A Understanding Barandes' microscopic theory of causality

[pines-demon]

Barandes argues that Bell's principle of local causality relies on a definition of common cause that is too narrow. Specifically, Bell's principle of local causality assumes common causes must take the form of "Reichenbachian variables". E.g. If two variables A and B are correlated, but not exerting influence on one another, then there must be variables λ that exert a common causal influence on A and B.

Barandes argues there can be non-Reichenbachian common causes that establish the correlations seen in entanglement, like local interactions at a previous time, that Bell's principle miss as they do not take the form of λ, and hence you can have causally local theories that violate Bell's principle of local causality.

As said in post #1, Barandes admitted that he attributed a bit much of Reichenbachianism to Bell in that paper (see later podcasts). Bell seems to have drifted from that or at least Bell seems to have different definitions not all fully Reichenbachian.

 

[Fra]

The non-Reichenbachian common cause is the nonseparable $U$.

I agree with this, this is a good way of putting it that is neutral and in line with the correspondence.

And this is also why the anzats in Bell's theorem makes not sense. But you can phrase this is many different ways.

This is part of the "quantum correspondence". The remaining - unanswered question - is the obvious follow up question: What is the deeper explanation for WHY U is nonseparable in the first place?

It helps the discussion to separate things.

1) Barandes "correspondence" between the two views . This reformulates problems, not necessarily solves them in a deeper sense.

2) The core problems that exists, in both formulations.

I might be wrong, but my impression is that Dr Chinese and others have issues to see the value in the correspondence simply because there are still core problems unsolved? (which are even more foundational than the reformulation of hilbert formalism).

If we separate the issues, can we agree on what we disagree with? or what we seek?

I can answer for myself: I seek the solutions to (2), and my opinon is that while Barandes correspondece does not solve it, it offers a better perspective for formulating difficult problems. But we are not done. That Barandes thinks along these lines as well, is something I am guess due to how he speaks and elaborates the matter, and in particular how he suggests that the stochastics are some deeper improvement over the "problematic" dynamical law that is timeless. But the evolving transition matrices is indeed in where the answer to (2) must hide.. and we dont have this answer yet. And as this thread also isnt' for speculating about it, we can just look and reflect on Barandes correspondence from different angles to maybe get new ideas.

/Fredrik

 

[Morbert]

As said in post #1, Barandes admitted that he attributed a bit much of Reichenbachianism to Bell in that paper (see later podcasts). Bell seems to have drifted from that or at least Bell seems to have different definitions not all fully Reichenbachian.

Do you have any links to the relevant podcasts?

[edit] - I found a discussion at this timestamp. Is this what you are referring to?

 

[Fra]

The vast majority of physicists no longer bother

I agree - but i think it is unfortunate

looking for a causal mechanism for length contraction and time dilation, they accept those are kinematic facts resulting from the observer-independence of c as justified by the relativity principle, not dynamical effects due to some causal mechanism (like the luminiferous aether). The analogy is completed by showing that Information Invariance & Continuity entails the observer-independence of Planck's constant h. Barandes could simply adopt this view and be done with it rather than engage in meaningless word plays.

I think the heart of the matter to the core problems in (2) is precisely how to understand observer independence. Should be understand it as a "constraint" or an emergent relation? What makes this distinction more acute is exactly when one considers a part of the system as an "observer". In this case, the meaning of the constraint interpretation seems to unavoidable lead to "non-local" perspectives, if we by locality refer to the "distance" between "observers".

I think progress into open question, make need to re-questions thinks that are traditionally just seem as constraints. It is easy to understand what a constraint is from a mahtmatical model perspective, but if the model should be encoded inside a part - this get highly nontrivial, not only technically but conceptaully.

/Fredrik

 

[pines-demon]

Do you have any links to the relevant podcasts?

[edit] - I found a discussion at this timestamp. Is this what you are referring to?

He has discussed it, twice (the other time is in the Know Time podcast, about min
3:04:24), see previous discussion thread, post #563 (quoted) and #609 (link to paper).

 

[RUTA]

I agree - but i think it is unfortunate

If you look at the theoretical structure of special relativity, the kinematics follows from an empirically discovered fact (observer-independence of c) that obtains per a compelling fundamental principle (relativity principle). The (Lorentz invariant) causal mechanisms supervene on the resulting M4 spacetime. That means causal mechanisms and dynamics are not fundamental. If you think that "is unfortunate," then you're stuck in a 19th century mindset and will remain forever mystified by superposition and entanglement because any explanation of those in terms of causal mechanisms must violate locality and/or statistical independence.

I think the heart of the matter to the core problems in (2) is precisely how to understand observer independence. Should be understand it as a "constraint" or an emergent relation? What makes this distinction more acute is exactly when one considers a part of the system as an "observer". In this case, the meaning of the constraint interpretation seems to unavoidable lead to "non-local" perspectives, if we by locality refer to the "distance" between "observers".

I think progress into open question, make need to re-questions thinks that are traditionally just seem as constraints. It is easy to understand what a constraint is from a mahtmatical model perspective, but if the model should be encoded inside a part - this get highly nontrivial, not only technically but conceptaully.

/Fredrik

"Observer independence" simply means "same in all inertial reference frames" (related by boosts, spatial rotations, spatial translations, or temporal translations).

Yes, you can think of such a principle-based account as "constraints." See for example Unifying Special Relativity and Quantum Mechanics via Adynamical Global Constraints.

 

[Sambuco]

Barandes argues that Bell's principle of local causality relies on a definition of common cause that is too narrow. Specifically, Bell's principle of local causality assumes common causes must take the form of "Reichenbachian variables". E.g. If two variables A and B are correlated, but not exerting influence on one another, then there must be variables λ that exert a common causal influence on A and B.

Barandes argues there can be non-Reichenbachian common causes that establish the correlations seen in entanglement, like local interactions at a previous time, that Bell's principle miss as they do not take the form of λ, and hence you can have causally local theories that violate Bell's principle of local causality.

This is precisely what makes me skeptical of Barandes' argument. The idea that correlation is merely a consequence of the local interaction in the past is not new. For those who wish to find a "mechanism" behind entanglement, the issue is not mere correlation but the combination of correlation plus indeterminacy before measurements.

Also, Barandes argues that for two entangled subsystems Q and R, there is no causal influence from R to Q if $p(q_t,t|(q_0,r_0),0) = p(q_t,t|q_0,0)$, but I think the issue of locality is not whether there is a dependence on the initial conditions, but on space-like separated measurement outcomes. In other words, the issue is about the probability of finding a result for a measurement in Q changes when the result of a remote measurement in R is known. If the transition matrix is interpreted as mere information, as in $\Psi$-epistemic interpretations, there is no problem, but he prefers to interpret $\Gamma(t)$ as a nomological (law-like) entity.

Lucas.

 

[Fra]

If you look at the theoretical structure of special relativity, the kinematics follows from an empirically discovered fact (observer-independence of c) that obtains per a compelling fundamental principle (relativity principle). The (Lorentz invariant) causal mechanisms supervene on the resulting M4 spacetime.

Yes. I always felt ever since beeing exposed to this, that special relativity and statistical mechanics are the cleanest and most beutiful theories we have with a minimum of ad hoc stuff with a clear logical structure, and the derivation of SR is indeed very clear. And I also like your principle accounts research, that's not my point. But I do not see why we have to settle with it, because I am convinced that to make more progress we need to understand emergence in nature. In this pictures, "constraints" are rarely fundamental, but there is a causal mechanism for their emergence, and the validity of constraints may depend on the state of the emergence process.

That means causal mechanisms and dynamics are not fundamental. If you think that "is unfortunate," then you're stuck in a 19th century mindset and will remain forever mystified by superposition and entanglement because any explanation of those in terms of causal mechanisms must violate locality and/or statistical independence.

No, on the contrary to seek a deeper explanation for WHY there seems to be certain "constraints" in nature, as seen from our observational scale, is not the same path as going back to 19th century.

No need to deny empirical observations, but there are two choices.

1) Treat empirical facts about observed symmetries as fundamental mathematical constraints with perfect confidence even when extrapolating theory into new territory. (Then by new territory here I refer to ultimate unification regmies, including QG and before matter was formed)

2) We take empirical observations for what they are, but without inductive fallacies that our limited observations are fundamental hard constraints. One asks questions like: Is there a way to understand WHY, we consistently observe a max limit on signalling between parts in 3D space that is also invariant to the observer frames? And why 3D? This is remarkable enough that it is hard not to seek to understand. So we don not seek to deny, and thus invalidate, relativity, only find a deeper explanation that may also be valuable when trying to understnand how to unify spacetime dynamics with dynamics of internal structures.

"Observer independence" simply means "same in all inertial reference frames" (related by boosts, spatial rotations, spatial translations, or temporal translations).

Yes, this is what it currently means, but if we look forward. It seems a bit simplistic to think that an "observer" such as a suffiently complex subsystem in contact wit the environment, like Baranders entertains, has no other descriptors beyond it's spacetime relation. This is fine in classical picture where one consider "observations" as gedanken probes at each spacetime point, beeing inserted from an external macroworld.

In QG it seems the inter-relation between spacetime dynamics and the dynamics of internal spaces, is where the trouble lies. The solution we have today is to describe the internal dynamics in terms of the external spacetime. Then the assymmetry which supports most empirical will get shaky. To try to use constraints that have support in one limite empirical domain, into new domains is the method theoretical physicists have spent the last 100 years on.

/Fredrik

 

[Morbert]

Also, Barandes argues that for two entangled subsystems Q and R, there is no causal influence from R to Q if $p(q_t,t|(q_0,r_0),0) = p(q_t,t|q_0,0)$

What Barandes shows is two subsystems that become entangled will fail that check. I.e. $p(q_t,t|(q_0,r_0),0) \neq p(q_t,t|q_0,0)$. This failure is entailed by when their time-evolution operator did not factorize. Hence, there must be a causal relation between entangled systems.

Whether or not this account is sufficient to capture all cases of entanglement (in particular, entanglement swapping experiments) is an interesting question.

but I think the issue of locality is not whether there is a dependence on the initial conditions, but on space-like separated measurement outcomes. In other words, the issue is about the probability of finding a result for a measurement in Q changes when the result of a remote measurement in R is known. If the transition matrix is interpreted as mere information, as in $\Psi$-epistemic interpretations, there is no problem, but he prefers to interpret $\Gamma(t)$ as a nomological (law-like) entity.

The spacelike separated measurement outcomes would depend on initial conditions no? E.g. If Alice is influenced by Bob's choice of measurement, and Bob's choice of measurement is influenced by Bob's initial state, then Alice must be influence by Bob's initial state. Non-interventionist accounts of causality are uncommon in these discussions, so perhaps Barandes's reformulation will spark new interest in them.

 

[Fra]

For those who wish to find a "mechanism" behind entanglement, the issue is not mere correlation but the combination of correlation plus indeterminacy before measurements.

Are you saying that you think those seeking a "mechanism" ALSO needs to resolve the inderterminacy? This is what Bell was thinking. But its not what Barandes is thinking. Or what did you mean?

If the transition matrix is interpreted as mere information, as in $\Psi$-epistemic interpretations, there is no problem, but he prefers to interpret $\Gamma(t)$ as a nomological (law-like) entity.

If so, we may misunderstand each other. I think the indeterminacy is irreducible, but there is mechanis for the correlation. And that "mechanism" is IMO encoded in the $\Gamma(t)$, which in turn encodes how the systems "evolve". So when maximally entangled, and thus isolated from interactions, they evolve in ways that are pre-tuned. But why this is the case, is IMO encodd in the physics of the systems, the internal structor of the particles. Baranders does not "explain" this first principle; he only shows that the "description" from QM, via correspondes implies that this exists(*).

So I would see it like this, the two subsystems that are entanglet evolve independently, but their evolutions are correlated due to beeing pre-tuned. But this "mechanism" can not be put in terms of the simple global beable lambda of bells ansatz.

(*) But once we see this, maybe hte motivation for finding a first principle explanation is larger? I seems I am the only one seeing it this way in this discussion. I know I've said this now several times.

/Fredrik

 

[RUTA]

Yes. I always felt ever since beeing exposed to this, that special relativity and statistical mechanics are the cleanest and most beutiful theories we have with a minimum of ad hoc stuff with a clear logical structure, and the derivation of SR is indeed very clear. And I also like your principle accounts research, that's not my point. But I do not see why we have to settle with it, because I am convinced that to make more progress we need to understand emergence in nature. In this pictures, "constraints" are rarely fundamental, but there is a causal mechanism for their emergence, and the validity of constraints may depend on the state of the emergence process.

This dynamical bias leads to all sorts of paradoxes, puzzles, and problems in physics. See "Beyond the Dynamical Universe" (Oxford UP, 2018) for a comprehensive review.

No, on the contrary to seek a deeper explanation for WHY there seems to be certain "constraints" in nature, as seen from our observational scale, is not the same path as going back to 19th century.

The dynamical/causal bias is 19th century.

No need to deny empirical observations, but there are two choices.

1) Treat empirical facts about observed symmetries as fundamental mathematical constraints with perfect confidence even when extrapolating theory into new territory. (Then by new territory here I refer to ultimate unification regmies, including QG and before matter was formed)

2) We take empirical observations for what they are, but without inductive fallacies that our limited observations are fundamental hard constraints. One asks questions like: Is there a way to understand WHY, we consistently observe a max limit on signalling between parts in 3D space that is also invariant to the observer frames? And why 3D? This is remarkable enough that it is hard not to seek to understand. So we don not seek to deny, and thus invalidate, relativity, only find a deeper explanation that may also be valuable when trying to understnand how to unify spacetime dynamics with dynamics of internal structures.

It is naive to believe you can base your most fundamental explanans on mathematical structure that does not refer explicitly or tacitly to space and/or time, etc. We choose to start with phenomenology a la Einstein for example, it's very clean and undeniable, but you can choose something else.

Yes, this is what it currently means, but if we look forward. It seems a bit simplistic to think that an "observer" such as a suffiently complex subsystem in contact wit the environment, like Baranders entertains, has no other descriptors beyond it's spacetime relation. This is fine in classical picture where one consider "observations" as gedanken probes at each spacetime point, beeing inserted from an external macroworld.

In QG it seems the inter-relation between spacetime dynamics and the dynamics of internal spaces, is where the trouble lies. The solution we have today is to describe the internal dynamics in terms of the external spacetime. Then the assymmetry which supports most empirical will get shaky. To try to use constraints that have support in one limite empirical domain, into new domains is the method theoretical physicists have spent the last 100 years on.

/Fredr

Principle constraints with phenomenology unifies (conceptually) the very successful physics we have today and resolves or even deflates a multitude of perceived puzzles, paradoxes, and problems with that beautiful physics. But, to each his own. We should end this discussion here, as we've drifted away from the thread topic.

My point was that Barandes doesn't have to address the kinematic mysteries of QM with his proposed non-Markovian dynamics. The kinematic mysteries can be resolved as I explained (QM as a principle theory), allowing him to move onto dynamical issues like the measurement problem.

 

[physika]

the indeterminacy is irreducible

who knows...

 

[Sambuco]

The spacelike separated measurement outcomes would depend on initial conditions no?

Well, something that I find difficult to understand in Barandes' formulation is the role of the "hidden variables". For example, in Bohmian mechanics, the future position of a particle depends on the wave function and, also, on its current position, since both enter into the guiding equation. However, there is, so to speak, no "guiding equation" in Barandes' formulation. In other words, it seems to me that the current position of a particle has no influence on its future evolution, its position is hidden, not only from observation, but even in the equations of the theory. As a concrete example, Barandes claims that, in the two-slit experiment, the particle passes through one of the slits (as in Bohmian mechanics). However, in Barandes's stochastic formulation, it seems to me that the particle can enter through one of the slits and immediately exit through the other. I don't see anything that prohibits it.

Lucas.

 

[Sambuco]

Are you saying that you think those seeking a "mechanism" ALSO needs to resolve the inderterminacy? This is what Bell was thinking. But its not what Barandes is thinking. Or what did you mean?

I don't think the "mechanism" should resolve the indeterminacy. What I was trying to say is that the past (local) interaction between particles that leads to correlation is not problematic. The real problem arises when we take into account that, in general, observables are not determined prior to measurement. In other words, any mechanism must explain how the result of one measurement completely eliminates the uncertainty in the other (I consider two measurements with exact correlation/anti-correlation, as in spin measurements along the same axis).

If so, we may misunderstand each other. I think the indeterminacy is irreducible, but there is mechanis for the correlation. And that "mechanism" is IMO encoded in the Γ(t), which in turn encodes how the systems "evolve". So when maximally entangled, and thus isolated from interactions, they evolve in ways that are pre-tuned.

I agree. I tend to think that indeterminacy is irreducible, but I'am less optimistic about discovering a mechanism for the correlation, apart from information about the past interaction of the particles encoded in the transition matrix $$\Gamma(t)$$.

Lucas.

 

[pines-demon]

Well, something that I find difficult to understand in Barandes' formulation is the role of the "hidden variables". For example, in Bohmian mechanics, the future position of a particle depends on the wave function and, also, on its current position, since both enter into the guiding equation. However, there is, so to speak, no "guiding equation" in Barandes' formulation. In other words, it seems to me that the current position of a particle has no influence on its future evolution, its position is hidden, not only from observation, but even in the equations of the theory. As a concrete example, Barandes claims that, in the two-slit experiment, the particle passes through one of the slits (as in Bohmian mechanics). However, in Barandes's stochastic formulation, it seems to me that the particle can enter through one of the slits and immediately exit through the other. I don't see anything that prohibits it.

Lucas.

This is a good point actually. That makes me wonder, how does Schrödinger equation (or von Neumann's equation) look like in his formalism?

 

[Morbert]

This is a good point actually. That makes me wonder, how does Schrödinger equation (or von Neumann's equation) look like in his formalism?

If you mean what do the dynamics look like, the directed conditional probabilities characterize the dynamics. And those dynamics can be associated with time-evolution in the standard formalism of quantum mechanics via a correspondence. The time-evolution might not be unitary. It might be represented by a quantum channel for example, but it can always be made unitary with the appropriate dilation of the Hilbert space.

So a sharp analog to the Schrödinger equation is not immediately present in the formalism, but can be recovered as describing time-evolution via a correspondence.

 

[Morbert]

Well, something that I find difficult to understand in Barandes' formulation is the role of the "hidden variables". For example, in Bohmian mechanics, the future position of a particle depends on the wave function and, also, on its current position, since both enter into the guiding equation. However, there is, so to speak, no "guiding equation" in Barandes' formulation. In other words, it seems to me that the current position of a particle has no influence on its future evolution, its position is hidden, not only from observation, but even in the equations of the theory. As a concrete example, Barandes claims that, in the two-slit experiment, the particle passes through one of the slits (as in Bohmian mechanics). However, in Barandes's stochastic formulation, it seems to me that the particle can enter through one of the slits and immediately exit through the other. I don't see anything that prohibits it.

Lucas.

I read this as a concern about the sparseness of the directed conditional probabilities used to establish causal relations. Bohmians are free to pick "current time" to compute future dependence, while indivisible stochastic systems constrain us to division events. This might be another example of our classical intuitions being an emergent feature, rather than fundamental. Even if, under this proposed scheme, causal relations only make sense with respect to these sparse conditional probabilities, these probabilities become very dense when we move to macroscopic systems.

 

[gentzen]

I read this as a concern about the sparseness of the directed conditional probabilities used to establish causal relations. Bohmians are free to pick "current time" to compute future dependence, while indivisible stochastic systems constrain us to division events.

The difficulty is that in Barandes' formulation, the "hidden variables" can do whatever they want between division events. Only their states at the moments of the division events have causal power (or any other importance).

 

[Morbert]

The difficulty is that in Barandes' formulation, the "hidden variables" can do whatever they want between division events. Only their states at the moments of the division events have causal power (or any other importance).

They can do whatever they want in the sense that the theory doesn't offer a distribution over trajectories, in contrast with e.g. EPE decoherent histories. But is this an objective difficulty or merely subjective distaste for indivisible stochastic maps as dynamical laws?

 

[pines-demon]

If you mean what do the dynamics look like, the directed conditional probabilities characterize the dynamics. And those dynamics can be associated with time-evolution in the standard formalism of quantum mechanics via a correspondence. The time-evolution might not be unitary. It might be represented by a quantum channel for example, but it can always be made unitary with the appropriate dilation of the Hilbert space.

So a sharp analog to the Schrödinger equation is not immediately present in the formalism, but can be recovered as describing time-evolution via a correspondence.

No I meant the actual equation, can you point to it?

 

[Morbert]

No I meant the actual equation, can you point to it?

I don't understand the question. Are you asking me to point to equation 59 here?

 

[Sambuco]

The difficulty is that in Barandes' formulation, the "hidden variables" can do whatever they want between division events. Only their states at the moments of the division events have causal power (or any other importance).

Yes, that's exactly my point!

Lucas.

 

[Sambuco]

But is this an objective difficulty or merely subjective distaste for indivisible stochastic maps as dynamical laws?

This is a good point. At the very least, it seems to me that Barandes' claim "According to the approach laid out in this paper, the particle really does go through a specific slit in each run of the experiment." (https://arxiv.org/pdf/2302.10778) is not supported by his stochastic formalism.

Anyway, as you said, maybe it's just a subjective issue.

Lucas.

 

[Fra]

The real problem arises when we take into account that, in general, observables are not determined prior to measurement. In other words, any mechanism must explain how the result of one measurement completely eliminates the uncertainty in the other (I consider two measurements with exact correlation/anti-correlation, as in spin measurements along the same axis).

I think this is less mysterious when you consider that uncertainty is contextual. Ie. the uncertainty in one context remains even if the uncertainty is cleared in the remote correlated context as long as they do not interact.

I think this is even what allows the "quantum interference" effects to persist at the remote site, even if the remote measurement is done. The separated contextual uncertainties are not affecting each other, because the hidden correlation is not about ignorance about objective beables.

but I'am less optimistic about discovering a mechanism for the correlation, apart from information about the past interaction of the particles encoded in the transition matrix

The vision I have is tha the "mechanism" we seek, is the one that explains the constraining transition matrix of the total system as "emergent" from interacting stochastic parts that obey the new causal locality principle.

But that emergence is going on at another timescale than dynamics. So the emergent things from evolutionary scale are then "effective constraint" for the dynamics. If you disregard the evolutionary mechanisms, then i think there simply is not explaination at all beyond empirical fine tuning (which is not wrong in any way; it's just unsatisfactory to leave it as that)

But this is beyond the "correspondence". The correspondence say nothing about this.

/Fredrik

 

[pines-demon]

I don't understand the question. Are you asking me to point to equation 59 here?

So Schrödinger equation is still Schrödinger equation? Can it not be formulated entirely just using his formalism?

 

[Morbert]

So Schrödinger equation is still Schrödinger equation? Can it not be formulated entirely just using his formalism?

It can't. The Schrödinger equation describes divisible, differentiable evolution. For indivisible stochastic processes, you have sparse directed conditional probabilities and concomitant stochastic maps.

What you can do, however, is show that both formalisms reproduce the same predictions, and hence quantum theories can be interpreted as theories of these stochastic processes. The Schrödinger equation becomes a useful bookkeeping tool.

 

[pines-demon]

It can't. The Schrödinger equation describes divisible, differentiable evolution. For indivisible stochastic processes, you have sparse directed conditional probabilities and concomitant stochastic maps.

What you can do, however, is show that both formalisms reproduce the same predictions, and hence quantum theories can be interpreted as theories of these stochastic processes. The Schrödinger equation becomes a useful bookkeeping tool.

Do I understand right that if you wish to solve any problem in quantum mechanics, then you have to write it in Barandes formalism, use the equivalence to write it as a Schrödinger equation problem, solve Schrödinger's equation, and then transform it back again into Barandes formalism?

 

[Morbert]

This is a good point. At the very least, it seems to me that Barandes' claim "According to the approach laid out in this paper, the particle really does go through a specific slit in each run of the experiment." (https://arxiv.org/pdf/2302.10778) is not supported by his stochastic formalism.

Anyway, as you said, maybe it's just a subjective issue.

Lucas.

For posterity, here are draft notes on the double-slit experiment by Barandes, where he shows the reading of which slit a particle goes through by an indicator qubit constitutes a division event.

I have been wondering if there is a way to connect this formalism to distributions over trajectories. Equation 54 here looks like a trace over a two-time history. Using Gell-Mann and Hartle's history operator $C_\alpha$ (equation 4.1 here) We could maybe write $\Gamma_{ij,\alpha} = \mathrm{tr}(P_i(t)C_\alpha P_j(0)C^\dagger_\alpha)$ as the probability for $i$ at time $t$ conditioned on both $j$ at time $0$ and the coarse-grained trajectory $C_\alpha$. This might let you infer from the indicator qubit that the configuration was not fluctuating across the slits from moment to moment.

[edit] - fixed broken link

 

[Morbert]

Do I understand right that if you wish to solve any problem in quantum mechanics, then you have to write it in Barandes formalism, use the equivalence to write it as a Schrödinger equation problem, solve Schrödinger's equation, and then transform it back again into Barandes formalism?

Useful application of the formalism is an open question. See e.g. this timestamp

 

[javisot]

It would be interesting to know a concrete example (assuming we're talking about a correspondence) in which a quantum problem that would normally be solved or understood using a standard interpretation can be solved more simply and in fewer steps using Barandes's formulation.

It may be that Barandes's proposed correspondence is correct, so the question is whether it reduces any computation.

 

[pines-demon]

It would be interesting to know a concrete example (assuming we're talking about a correspondence) in which a quantum problem that would normally be solved or understood using a standard interpretation can be solved more simply and in fewer steps using Barandes's formulation.

It may be that Barandes's proposed correspondence is correct, so the question is whether it reduces any computation.

Barandes says he is working on that example. Not because it reduces the computation, but because it clarifies the intepretation of superposition.

 

[pines-demon]

Useful application of the formalism is an open question. See e.g. this timestamp

But you did not answer, is that the way to do things so far? Barandes picture->correspondance->Schrödinger equation->Solve->Correspondence->Barandes picture?

 

[martinbn]

It would be interesting to know a concrete example (assuming we're talking about a correspondence) in which a quantum problem that would normally be solved or understood using a standard interpretation can be solved more simply and in fewer steps using Barandes's formulation.

It may be that Barandes's proposed correspondence is correct, so the question is whether it reduces any computation.

Is that ever the case with interpretations!?

 

[gentzen]

Is that ever the case with interpretations!?

Don't you think that Copenhagen or MWI often reduce computations compared to Bohmian mechanics or a collapse interpretation like GRW?

And that MWI advocates might argue that MWI reduces computation even further compared to Copenhagen, to which a Copenhagen advocate might react with protest, because MWI didn't really manage to write down what actually happened in the experiment, from his point of view?

 

[PeterDonis]

Barandes says he is working on that example.

It seems to me that this is something he should have done before embarking on a huge public relations campaign and making fairly strong claims about his formalism.

 

[Fra]

As has been said, I don't think practical computational issues is the main motivation.

It would be interesting to know a concrete example (assuming we're talking about a correspondence) in which a quantum problem that would normally be solved or understood using a standard interpretation can be solved more simply and in fewer steps using Barandes's formulation.

The "simplification" I see as a future potential is this

"The laws of this unistochastic process take the form not of differential equations, but of directed conditional probabilities, which have a long history of admitting an interpretation as encoding causal relationships."
-- p13 arXiv:2402.16935v1

ie. going from the dynamical law that tends to require fine tuning (ie. lots of free parameters that need empirical fixing) in a system dynamics picture, to interacting stochastic parts, is that if we can find an understanding on the constraints (transition matrix) where it is emergent we might be able to reduce the number or free parameters by instead allowing the models to evolve and tune itself.

Unfortunately "simulating" this, will probably be MORE computational intense as the emergent process seems to be to essentially be a kind of "parallell stochastic computing" using agent based models, but will in return require less fine tuning. but this high computational requirement is not for solving everyday problems, its for evolviong the theory I think. Baranders said in some of the clips, not sure which one, that he doesnt suggest we should abandon hilber space as a practical tool for say engineering. I don't think that is the motivation.

On the contrary hilbert space and dynamical laws are mathematically "simple" to handle. It's just conceptually strange. It doesnt get much simplerar than a linear space but the problem is what hte space means, and how that "transforms" as you build or shrink the system, or split it into parts, or divide parts and send them apart etc.

/Fredrik

 

[martinbn]

Don't you think that Copenhagen or MWI often reduce computations compared to Bohmian mechanics or a collapse interpretation like GRW?

Copenhagen and MWI don't do different computations compare to a text book QM. They add words to the explanation. Bohmian does need more computations. That's my point.

 

[gentzen]

Copenhagen and MWI don't do different computations compare to a text book QM.

They do differ for text book quantum computing. In that context, MWI feels like the T->0 limit to me, +over-idealization of the feedback from quantum gates applied dependent on classical measurement results.

Copenhagen „supports“ this sort of round-trip over the classical domain. MWI emulates this by adding sufficiently many ancillary qubits such that the measurement results can be stored in the quantum domain.

Those sorts of idealization can be fine for general understanding. But at some point you also want to go back to model the experimental reality more accurately than that. I don‘t know how to do that in MWI, where neither temperature nor classical stuff exists.

 

[martinbn]

They do differ for text book quantum computing. In that context, MWI feels like the T->0 limit to me, +over-idealization of the feedback from quantum gates applied dependent on classical measurement results.

Copenhagen „supports“ this sort of round-trip over the classical domain. MWI emulates this by adding sufficiently many ancillary qubits such that the measurement results can be stored in the quantum domain.

Those sorts of idealization can be fine for general understanding. But at some point you also want to go back to model the experimental reality more accurately than that. I don‘t know how to do that in MWI, where neither temperature nor classical stuff exists.

Ok, Copenhagen and MWI also do the calculations less effitiently than QM. My point stands. Interpretations don't make the calculatuons easier, they just add "explanations".

 

[gentzen]

Ok, Copenhagen and MWI also do the calculations less effitiently than QM. My point stands.

What is the difference between Copenhagen and QM? Why do you think that Copenhagen does calculations less efficiently than QM?
I don't get your point.

Interpretations don't make the calculatuons easier, they just add "explanations".

I thought the criticism of Copenhagen is exactly that it doesn't care to add "explanations". It only gives explanations why it doesn't need to provide explanations, especially not causal ones.

 

[Fra]

Well, something that I find difficult to understand in Barandes' formulation is the role of the "hidden variables". For example, in Bohmian mechanics, the future position of a particle depends on the wave function and, also, on its current position, since both enter into the guiding equation. However, there is, so to speak, no "guiding equation" in Barandes' formulation. In other words, it seems to me that the current position of a particle has no influence on its future evolution, its position is hidden, not only from observation, but even in the equations of the theory.

I personally think that speaking in terms of "position" and "particle" is not the ideal as it leads to unfavourable mental pictures.

As the probability of a transition of the subsystem to a different configuration is a stochastic transition from the previous configuration, that "current configuration" influence the future, the future unravels like a random walk. The walk has a real "path", but this path is not an objective beable, it is contextual to the subsystem itself.

I think "memory effects" are encoded in the structure of the configuration spaces, and the transition matrices. But I think there is a more subtle causal link as well, between the past and the emergence of the spaces and transition matrices. But Barandes correspondence seem to not explain than more than hilbert space formulation does. But this causal link would I think not regard normal dymamics, but the evolution of the constraints. Its like two levels of evolution or two kinds of "time", a problem which we also have already in existing theory in evolutionary time and and parameter time for short timescale phenomena.

When a subsystem eventually interacts with a different subsystem, other systems "configuration history" remains in a kind of superposition to the other system. So it's is hidden because the beable is contextual, not hidden because its an non-contextual beable that everyone is accidently ignorant about. This is how uncertainty and definite coexists in difference contexts. It is not a contradiction. It only gets problematic if you try insist that there at all times must exists a transformation between the contexts that restores equivalence. But that to me is the same as to assume evolutionary steady state. Ie. that the dynamical laws are stable. But then this assumption, leaves us with an overwhelming fine tuning task.

So if we are looking for a "handle" to make progress here, I think Barandes perspective suggests a new handle... but it's still an open problem.

/Fredrik

 

[Morbert]

But you did not answer, is that the way to do things so far? Barandes picture->correspondance->Schrödinger equation->Solve->Correspondence->Barandes picture?

There is no fixed procedure, but generally you would identify the directed conditional probabilities of interest. You could then use the Hilbert space formalism and quantum channels to express them. See e.g. section VIII here