A Understanding Barandes' microscopic theory of causality

[iste]

Beables have diagonal matrices wrt configurations, as they can be read off from the existing configuration (see equation 19 in the correspondence paper). Emergeables don't, and hence are given meaning by a measurement context.

But it doesn't seem to me that there is any preferred basis of configurations. Surely, Barandes formulation doesn't stop you from creating beables with a configuration space for any quantum observable? Moreover, the diagonal vs. non-diagonal aspect I am not sure is relevant because under Barandes' formulation, beables and emergeables act similarly with regard to the measurement device and you would assume always produce definite outcomes, and regardless of indivisibility or divisibility, your stochastic process always produces definite outcomes. I still don't understand how the distinction between beable and emergeable is anything other than perspectival.

Regarding your second quote, I don't see you refuting the idea that the configuration space can't be describing a counterfactual ontology like the fisherman example.

 

[Morbert]

But it doesn't seem to me that there is any preferred basis of configurations. Surely, Barandes formulation doesn't stop you from creating beables with a configuration space for any quantum observable? Moreover, the diagonal vs. non-diagonal aspect I am not sure is relevant because under Barandes' formulation, beables and emergeables act similarly with regard to the measurement device and you would assume always produce definite outcomes, and regardless of indivisibility or divisibility, your stochastic process always produces definite outcomes. I still don't understand how the distinction between beable and emergeable is anything other than perspectival.

Barandes's formalism involves a standard classical configuration space $\mathcal{C}$. Whether it is, for example, a space of particle or field configurations depends on the theory you are constructing a correspondence to. Observables that are not diagonal wrt these configurations cannot be read off from these configurations, and are hence not beables.

Regarding your second quote, I don't see you refuting the idea that the configuration space can't be describing a counterfactual ontology like the fisherman example.

You are free to construct alternative ontological models, just as you are free to construct them for ordinary Markovian stochastic processes. For the purposes of this thread I am discussing the one presented by Barandes.

 

[iste]

Barandes's formalism involves a standard classical configuration space $\mathcal{C}$. Whether it is, for example, a space of particle or field configurations depends on the theory you are constructing a correspondence to. Observables that are not diagonal wrt these configurations cannot be read off from these configurations, and are hence not beables.You are free to construct alternative ontological models, just as you are free to construct them for ordinary Markovian stochastic processes. For the purposes of this thread I am discussing the one presented by Barandes.

Yes, but my point is that surely position and momentum basis in quantum mechanics would each be translated to respective classical configuration bases where they are beables.

Again, I don't think diagonal nature matters because indivisibility and interference itself is characterized by non-diagonality and yet the stochastic process produces definite realizations of configurations regardless. In DOI: 10.31389/pop.186 Barandes describes a beable as having a non-diagonal density matrix several times with regard to coherence and uncertainty principle sections.

Barandes does not present a specific ontological model other than the use of classical configurations. My point is that there is nothing stopping you using them to represent counterfactual classical configurations describing something that can only said to exist as a consequence of a measurement interaction.

 

[Morbert]

Yes, but my point is that surely position and momentum basis in quantum mechanics would each be translated to respective classical configuration bases where they are beables.

Show me what that configuration space (note, not phase space) would look like.

Again, I don't think diagonal nature matters because indivisibility and interference itself is characterized by non-diagonality and yet the stochastic process produces definite realizations of configurations regardless. In DOI: 10.31389/pop.186 Barandes describes a beable as having a non-diagonal density matrix several times with regard to coherence and uncertainty principle sections.

It's the observable itself that is diagonal or not diagonal. See equation 19.

Barandes does not present a specific ontological model other than the use of classical configurations. My point is that there is nothing stopping you using them to represent counterfactual classical configurations describing something that can only said to exist as a consequence of a measurement interaction.

Barandes's kinematic axiom is clear. Let's stick to it for this thread.

 

[iste]

Show me what that configuration space (note, not phase space) would look like.

It's the observable itself that is diagonal or not diagonal. See

Barandes's kinematic axiom is clear. Let's stick to it for this thread.

i'm thinking that maybe the issue is that the stochastic correspondence clearly overs more than just what you are referring to in terms of configuration basis then. Clearly you can give momentum and anything else you want a representation which is as a beable in the configuration basis is described, using the dictionary; and from the indivisible perspective, that must actually be the explanation for different measurement bases (all representable as indivisible stochastic processes). But once you are able to do this, I think it does really make it questionable whether the stochastic process in the formalism always has to have a stringently realist ontology if plausibly you can use it to describe things which may not have that interpretation in a straightforward way (or its at least ambiguous whether they do). Sure you can postulate about a preference for a configuration basis and so thats where the only real beables are, but I guess thats a difference betwern an assumption about what you  want your formulation to represent and the capabilities of what the formulation can represent; after all, Barandes thinks this formulation can potentially be used to describe systems in the special sciences from neuroscience to psychology to even more abstract things like financial systems perhaps.

 

[Morbert]

@iste You keep straying from Barandes's literature.

i) Barandes presents a kinematic axiom which says the system always has a configuration $i,\ldots,N$ in the configuration space $\mathcal{C}$ we use to model the system.
ii) Beables are the random variables $A(t) = \sum_i^Na_i P_i = \mathrm{diag(\ldots,a_i,\ldots)}$ which can be read off from the configuration the system is in.
iii) Emergeables cannot be read off from the configuration the system is in. Instead they mix in dynamical information and determine the probabilities for the configurations an ancillary measurement apparatus can evolve into should it interact with the system.

If you want to posit an alternative model, which places beables and emergeables on equal ontic footing, I wish you the best of luck.

 

[Morbert]

PS this conversation is also straying from the recent paper by Albert. Unless there's something novel and specific in your response I'll leave it here.

 

[iste]

@iste You keep straying from Barandes's literature.

i) Barandes presents a kinematic axiom which says the system always has a configuration $i,\ldots,N$ in the configuration space $\mathcal{C}$ we use to model the system.
ii) Beables are the random variables $A(t) = \sum_i^Na_i P_i = \mathrm{diag(\ldots,a_i,\ldots)}$ which can be read off from the configuration the system is in.
iii) Emergeables cannot be read off from the configuration the system is in. Instead they mix in dynamical information and determine the probabilities for the configurations an ancillary measurement apparatus can evolve into should it interact with the system.

If you want to posit an alternative model, which places beables and emergeables on equal ontic footing, I wish you the best of luck.

You don't need another model because its in the theory. The stochastic-quantum correspondence surely says that momentum basis and any other observable are describable as and translatable to an indivisible stochastic process in the same way as one would for the configuration basis beable. This would then give you the division events for these other "emergeables".

 

[Morbert]

You don't need another model because its in the theory. The stochastic-quantum correspondence surely says that momentum basis and any other observable are describable as and translatable to an indivisible stochastic process in the same way as one would for the configuration basis beable. This would then give you the division events for these other "emergeables".

I wish you the best of luck in showing this. Please be specific with your example. And please cite the relevant literature.