A Understanding Barandes' microscopic theory of causality

[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.