A Understanding Barandes' microscopic theory of causality

[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

 

[A. Neumaier]

Possibly of interest:

Albert, David Z. (2025) NOTES ON JACOB BARANDES’ VERSION OF QUANTUM MECHANICS. - Preprint, https://philsci-archive.pitt.edu/26777/

 

[RUTA]

Possibly of interest:

Albert, David Z. (2025) NOTES ON JACOB BARANDES’ VERSION OF QUANTUM MECHANICS. - Preprint, https://philsci-archive.pitt.edu/26777/

It is very relevant, thnx for posting it!

 

[pines-demon]

Possibly of interest:

Albert, David Z. (2025) NOTES ON JACOB BARANDES’ VERSION OF QUANTUM MECHANICS. - Preprint, https://philsci-archive.pitt.edu/26777/

Not only is it relevant, it is even worth its own forum post I would say.

Edit: very unfortunately it is not written with $\LaTeX$, and it is not even a PDF file!

 

[Morbert]

I don't understand this paragraph

And perhaps it is worth emphasizing, at this juncture, that the fact that the positions of macroscopic material bodies are being measured, millions of times a second, by their environments - and the fact that those measurements are going to be generating, millions of times a second, new “division events” – is completely irrelevant to the considerations of the previous four paragraphs. Those “division events” are going to give rise to probability-distributions over the possible configurations of the world which display all of the instantaneous “statistical vestiges” of Bohmian effective collapses or Everettian branchings that I was talking about above – but the facts about which branch the world is (apparently) on, or which outcome (apparently) merged in some past experiment, or which quasi-classical macroscopic trajectory the world is (apparently) following, are going to jump around, with no pattern, and no continuity, and no rules, and no limits, at each new instant.

Division events will give rise to more than probability distributions. They will give rise to directed conditional probabilities that make up the dynamics of the theory. And these directed conditional probabilities will prohibit the world from jumping from branch to branch.

But I have only skimmed the paper so far.

 

[Sambuco]

I don't understand this paragraph

I interpreted that paragraph as the same concern I raised in post #63. The idea that the system can jump wildly from one configuration to another is what I summarized as:

"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."

This is the main shortcoming I see in Barandes's formulation, so I'm glad to see that Albert shares a similar opinion. At least, that is how I interpret what he says in section 5 about the "incompleteness" of Barandes's formulation.

One important difference is that I limited myself to those cases where there is no decoherence (as in the two-slit experiment), but it seems to me that Albert analyzes such "wild jumps" even in the presence of division events.

Lucas.

 

[PeterDonis]

Division events will give rise to more than probability distributions. They will give rise to directed conditional probabilities that make up the dynamics of the theory.

Why will this be the case?

 

[RUTA]

Here are two serious shortcomings that Albert points out:

And so the incompleteness of Jacob’s theory – as it currently stands – seems like a very serious shortcoming. It seems to me that in the absence of any particular suggestion for completing the theory with a law governing these trajectories through configuration-space, the question of its empirical adequacy, and the deeper and prior question of whether it has any empirical content at all, remains (at best) radically unsettled.

On the question of locality – or the lack of it - much of what Jacob has said and written strikes me as confused and misleading. ... I am not going to say anything about Jacob’s new conception of locality here. I simply want to point out that his critique of the old conception - the EPR-Bell conception – is unmotivated and confused. ...

Jacob seems to think that the conception of locality that is implicit in this second premise is (as I said above) somehow not right or not interesting or not relevant or not deserving of the name – and that there is consequently nothing particularly momentous or unsettling about the discovery that the world fails to be local in that sense of the term. But he has not given us any reason – in so far as I can tell – for thinking anything of the sort.

He has some other principle in mind – something he calls “causal locality” – which he regards as interesting and important, and which he thinks it would be crazy for the world not to obey, and which he claims his theory does obey. And I have no reason to doubt that whatever principle it is that Jacob has in mind will be well worth looking at, and thinking about. But if his principle can hold in worlds where EPR-Bell locality does not, then I would claim that it is his principle, and not the one that EPR and Bell had in mind, that does not deserve to be called a principle of “locality”.[1] And Jacob’s numerous announcements to the effect that he had found a formulation of quantum mechanics which is “causally local” must have suggested to many students of the foundations of quantum mechanics that he had found a formulation of quantum mechanics that is “local” in the usual and familiar and canonical and correct sense of EPR and Bell. And that is certainly not the case.

---

[1] Jacob has remarked to me, in conversation, that – on his conception of “locality” – the question of whether or not Bohmian Mechanics is local is simply not well posed. That sounds really bad. If Bohmian Mechanics isn’t clearly and unambiguously non-local, then I don’t know what is.

I've been researching quantum foundations since 1994 and I've seen my colleagues propose many such hypothetical ways to "fix quantum mechanics." I have yet to see any such ideas completed as promised. I doubt Jacob's idea will do any better, given its extreme shortcomings.

 

[gentzen]

Here are two serious shortcomings that Albert points out:

And so the incompleteness of Jacob’s theory – as it currently stands – seems like a very serious shortcoming.
..., remains (at best) radically unsettled.

On the question of locality – or the lack of it - much of what Jacob has said and written strikes me as confused and misleading. ...

I've been researching quantum foundations since 1994 and I've seen my colleagues propose many such hypothetical ways to "fix quantum mechanics." I have yet to see any such ideas completed as promised. I doubt Jacob's idea will do any better, given its extreme shortcomings.

Since quantum mechanics is non-local, any attempts to "fix" that is bound to be unsatisfactory. But fixing the "incompleteness" of his current proposal might well be possible. The main thing preventing him from fixing it is to first acknowledge that it is currently incomplete.

With respect to non-locality, I think the better approach would be to try to understand why quantum mechanics is non-local, and why this is not a bad thing. But that can be done independent of any specific proposal.

 

[Morbert]

Why will this be the case?

Equation (56) from this paper is an example of a subsystem's transition matrix divisible at $t'$. The transition matrix $\Gamma^\mathcal{S}(t\leftarrow t')$ on the left hand side will have the form (as per equation 1)$$\Gamma^\mathcal{S}_{ij}(t\leftarrow t') = p^\mathcal{S}(i,t|j,t')$$In a quasiclassical context, these conditional probabilities encode our quasiclassical expectations, and are how Barandes's formalism recovers quasiclassical physics at the appropriate limit, analogous to the way Everettian quatum mechanics recovers it with quasiclassical, decoherent branches. E.g. The probability that it will rain presently where you are, given there are no clouds where you are, is 0. The earth subsystem will not spontaneously evolve into a configuration where it will in fact immediately start to rain.

I suspect what Albert is doing is considering the transition matrix of the entire universe modeled as an isolated system, which does not contain any division events, and hence the standalone probability does not constrain any quasiclassical evolution. The mistake here is that standalone probabilities, are epistemic, not dynamical/nomological. It is only the directed conditional probabilities that make up transition matrices that are dynamical.

 

[gentzen]

I don't understand this paragraph

Division events will give rise to more than probability distributions. They will give rise to directed conditional probabilities that make up the dynamics of the theory. And these directed conditional probabilities will prohibit the world from jumping from branch to branch.

Barandes is free to clarify this, if he wants. Perhaps he wants the minimal version, where each division event is global, and has the same status as t=0. Then t=0 would be just one division event among many. And as a further clarification, give time a clear direction, so that each division event is only important for what happens in its future (and not its past), until the next division event happens.

 

[Morbert]

Barandes is free to clarify this, if he wants. Perhaps he wants the minimal version, where each division event is global, and has the same status as t=0. Then t=0 would be just one division event among many. And as a further clarification, give time a clear direction, so that each division event is only important for what happens in its future (and not its past), until the next division event happens.

See this timestamp, where he distinguishes the dynamical conditional (transition) probabilities from the epistemic standalone probabilities.

 

[Morbert]

Since quantum mechanics is non-local, any attempts to "fix" that is bound to be unsatisfactory.

"Bound to be unsatisfactory" needs to be unpacked. There are objective conditions of a good interpretation of quantum mechanics: Empirically adequate, unambiguous, generalizeable to all quantum theories (e.g. QFT). A good few interpretations meet these conditions.

Then there are subjective conditions: Must be realist, must be deterministic, must be local. These subjective conditions are where things become "unsatisfactory".

 

[gentzen]

See this timestamp, where he distinguishes the dynamical conditional (transition) probabilities from the epistemic standalone probabilities.

Are you sure you have the correct timestamp? It doesn't clarify the points where David Albert sees the incompleteness. But I could even find anything where he would distinguish "dynamical conditional" from "epistemic standalone" probabilities.

 

[gentzen]

A good few interpretations meet these conditions.

And some sometimes claim to be local, for example MWI. But this claim risks to make MWI "unambiguous", and hence no longer satisfying all "objective conditions of a good interpretation". Why? Because before that claim, MWI was just a wavefunction in Hilbert space which evolves according to the Schrödinger equation. But such claim that MWI would be local refer to papers where the Heisenberg picture is used instead. It remains unclear whether this is still the same MWI or not.

Then there are subjective conditions: ..., must be local.

And this last one is bound to cause trouble.

 

[PeterDonis]

such claim that MWI would be local refer to papers where the Heisenberg picture is used instead

Can you give any specific references?

 

[gentzen]

Can you give any specific references?

Bell on Bell’s theorem: The changing face of nonlocality
Harvey R Brown, Christopher G Timpson
https://arxiv.org/abs/1501.03521

In our view, the significance of the Bell theorem, both in its deterministic and stochastic forms, can only be fully understood by taking into account the fact that a fully Lorentz covariant version of quantum theory, free of action-at-a-distance, can be articulated in the Everett interpretation.

So here we have a claim that MWI is local, at least that is how David Marcus interpreted that paper here. Not sure how they argue themselves, but they certainly cite and comment on
Rubin, Mark A. 2001. Locality in the Everett Interpretation of Heisenberg Picture Quantum Mechanics. Foundations of Physics Letters, 14, 301–322.
Deutsch, David, and Hayden, Patrick. 2000. Information Flow in Entangled Quantum Systems. Proceedings of the Royal Society of London A, 456, 1759–1774.

We also had a thread "How Does the Many-Worlds Interpretation Address Nonlocality?" recently, with examples of claims that MWI is a "local interpretation":

To follow up, David Deutsch argues for a local interpretation here. I note this is an old paper. https://arxiv.org/pdf/quant-ph/9906007

Many "Oxford Everettians" (Deutsch, Wallace, Vaidman et al) hold a local (in the sense of no spooky action) account of MWI.

(I don't think that Vaidman himself is an "Oxford Everettian", but maybe one of his "et al" coauthors was.)

 

[PeterDonis]

here we have a claim that MWI is local

By "local" here is meant "free of action-at-a-distance", which, if you unpack further based on what's said in section 9 of the paper, means that the dynamics is derived from a Hamiltonian that only includes point interactions. But in the very next sentence, the paper says that the fundamental states of the theory are non-separable, due to entanglement--which is exactly where things like correlations that violate the Bell inequalities come from.

In other words, the claim the MWI is local is based on picking a definition of "local" that makes it true. But that might not be the definition of "local" that other people actually care about. Much of the argument in the literature about this, and indeed about QM interpretations in general, is based on different people picking different definitions of a key term and then talking past each other.

 

[RUTA]

From SEP on Many-Worlds (written by Vaidman):

Although the MWI removes the most bothersome aspect of nonlocality, action at a distance, the other aspect of quantum nonlocality, the nonseparability of remote objects manifested in entanglement, is still there. A “world” is a nonlocal concept. This explains why we observe nonlocal correlations in a particular world.

 

[Fra]

Many subquestions here, and Alberts paper was long i skimmed it yeasterday but i think one of his issues is that Barandes seems to not release himself from the hamiltonian flow in the hilbert space, thus the lack of first principle construction of dynamical law.

I think this is correct, but it's because Barandes only provides the correspondence. He does not supply a complete first principle construction of the timedependent transition matrix(gamma). And in Baranders view, it is excatly the transition matrix that encodes the information that is equivalence to the system dynamical law. Ie the time dependence of the transition matrix, replaces all the information encoded in schrödinger equation and hamiltonian.

I think that is how it is, something is missing I agree.
My own opinion on what is missing, and what would in principle resolve this, is as i mentioned in other posts.

While Barandes does not mention observers/agents, he instead considers a sufficienty complex subsystem to take that role. This is a LIMIT.

My conceptul perspective/interpretation of this and how it sees Barandes work is this
- Baranded indivisiable stochastics, encoded by the time dependent transition matrix encodes corresponds to a LIMIT of an agent based model (that we do not have yet!) where in the limit of many observers and t -> infinity, we get the transitiion matrix of barandes that represents an asymptotic behaviour of the interactions.

Ie the missing "first principle" construction of gamma, in order NOT to still rest on the information encoded in the hilbert space hamiltoniani, would be to explain the emergence of this limit, from some yet unknonwn microscopic agent agent interations. It is IMO at THIS level that the true causality is encoded. In principle that is, because this is not yet unlocked. But it is the "completion" I see as missing to make full sense of Barandes view.

This is what mean before when I've said that I view both quanutm mechanics as it stands; and the reformulation via indivisiable stochastics as a limiting case (effective description) or a more complex agent based model, corresponding to an asymptotic steady state. And if we can understand that in detail, we should get that missing first principle "explanattion" of the "effective dynamical law" we are used to see at system dynamics level. This also merges fined with "effective theory" perspectives of modern physics. And before the limit is taken; we might expect an "evolving law", like a PDE/ODE with external explicit time dependence, that would relate to some "absolute time".

Note that, this is a genereal interpretion. I have not actual on the table ABM models for this (so it's not a speculation just to be belar, but this my conceptual understnading of Barandes work in the context of how to complete it.

Edit: this is also I think what Barnades in one of his other videos hints that the nothion of "causality" is highly suspicious or questionable in the system dynamical view if the law is timeless; then the future is alreadty determined from the past. So the notion of causal mechanism is hidden. So I agree with Barandes that the non-locality notion Bell uses is not very useful thinking tool, so I am with Barandes on this one.

/Fredrik

 

[gentzen]

Many subquestions here, and Alberts paper was long i skimmed it yeasterday but i think one of his issues is that Barandes seems to not release himself from the hamiltonian flow in the hilbert space, thus the lack of first principle construction of dynamical law

No, even so this is a point which came up in the discussions here (on PhysicsForums), the two main objections raised by David Albert (incompleteness and locality) are not directly related to this. The incompleteness he highlights is that the „causal power“ of the current configuration is not clarified sufficiently. To illustrate this, he discusses a minimal completion, where not even the configurations at division events have „causal power“.

 

[Fra]

No, even so this is a point which came up in the discussions here (on PhysicsForums), the two main objections raised by David Albert (incompleteness and locality) are not directly related to this. The incompleteness he highlights is that the „causal power“ of the current configuration is not clarified sufficiently. To illustrate this, he discusses a minimal completion, where not even the configurations at division events have „causal power“.

But in the traditional view (system dynamics) where else is causal power encoded, if not in initial conditions and dynamical law?

As I see it the topics are related. IMOH the true causal power, would be best understood in an expanded ABM model if which not onlt barandes formulation but also QM itself is a limitind case.

But lets me digest Alberts words again to see if there is som subquestions here. But to me "causal power" can sit on two places depending on perspective.

1)In system dynamics perspectice, we have dynamical law, either inform of transition matrix or differential equations.

2) In agent based model (meaning not "observers" necessarily if that is annouing, but seeing the system as interacting PARTS) the causal power likes in the decentralized agent update rules (which could very very be reduce to evolving stochastics themselves -> meaning it's fundamentally non-markovian interactions)

And then of course the two views are not in contradiction. But (1) is a limiting case of (2), and at least in MY understnading the true causal power lies at part-part inteactions, not system level laws. (The general perspective are in the links of https://www.physicsforums.com/threa...-quantum-interpretations.1082027/post-7283566)

I'll read the paper again later... it was quite long and i skimmed it.

/Fredrik

 

[gentzen]

But in the traditional view (system dynamics) where else is causal power encoded, if not in initial conditions and dynamical law?

What you are missing is that Barandes’ proposal is not just a different perspective, but incomplete in some very concrete ways.

One can argue about whether staying silent about the dynamical laws is a problem, but at least it is clear that those laws are unrelated to his proposal.

But clarifying the precise role of the configurations is both closely related to his proposal itself, and something Barandes could be able to do, and what he really should try to do.

 

[Morbert]

Are you sure you have the correct timestamp? It doesn't clarify the points where David Albert sees the incompleteness. But I could even find anything where he would distinguish "dynamical conditional" from "epistemic standalone" probabilities.

At the timestamp, Barandes remarks on the distinction between standalone probabilities and transition probabilities, the latter of which make up the objective dynamics of subsystems Albert concerns himself with, like the earth and Napoleon. The "jumping around" from branch to branch that Albert asserts is, as far as I can tell, inferred from some standalone probability of the entire universe, devoid of any consideration of the transition probabilities of subsystems which would prevent such jumping around.

An analogous objection to Everettian QM would look like this: In this paper, David Wallace sketches how quasiclassical behavior is found in the Everettian formalism.

So: if we pick a particular choice of system-environment split, we find a “strong” form of quasi-classical behaviour: we find that the system is isomorphic to a collection of dynamically independent simulacra of a classical system. We did not find this isomorphism by some formal algorithm; we found it by making a fairly unprincipled choice of system-environment split and then noticing that that split led to interesting behaviour. The interesting behaviour is no less real for all that.

Albert might object by saying if you don't consider such system-environment splits, and only consider the universe as a whole, you lose the quasiclassical branch structure.

 

[Sambuco]

In a quasiclassical context, these conditional probabilities encode our quasiclassical expectations, and are how Barandes's formalism recovers quasiclassical physics at the appropriate limit, analogous to the way Everettian quatum mechanics recovers it with quasiclassical, decoherent branches.

I think the comparison with Everett is pertinent. In Everett's interpretation, if the wavefunction splits into two decoherent branches with probability 1/2, the theory predicts the superposition of two non-interacting "worlds," and the classical case is recovered (albeit with multiple worlds, of course). On the other hand, in Bohmian mechanics, the particle is located on one of the two branches, and the wavefunction (either the "global" one or the one resulting from the effective collapse) predicts the correct probabilities, so the classical limit is also recovered. In my opinion, this is not the case in Barandes's formulation, and this is precisely the problem Albert points out (and which I also pointed out in post #63 for the two-slit experiment).

Suppose we have an initial one-particle wavefunction at time $t_0$ and consider configurations of the system at two times $t_1$ and $t_2$ $(t_0 < t_1 < t_2)$. If a division event ocurrs at $t_1$, then the probability that the system is in a certain configuration at time $t_2$ can be written as $$P(q_2|q_0) = \sum_{q_1} P(q_2|q_1)P(q_1|q_0)$$ where $q_i$ is the configuration at time $t_i$. The problem I see is that, if the transition matrix (or the wavefunction) plays a nomological role, then, the configuration of the system at $t_2$ does not depend on the configuration at $t_1$ (hidden variables are too hidden!), so the particle can be at $t_1$ within one of the branches and jump at $t_2$ to the other. As we know, this is ruled out by experiments. Nothing in Barandes's formulation prevents this from happening. In line with what Albert says, one can add to the laws a dependence between the configurations at two different times, as occurs in Bohmian mechanics. Another possibility is to simply say that all the possibilities are equally "real", but this is just many-worlds. In my opinion, the problem becomes even clearer if we consider another possible solution: we can postulate that, when a division event occurs, only the branch where the particle is located should be consider when calculating future probabilities, but this is the collapse postulate of textbook QM! Of course, when the collapse postulate is added, the measurement problem is back to life.

Lucas.

 

[Fra]

I think already at the introduction, I can sense the approach and the immediate hunch is that I do not share Alberts analysis...

Albert writes:

"The fundamental ontology of Jacob’s version of quantum mechanics – at least in the non-relativistic first-quantized case - consists entirely and exclusively of some presumably finite collection of particles. Just as in the case of Classical Mechanics, each of these particles invariably has some perfectly determinate position in space – and the history of those positions, the history (that is) of the configuration of that collection of particles, constitutes the complete physical history of the world."

This is indeed makes it sound like Bohmian mechanics, but I do not agree with this characterization. Although in a way, it is the case, the language makes if confusing and IMO misleading.

First of all Barandes considers a system composed of subsystems. To label these particles, IMO induces an mental image that is at least misleading. Because often the notion of particles, make no sense unless given some dynamical law (in the ordinary sense). And it is also not really brownian motion, as the particles are not doing markovian random walks.

This is why I might stretch myself to relabel "the collection of subsystem" as a "collection of composite-agents". While an agent is simply material like a particle, the key difference is that the concept of "agent" makes sense without reference to global dynimcal law - the conditional transition probabilities are rather than corresponds to the decentralized agent rules. This is a key difference. And talking about "particles" is just hiding this difference, causing confusion IMHO at lesat.

Also to say that they all have determinate position and history in space, I find somewhat misleading as well, because while the history of each subsystem is determinate, this context of this history (which I personally attribute to the "agent" corresponding to that syssystem) is different than the context in which a fellow nearby "subsystems" history is determinate. This is why one has a "collection" of determinate histories, but the collection is a unition of "incompatible context". And it's when these contexts (subsystems) interact that things happen.

In this view, the notion of "causality" is also NOT defined at global system level, its defined on subsystem level, in that two distinct subsystems have independent transition probabilities. This is exactly also what on would naturally have in decentralised agent interactions.

To NOT use the word agent(which Barandes does not) is probably a good way to avoid people confuising it will all the other stuff like conscioussness etc(!), so lets just call it "subsystem". But also to avoid calling it "particle" is also I think good as it makes people associate to bohmian mechanics.

The only bohmian mechanics interpretation I've aware of that at least conceptaully might be compatible with this, is Demystifiers version of "solipsist HV", where the HV are associated to the content of the "bohmian particles" themselves. That is essentially, conceptually very close IMO. But the math may be different. So - had I been forced to convert to a Bohmian, that is the hole I would dig in.

This is how I view it and it's why I overally disagree with Alberts paper.

/Fredrik

 

[Morbert]

I think the comparison with Everett is pertinent. In Everett's interpretation, if the wavefunction splits into two decoherent branches with probability 1/2, the theory predicts the superposition of two non-interacting "worlds," and the classical case is recovered (albeit with multiple worlds, of course). On the other hand, in Bohmian mechanics, the particle is located on one of the two branches, and the wavefunction (either the "global" one or the one resulting from the effective collapse) predicts the correct probabilities, so the classical limit is also recovered. In my opinion, this is not the case in Barandes's formulation, and this is precisely the problem Albert points out (and which I also pointed out in post #63 for the two-slit experiment).

It is the case in Barandes's formalism.

Consider for example a simple model of the Stern-Gerlach Experiment with initial particle, pointer and environment states $\ket{\psi}$, $\ket{\omega}$ and $\ket{\epsilon}$ respectively.$$U(t'\leftarrow 0)\ket{\psi}\ket{\omega}\ket{\epsilon} = \frac{1}{\sqrt{2}}(\ket{z_+}\ket{\omega_+}\ket{\epsilon_+} + \ket{z_-}\ket{\omega_-}\ket{\epsilon_-}
)$$The corresponding transition matrix of the particle and pointer device is $$\Gamma(t\leftarrow 0) = \Gamma(t\leftarrow t')\Gamma(t'\leftarrow 0)$$The correlation between the pointer device and the particle spin with the environment will give rise to a division event at $t'$. The transition matrix $\Gamma(t\leftarrow t')$ will have the form$$\Gamma_{ij}(t\leftarrow t') = p(z_i\omega_i, t | z_j\omega_j,t') = \delta_{ij}$$I.e. The probability for jumping from branch $i$ to branch $j$ at any time $t$ after $t'$ is 0.

More generally, correspondence between this formalism and QM is exact, and QM does not predict our quasiclassical experiences jumping from branch to branch.

[edit] - PS Keep in mind that your concern is not quite the same as Albert's. Albert is considering high-frequency division events giving rise to a branching structure. You brought up the behavior of the quantum system prior to a sparse division event. They are related, but distinct in important ways. For now I am focusing on Albert's, as I have previously discussed your concern, but we can revisit later.

[edit 2] - Added explicit reference to environment.

 

[gentzen]

At the timestamp, Barandes remarks on the distinction between standalone probabilities and transition probabilities, the latter of which make up the objective dynamics of subsystems Albert concerns himself with, like the earth and Napoleon.

Thanks, now I see what you mean. And based on Barandes' answer (he doesn't want to make any "arbitrary" clarifications beyond what is enforced by his definition of indivisible stochastic dynamics), I also see why David Albert had to use his minimal completion, which doesn't give any special status to division events.

Both independence of subsystems and division events in independent subsystems can be defined purely in terms of the indivisible stochastic dynamics. And in the end, this must be Barandes' intention, independent of whether he says so explicitly or not. Hence David Abert has to reason that since division events are just a property of an indivisible stochastic dynamics (especially they are not given externally), they should have no special ontological status, unless Barandes clarifies that he wishes to given them such a special ontological status.

 

[Morbert]

Thanks, now I see what you mean. And based on Barandes' answer (he doesn't want to make any "arbitrary" clarifications beyond what is enforced by his definition of indivisible stochastic dynamics), I also see why David Albert had to use his minimal completion, which doesn't give any special status to division events.

It's quite simple: Transition probabilities, not standalone probabilities, make up the nomological content of the reformulation. No completion is needed. I suspect Albert just subjectively wants the formalism to look a bit more like Bohmian mechanics.

Both independence of subsystems and division events in independent subsystems can be defined purely in terms of the indivisible stochastic dynamics. And in the end, this must be Barandes' intention, independent of whether he says so explicitly or not. Hence David Abert has to reason that since division events are just a property of an indivisible stochastic dynamics (especially they are not given externally), they should have no special ontological status, unless Barandes clarifies that he wishes to given them such a special ontological status.

The transition probabilities of subsystems given by division events have a nomological status. They are objective, and describe the evolution of subsystems. We should not contrive to ignore them and then declare some absurdity based on this contrivance.