certainly will contribute to the theoretical quantum expectation value. The fact that experiments to date and the literature in general has not considered such states does not mean they don't exist.

we wish to factor out things like outside noise, source or detector inefficiency, distinguishability, any contribution other than the purest of entangled states

I understand that this is why experiments to date and the literature in general have focused on particular entangled states like the singlet state. And if you had limited your claim about what "contributes" to the expectation value to those states, that would have been fine. But you didn't. As a fully general claim about an arbitrary entangled state, your statement that the entangled state itself does not contribute to the quantum expectation value is simply false. That's why I objected to it.

 

[vanhees71]

What "time evolution" are we talking about? It looks to me like this concept in QFT as you are describing it is frame-dependent.

It is not because of the microcausality condition! That's another reason for assuming it.

 

[PeterDonis]

It is not because of the microcausality condition!

The equations you wrote down are written in some particular frame; that's where the $t$ in the first equation and the $\mathbb{R}^3$ that is integrated over in the second come from.

Is the idea that the microcausality condition ensures that these equations are valid regardless of what frame you pick?

 

[vanhees71]

I'm not talking about "adding variables". An entangled state of two qubits will have at least two terms, and those terms will have relative amplitudes that have physical meaning. Those "variables" are already there. There's no need to "add" anything.Bell test experiments and theoretical discussions, including the paper you reference, are all done using only a very limited number of all of the possible entangled states of the qubits involved. Those states, as I've already said, are constructed so the amplitudes of all the terms (or more precisely their squared moduli) are equal, so their ratios are $1$ and drop out of the formulas. That doesn't mean those "variables" aren't there; it just means the experiments and theoretical discussions are focused on particular states where those "variables" drop out of the formulas.Of course not, because you're looking at the formula for states where all of the amplitudes of the terms are equal so their ratios drop out of the formulas.

If you want to see what happens when the amplitudes of the terms are not equal, try doing a similar analysis to the one that predicts violations of the CHSH inequality, but for this state:

$$
\ket{\Psi} = \sqrt{\frac{1}{3}} \ket{H}_1 \ket{V}_2 + \sqrt{\frac{2}{3}} e^{i \varphi} \ket{V}_1 \ket{H}_2
$$

When dealing with photons or other relativistic particles we should rather write this as
$$\ket{\Psi} = \left [\sqrt{\frac{1}{3}} \hat{a}^{\dagger}(\vec{p}_1,H) \hat{a}^{\dagger}(\vec{p}_2,V) + \sqrt{\frac{2}{3}} \exp(\mathrm{i} \varphi) \hat{a}^{\dagger}(\vec{p}_1,V) \hat{a}^{\dagger}(\vec{p}_2,H) \right] \ket{\Omega},$$
where $\ket{\Omega}$ is the vacuum state. This ensures that we take into account properly the Bose properties of photons.

 

[vanhees71]

The equations you wrote down are written in some particular frame; that's where the $t$ in the first equation and the $\mathbb{R}^3$ that is integrated over in the second come from.

Is the idea that the microcausality condition ensures that these equations are valid regardless of what frame you pick?

Imposing the equal-time commutation relations of canonical quantization in one frame together with Poincare covariance implies the microcausality condition and ensures the Poincare covariance of observables. For a very thorough discussion of all this, see

A. Duncan, The conceptual framework of quantum field
theory, Oxford University Press, Oxford (2012).

 

[Fra]

A: There is no variable from the entangled state (other than I guess a selection of type of conservation rule) that is a part of the quantum expectation value. Further, Bell ruled out predetermined elements of the superposition/entanglement as being an explanation of the outcome statistics. That only leaves things that happen from the first measurement to the second measurement (and regardless of order or reference frame) as being part of the mechanism we wish to understand. That's the time during which we go from an entangled 2 particle system to 2 systems of 1 particle.

I think the likely reason for Bells ansatz is that he is not just trying to see if some sort of hidden variable, can explain the correlation within the context of some causal quantum mechanisms, but he is implicitly trying to recover full determinism.

Bell rules out hidden variables that (if known) in principles recovers determinism of the probabilities, and explain statistic as averaging over classical actions.

But Bell does not rule out hidden variables that account for correlation, where the probabilities involve non-classical actions, ones that does not lend themselves to be indexed by a hidden variable that can in principle be sampled. Such hidden variables are stranger to conceptualize as they are not of ignorance type? Conceptually I think of this as information shared only between the two entangled system. So if you would have an hypothetical "inside observer" as one of the entangled parts, this would be observable by it, but not by external observers. The external observer sees just the "entangled system" as one unit. A theory of this sort is not excluded by Bell. Of course this is essentially what QM is, but the difference is that we do not understand QM in this way, or at all! That is essentially my only point.

The idea that there is some stuff going on between A and B, between their observations seems to be the direction you entertain. But it seems very strange to me, to the point that I don't understand the vision.

/Fredrik

 

[vanhees71]

I'd rather say, Bell rules out the assumption that all observables of a system always take determined values, i.e., that the values of observables are deterministic. The quantum state is "deterministic" also in QT in the sense that for a given initial state at time $t_0$ and given the Hamiltonian of the system, the state is determined at any later time $t$. The indeterminism of the observables comes from the probabilistic meaning of the quantum states in standard QT.

What's for sure is that, within microcausal relativistic QFT, there is not "going on some stuff" between A and B, if A and B are spacelike separated.

 

[Fra]

I'd rather say, Bell rules out the assumption that all observables of a system always take determined values, i.e., that the values of observables are deterministic. The quantum state is "deterministic" also in QT in the sense that for a given initial state at time $t_0$ and given the Hamiltonian of the system, the state is determined at any later time $t$. The indeterminism of the observables comes from the probabilistic meaning of the quantum states in standard QT.

What's for sure is that, within microcausal relativistic QFT, there is not "going on some stuff" between A and B, if A and B are spacelike separated.

I was going to object at first, but then I realized that by "observables" having "determined values" you probably mean that it can be communicated into the classical domain, be poincare invariants, and become "common knowledge" and shared. Then I agree.

But I entertained the concept of a different kind of HV, something that is not "observable" in the sense of QFT, but still having all the standards of that they have been inferred and encoded. It's just similar to that I can KNOW something that you do not, and vice versa. But my actions are independent of what YOU know, and your actions are independent of what I Know - regardless of wether the information is correct or not. So all the locality is built in the hard way. But not not referencing 3Dspace, but some "information"space. ie. two observers are at the same point iff they have the same information, which would make them indistinguishable. In this sense, certain HV can have determined values with respect to the entangled parts itself, but not to anyone else. That isn't ruled out by bells theorem, because it makes not sense to partition the interaction based one someone elses decomposistion. It's a invalid mixing of inference elements as I see it. As far as I understand Demystifier, this seems a similar concept as what he called solipsist HV. I am not at all in line with that bohmian stuff, but I just find the conceptual analogy interesting.

My point is that these "solipsist HV", does not have the same causal role as the "ignorance type HV", their determinsation are not "classical knowledge" that is averaged out, or "ignored". But they can still serve as as conceptual explanation of that the correlation is defined when the entangled pair is created. But it does not mean that the physics as the detector can be paritioned as ignorance action sum.

/Fredrik

 

[vanhees71]

I think that the idea of "hidden variables" is that they are not observable but determine the values of the observables and are themselves determined, and we just cannot know their values (for whatever reasons) and thus treat them probabilistically. The strength of Bell's argument, of course, is that the conclusion that such a deterministic and local theory contradicts the probabilistic predictions of QT for entangled states and specific measurements, is independent of the concrete probabilities (or probability distributions) one assumes for these hidden variables.

 

[Fra]

I think that the idea of "hidden variables" is that they are not observable but determine the values of the observables and are themselves determined, and we just cannot know their values (for whatever reasons) and thus treat them probabilistically.

While this describes well the "naive causality" we are used to and the historical reasoning around this. The idea comes out as irrational from the perspective of inference as I see it:

If observables are determined by hidden variables, it means there exists a deductive scheme for this.
To rationally beeing able to abduce this deductive scheme in the first place, we must be able to "observe" the hidden variables and the observables to find the rule but fitting data. But now we can not do so because we somehow can not observe these hidden variables, perhaps because nature physically limits our inference. IF this is the case, there is not rational empirical justification (within the inference) for expecting the existence of this deductive rule? ie. this idea appear irrational.

The only way this can make any sense is if we actually CAN observe the hidden variables (but don't due to our ignorance or because we CHOOSE to average them out).

/Fredrik

 

[vanhees71]

While this describes well the "naive causality" we are used to and the historical reasoning around this. The idea comes out as irrational from the perspective of inference as I see it:

One should also clearly destinghish between "causality" (be it naive or not) and "determinism":

Causality means that if you know the state of a system at all times $t<t_0$, then the state of the system is known (can in principle be calculated) uniquely at all times $t>t_0$. On the fundamental level, we even have a stronger kind of causality, because it's sufficient to know the state of the system at one point $t=t_0$ to know the state at all later times $t>t_0$.

Determinism means that all physical observables always take precise values. That's the case for classical physical theories, be it for discrete (point-particle mechanics) or continuous observables (fields). In deterministic theories the state is described by the determined values of the observables, within classical theories there's no need to distinguish between causality and determinism, because both together mean that when knowing the values of all observables (or of all independent observables, out of which all other observables can be calculated using well-defined functions) at all times $t \leq t_0$, one also knows the values of all observables at all later times $t>t_0$. On a fundamental level (Newtonian or relativistic point-particle mechanics, classical electrodynamics) again the stronger "time-local" initial condition is sufficient.

I think the big quibble for the physicists at the time when modern QT has been discovered, leading to Born's probabilistic interpreation of the quantum state, indeed was that now one had a causal theory but indeterminism, i.e., the state of a system does not imply the determinism of all observables and even more, the impossibility to prepare the system in any state, where all observables take determined values (Heisenberg's uncertainty relations).

If observables are determined by hidden variables, it means there exists a deductive scheme for this.

This would have to be worked out in detail, if there were any necessity for it, but to the contrary it's not necessary, because quantum theory turned out to describe all phenomena correctly. This also implies that it is impossible to find out, within "local realistic HV theories" how such a deductive scheme should look like, i.e., there's no way to empirically get hints for building a concrete model (and be it "only" probabilistic!) nor is there the possibility to empirically test any given such model.

To rationally beeing able to abduce this deductive scheme in the first place, we must be able to "observe" the hidden variables and the observables to find the rule but fitting data. But now we can not do so because we somehow can not observe these hidden variables, perhaps because nature physically limits our inference. IF this is the case, there is not rational empirical justification (within the inference) for expecting the existence of this deductive rule? ie. this idea appear irrational.

Precisely! There's no need for hidden variables and their meaning and behavior cannot be empirically tested. As with the aether of the 19th century with the discovery of (special) relativity, it's more economic and much simpler, to simply say "hidden variables don't exist".

The only way this can make any sense is if we actually CAN observe the hidden variables (but don't due to our ignorance or because we CHOOSE to average them out).

/Fredrik

That's indeed what was behind this idea of hidden variables: It's as with classical statistical physics. We use statistical descriptions only to describe some coarse-grained "macroscopic observables" as "averages over a lot of microscopic observables", we cannot resolve anyway (neither theoretically in our models nor by observations).

 

[Fra]

I agree with all except...

One should also clearly destinghish between "causality" (be it naive or not) and "determinism":

Yes, that is exactly what I try todo as well.

Causality means that if you know the state of a system at all times $t<t_0$, then the state of the system is known (can in principle be calculated) uniquely at all times $t>t_0$. On the fundamental level, we even have a stronger kind of causality, because it's sufficient to know the state of the system at one point $t=t_0$ to know the state at all later times $t>t_0$.

This sounds like some stronger causal determinism to me? By causality I mean that the future depends on the past(lightcone) as per some sort of logic/scheme(not necessarily deductive), and NOT on some ad hoc stuff. The past can induce a probability distribution of the future, I think of that as causality as well.

(As a reference: In my agent interpretation, I take causality to mean the action of the agent depends on (but is not deductively determined by) it's current state, meaing it responds to what it is informed about only. Locality supposedly follows from the same principles, once spacetime emerges, but causality is more fundamental than locality)

Determinism means that all physical observables always take precise values. That's the case for classical physical theories, be it for discrete (point-particle mechanics) or continuous observables (fields). In deterministic theories the state is described by the determined values of the observables, within classical theories there's no need to distinguish between causality and determinism, because both together mean that when knowing the values of all observables (or of all independent observables, out of which all other observables can be calculated using well-defined functions) at all times $t \leq t_0$, one also knows the values of all observables at all later times $t>t_0$. On a fundamental level (Newtonian or relativistic point-particle mechanics, classical electrodynamics) again the stronger "time-local" initial condition is sufficient.

For me "determinism" is equivalent to "deductive causation". Ie. a unique initial condition leads always to a unique future state. Ie. the whole timehistory is just "one" piece of information. Also as you say, in this scheme, the notion of "causation" becomes meaningless as everything is determined, so there is not really any way to "explain" mechanisms. (the ultimately consistent view here would lead to superdeterminism which I find irrational for other reasons)

As you wrote yourself, if one considers individual events, then QM is indeterministic. But as the "state" in QM is "probabilistic", and evolves deterministically its still deterministic in that sense, and it's how I view it.

I personally don't think of HUP as implying "indeterminism". As the conjugate variables are not commuting, they are not even by construction supposed to be known at the same time, that is the whole point of them beeing conjugate and I see them as different ways to encode the same information. No one would even ask why we can not know the frequency and the time at the same time. How come these conjugate codes are utilized by nature, is one of the things remaining to be understood in terms of some choice of paradigm (my choice is physical inference, others like geometry or other things). It's part of the quest for causal mechanism. But when I say that I do not mean searching for determinism. Then there has probably been a big misunderstandings in plenty of past threads?

/Fredrik

 

[vanhees71]

I agree with all except...

Yes, that is exactly what I try todo as well.

This sounds like some stronger causal determinism to me? By causality I mean that the future depends on the past(lightcone) as per some sort of logic/scheme(not necessarily deductive), and NOT on some ad hoc stuff. The past can induce a probability distribution of the future, I think of that as causality as well.

Sure, that's why QT is perfectly causal. The state is represented by the statistical operator, which can be computed given the initial condition at $t=t_0$ at any later time $t>t_0$ (note that we have the stronger case that you don't know the entire history but only the state at one point in time $t_0$).

(As a reference: In my agent interpretation, I take causality to mean the action of the agent depends on (but is not deductively determined by) it's current state, meaing it responds to what it is informed about only. Locality supposedly follows from the same principles, once spacetime emerges, but causality is more fundamental than locality)

It's not so clear to me, what you mean by "agent".

For me "determinism" is equivalent to "deductive causation". Ie. a unique initial condition leads always to a unique future state. Ie. the whole timehistory is just "one" piece of information. Also as you say, in this scheme, the notion of "causation" becomes meaningless as everything is determined, so there is not really any way to "explain" mechanisms. (the ultimately consistent view here would lead to superdeterminism)

I think this coincides with what I tried to say. However, I don't know what you mean by "explain mechanisms".

As you wrote yourself, if one considers individual events, then QM is indeterministic. But as the "state" in QM is "probabilistic", and evolves deterministically its still deterministic in that sense, and it's how I view it.

The state in QM provides the probabilities for the outcome of measurements. QM is indeterministic, because not all observables can take determined values. Only compatible observables can take determined values when the system is prepared in a corresponding state. If you choose a complete set of compatible observables, then the state is a unique pure state, and that's a state of "complete information", but still this "complete information" does not mean that all observables take determined values.

I personally don't think of HUP as implying "indeterminism". As the conjugate variables are not commuting, they are not even by construction supposed to be known at the same time, that is the whole point of them beeing conjugate and I see them as different ways to encode the same information.

That's also not entirely true. There can be states, where non-commuting observables have determined values. E.g., if you have $J=0$ all components of the angular momentum take the determined value $0$ although the components don't commute. The information (state) about the system is not "encoded" in the values of observables uniquely but in the statistical operator.

No one would even ask why we can not know the frequency and the time at the same time. How come these conjugate codes are utilized by nature, is one of the things remaining to be understood in terms of some choice of paradigm (my choice is physical inference, others like geometry or other things). It's part of the quest for causal mechanism. But when I say that I do not mean searching for determinism. Then there has probably been a big misunderstandings in plenty of past threads?

Frequency (energy) and time are a very bad example since time is not an observable in quantum mechanics, and the "uncertainty relation" between time and energy has a different meaning than the Heisenberg uncertainty relation for observables. See Appendix B in

https://arxiv.org/abs/2207.04898

 

[PeterDonis]

In my agent interpretation

Please be advised that personal theories and interpretations are off limits. Even in the QM interpretations forum (which this is not), only interpretations that appear in the published literature can be discussed.

 

[Morbert]

Huh? That scenario, like all of the scenarios discussed in that chapter, is about a measurement on a single particle. None of them are about measurements on entangled pairs of particles.

Even if we leave that aside, the only scenario that even discusses counterfactuals where a measurement that is made in the "actual" world is not made in a counterfactual world is the one shown in equation 19.14.

Consider the scenario: A particle pair is prepared in the state $\frac{1}{\sqrt{2}}(|x_1^+x_2^+\rangle + |x_1^-x_2^-\rangle)$ and one particle is given to Alice and Bob each (subscripts $a$ and $b$ will denote alice and bob respectively). Bob always measures spin-x of his particle with his apparatus $X_b$. Alice either measures spin-x of her particle with her apparatus $X_a$, or she performs no measurement by swinging her apparatus out of the way (we'll denote the apparatus in this state with the symbol $N_a$).

The question we want to answer: "Bob and Alice measure their particles and obtain the respective spin-x = up results $x_a^+,x_b^+$. Would Bob have definitely obtained the same result if Alice had instead swung her apparatus out of the way?"

To build an appropriate family of histories, we'll consider three times $t_1,t_2,t_3$. We have a history space $\mathcal{H}_{t_1}\otimes\mathcal{H}_{t_2}\otimes\mathcal{H}_{t_3}$ with identity operator $I_{t_1}\otimes I_{t_2}\otimes I_{t_3}$.

At $t_1$ we consider assertions about the spin-x of Bob's particle. It has spin up or down so we projectively decompose the identity into these two possibilities $\left\{[x_b^+]_{t_1}\otimes I_{a,t_1},[x_b^-]\otimes I_{a,t_1}\right\}$ where $I_a$ denotes the identity operator on the space of Alice's particle.

At $t_2$, Alice's apparatus is in position ($X_a^0$) or it isn't ($N_a$), so we use the decomposition $\left\{[X_a^0]\otimes I_{b,t_2},[N_a]\otimes I_{b,t_2} \right\}$

At $t_3$ we account for the measurement outcomes appropriate for each history. We end up with the support
$$\left\{\begin{array}{lll}
\left[x_b^+\right]_{t_1}&\otimes&\left\{\begin{array}{lll}\left[X_a^0\right]_{t_2}&\otimes&\left[X_a^+,X_b^+\right]_{t_3}\\
&&\\
\left[N_a\right]_{t_2}&\otimes&\left[X_b^+\right]_{t_3}\end{array}\right.\\
&&\\
\left[x_b^-\right]_{t_1}&\otimes&\left\{\begin{array}{lll}\left[X_a^0\right]_{t_2}&\otimes&\left[X_a^-,X_b^-\right]_{t_3}\\
&&\\
\left[N_a\right]_{t_2}&\otimes&\left[X_b^-\right]_{t_3}\end{array}\right.
\end{array}\right.$$
I have suppressed the identity operators $I_a,I_b$ in the above notation to make it more readable. We use this support to navigate counterfactual reasoning described in chapter 19 of consistent quantum theory. Bob and Alice have both measured spin-x = up, meaning we are on the top branch of this support. If we pose the counterfactual of Alice deciding not to measure her particle, we go backwards to $t_2$ and pivot to that alternative, the 2nd branch, and see that Bob still would have obtained the same result.

To paraphrase Murray Gell-Mann here

"People say, loosely, crudely, wrongly, that Alice's measurement does something to Bob's particle. It doesn't. Alice measuring her particle and not measuring her particle happen on different branches of history, decoherent with each other, only one of which occurs."

 

[PeterDonis]

If we pose the counterfactual of Alice deciding not to measure her particle, we go backwards to $t_2$ and pivot to that alternative, the 2nd branch, and see that Bob still would have obtained the same result.

Yes, but that's because you picked the ordering of what to specify to make that result come out. Changing the ordering would change the result. Your ordering is equivalent to claiming that Bob's particle has a definite spin before Alice chooses whether or not to make her measurement. But what justifies that claim?

 

[vanhees71]

Nothing. If the particles are in a Bell state, the single-particle properties are maximally indetermined, i.e., their "reduced state" is a state of maximum entropy. E.g., if you have spin-1/2 particles, then Bob will simply measure ideally unpolarized particles, no matter what Alice does with her particle. If Alice doesn't measure anything, you also cannot choose subensembles from the measurement protocols taken by both experimenters, and you can never observe that the two particles were prepared in an entangled state. It's a trivial example for the rule that in quantum theory you describe experiments which are really done, and speculating about what might have been measured but isn't really measured either leads to confusion or it's something trivial.

 

[Fra]

The only "probabilities" that I think are physically intereting are the expectations (ie the optimally infered probability for it's future observations) any given specificed observer can make, from the information it has.

As soon as one starts to mix and filter collected "classical data" post-mesaurement from different observers, one gets a descriptive probability, but one that does not correspond to and expectation having the normal form. So what are we supposed to compare it with? This only makes confusion.

As long as we stick to one observer, the expectations post-measurement, should be consistent with the post-measurement descriptive probability (statistics). But when one started to mix and filter data post-measuremnet, there is nothing to level it against?

/Fredrik

 

[vanhees71]

Then you cannot make coincidence measurements, or what? It doesn't make sense to forbid experimentalists to measure whatever they want for some strange philosophical reason. It's the obligation of theory to describe all kinds of experiments, including coincidence measurements on subsystems of an entangled system.

 

[Fra]

Sure you can, but then one needs to note which observer has the expectations and which one makes the observations. Then it might be nether bob nor alice but a third observer which is also informes about the original prepararion.

My only point is that while i did not follow morbert logic it looks like what ia common elsewher one one makes strange combinations of observers and arrives at unnevessary weirdness.

/Fredrik

 

[vanhees71]

I don't understand, which problem you are discussing. You just have two detectors at far-distant places which store their setup and measurement results with accurate timestamps. Then you use the collected data of both detectors to investigate correlations between these measurements. There's no problem whatsoever with this.

 

[Morbert]

Yes, but that's because you picked the ordering of what to specify to make that result come out. Changing the ordering would change the result. Your ordering is equivalent to claiming that Bob's particle has a definite spin before Alice chooses whether or not to make her measurement. But what justifies that claim?

So long as both sets of histories are consistent, a consistent histories interpretation of quantum theory won't privilege one set as more valid than another, and so long as a set is indeed consistent, microscopic properties of particles can be considered, independent from whether or not they are measured.

We might say my ordering, because it considers microscopic properties of Bob's particle prior to choice of measurement, is a "sharper" set (Consistent quantum counterfactuals) (arxiv) i.e. a more fine-grained set and so we would expect more extended inferences to be possible. Though there is an interesting exchange between Griffiths and Stapp about counterfactuals concerning a slightly more complicated iteration of the EPR experiment, where a counterfactual is derived or not depending on a choice from two equally fine-grained sets (Quantum counterfactuals and locality) (arxiv)

 

[Fra]

I don't understand, which problem you are discussing. You just have two detectors at far-distant places which store their setup and measurement results with accurate timestamps. Then you use the collected data of both detectors to investigate correlations between these measurements. There's no problem whatsoever with this.

Well I am not sure I understood the problem discussed in post#266 either or if i misinterpreted it, but I it was what my comment had in mind.

An observer is of course free to gather data from past measured and recorded results from the classical domain, even those mixing different times and recordings from distributed locatations, and compute any correlation measures, but I question to what deductions you can make from such "scores" regarding causality and locality in particular becuase it tends to blur the proper sequence of inference IMO. I think it is easier if you pay close attentation to the "original observers", and how the information between different observers are "communicated". In a way the whole classical environment is often considered part of the observer, as its where the presumed irreversible pointes are store. This is where I think one enters gray area of the foundations, and it's easy to loose track of the arguments here when considers a "fact" definitive, as soon as it is recorded in the classical domain, because it makes the "observer" context delocalized in the first place. (This is one motivator why I think the QM foundations are problematic, and this is probably what allows for "interpretations" where once chooses stranges stances)

Then Morbert posted a link in #273 to Griffith's paper, and he questions the validity of various conclusions on causality or locality based on the counterfactual arguments, which relates to my point.

Quantum Counterfactuals and Locality​

"Henry Stapp [1] has challenged an argument by the author [2, 3] which claims to demonstrate that
quantum mechanics is a local theory, in the sense that it contains no long-range dynamical influences. Stapp
asserts that the validity of a certain counterfactual statement
...
Our major disagreement is over the conclusions which can be drawn from these analyses. Stapp believes
that because he has identified a framework which properly corresponds to his earlier argument for nonlocal
influences
...
is my opinion, he has only demonstrated the hazards involved in trying to use this mode of counterfactual
reasoning to reach sound conclusions about the quantum world."
-- https://arxiv.org/abs/0908.2914

From a quick skimming I side with Griffiths here. The main point beeing that the conterfactual arguments are questionable. Thich was essentially my point as well.

(I don't disagree with any of your last few post though)

/Fredrik

 

[PeterDonis]

So long as both sets of histories are consistent, a consistent histories interpretation of quantum theory won't privilege one set as more valid than another

Which means that consistent histories is useless for answering counterfactual questions like the one we've been discussing, since it does not give a unique answer but multiple answers.

 

[Morbert]

Which means that consistent histories is useless for answering counterfactual questions like the one we've been discussing, since it does not give a unique answer but multiple answers.

Consistent histories is useless for answering counterfactual questions like the ones we've been discussing only if you adopt the position that counterfactual questions, made sufficiently precise, always have unique answers. Instead, the usefulness consistent histories offers is in the way it let's us reason consistently about counterfactuals from whatever propositions we are willing to include.

Both the original family I presented and the reordering you propose are consistent sets of histories, defining domains for which classical reasoning is valid from their respective premises. If we want to premise our reasoning on orthodox traditions in quantum mechanics where microscopic properties are only asserted in the context of their imprinting on classical apparatus, then we will use sets where microscopic properties are considered only after their measurement. If we want to premise our reasoning on the idea that classical apparatus reveal pre-existing microscopic properties, as Robert Griffiths does, at least in his early presentations of quantum theory, then we can use the set I posted.

"None of this should be taken to imply that the study of counterfactual reasoning in the quantum domain
is impossible or uninteresting or must always lead to ambiguous results. Instead, it is a tool that needs to
be used carefully, with full recognition of its ambiguities" -- Robert Griffiths

 

[PeterDonis]

Consistent histories is useless for answering counterfactual questions like the ones we've been discussing only if you adopt the position that counterfactual questions, made sufficiently precise, always have unique answers.

If they don't have unique answers, then it seems pointless to ask them in the first place. In any case, this is getting into interpretation territory, which is off limits in this forum; it should be discussed, if further discussion is desired, in a separate thread in the interpretations subforum.