A Understanding Barandes' microscopic theory of causality

[Morbert]

I will attempt to describe a position that seems reasonable to me. First, transition matrices define a nomological entity that is only relevant to the extent that we have (contingent) information about the outcome of an event. That is, given a division event at $t'$, the standalone probability $p_i(t)$ can be written as $p_i(t) = \sum_j \Gamma_{ij}(t \leftarrow t') p_j(t')$, where $p_j(t')$ are, in Barandes's words, "the contingent ingredient". Then, if we have precise information about the system configuration at $t'$, all of the probabilities $p_j(t')$ become zero, with the exception of one, which corresponds to the observed value. Applying this information to our expression for the standalone probability $p_i(t)$, we obtain $p_i(t) = \Gamma_{ij}(t \leftarrow t')$ where $j$ refers here to the system configuration $q_j(t')$ for which we have information. That's the "collapse" in this stochastic formulation.

Now, how is it possible for all the other branches still exist if the aforementioned standalone probability only includes one of them? In other words, how is that possible for different branches to recohere (as in Wigner's friend thought experiments) if they are not included in this standalone probability? Well, the answer lies in the fact that what is "objective" is the transition matrices, not the standalone probabilities, since the latter also depend on contingent information about the ocurrence of other events. In cases such as Wigner's friend scenarios, the recoherence of different branches is intrinsically related with the loss of information about the system configuration at $t'$. Without this information, we have to use again the $\Gamma(t \leftarrow 0)$ transition matrix because, in addition, the dynamics are no longer divisible at $t'$.

@Morbert, I think you'll agree. Am I right?

Lucas.

The divisible transition map of quasiclassical subsystems are near exact. This means they will effectively never fail. You would need to introduce superobservers capable of suspending irreversibility or specific models of the universe permitting Poincare recurrence (for such a universe the size of our observable universe the recurrence time would be something like 10^(10^122)).

Note that Albert is not considering these speculative scenarios. He is considering timescales of at most a couple centuries. The divisible stochastic map obtained from marginalizing over environmental degrees of freedom is effectively exact for these timescales.

 

[Sambuco]

The divisible transition map of quasiclassical subsystems are near exact. This means they will effectively never fail. You would need to introduce superobservers capable of suspending irreversibility or specific models of the universe permitting Poincare recurrence (for such a universe the size of our observable universe the recurrence time would be something like 10^(10^122)).

I agree, but... The issue I tried to address in my last post is about how it is possible, within Barandes's formulation, to restrict the system configuration for $t > t'$ to only one of the possible branches, while still preserving the other branches for those cases with superobservers, Poincaré recurrence and so on. The only way I see to achieve this within Barandes' formulation is by letting the information about the occurrence of an event at $t'$ play an active role through the (contingent) probabilities $p_j(t')$. As long as we are certain of the outcome of the event at $t'$, the probability of a future event will be determined exactly by the transition matrix $\Gamma_{ij}(t \leftarrow t')$ associated with the branch corresponding to the outcome at $t'$. Interference between different branches is still possible whenever something happens that is equivalent to erasing all information about the outcome of the event at $t'$.

Note that Albert is not considering these speculative scenarios. He is considering timescales of at most a couple centuries. The divisible stochastic map obtained from marginalizing over environmental degrees of freedom is effectively exact for these timescales.

I disagree. Marginalizing over environmental degrees of freedom only causes the probability of a future event to be represented by a statistical mixture, not the system to remain on a single branch.

Lucas.

 

[Morbert]

I agree, but... The issue I tried to address in my last post is about how it is possible, within Barandes's formulation, to restrict the system configuration for $t > t'$ to only one of the possible branches, while still preserving the other branches for those cases with superobservers, Poincaré recurrence and so on. The only way I see to achieve this within Barandes' formulation is by letting the information about the occurrence of an event at $t'$ play an active role through the (contingent) probabilities $p_j(t')$. As long as we are certain of the outcome of the event at $t'$, the probability of a future event will be determined exactly by the transition matrix $\Gamma_{ij}(t \leftarrow t')$ associated with the branch corresponding to the outcome at $t'$. Interference between different branches is still possible whenever something happens that is equivalent to erasing all information about the outcome of the event at $t'$.

The divisible subsystem transition map prevents the configuration of the subsystem from jumping across quasiclassical branches. The divisible transition map is a near exact description of the subsystem, and only fail to apply in the superobserver/recurrence scenarios I mentioned above. You seem to be suggesting the divisible transition map applies even in these speculative scenarios. It does not.

I disagree. Marginalizing over environmental degrees of freedom only causes the probability of a future event to be represented by a statistical mixture, not the system to remain on a single branch.

The transition map obtained by marginalizing over environmental degrees of freedom will indeed prevent the system from jumping across branches.

 

[Sambuco]

You seem to be suggesting the divisible transition map applies even in these speculative scenarios. It does not.

No. What I said (or at least tried to say) is that if there is information (even in the environmental degrees of freedom) about the outcome of the event at $t'$, this makes it a division event, and the standalone probability of a future event is exactly $p_i(t) = \Gamma_{ij}(t \leftarrow t')$. If, on the other hand, that information is erased, there is no longer a division event at $t'$, so the stochastic map is now $p_i(t) = \Gamma_{ik}(t \leftarrow 0) p_k(0)$. I think we both agree on that.

The transition map obtained by marginalizing over environmental degrees of freedom will indeed prevent the system from jumping across branches.

Maybe I'm misunderstanding you. Marginalizing over environmental degrees of freedom produces the transition map $p_i(t) = \sum_j \Gamma_{ij}(t \leftarrow t') p_j(t')$. Are you also saying something like "What this statistical mixture means is that the system is constrained to a single branch, we just don't know which one it is"? If that is the case, I agree.

Lucas.

 

[Morbert]

No. What I said (or at least tried to say) is that if there is information (even in the environmental degrees of freedom) about the outcome of the event at $t'$, this makes it a division event, and the standalone probability of a future event is exactly $p_i(t) = \Gamma_{ij}(t \leftarrow t')$. If, on the other hand, that information is erased, there is no longer a division event at $t'$, so the stochastic map is now $p_i(t) = \Gamma_{ik}(t \leftarrow 0) p_k(0)$. I think we both agree on that.

I'm not sure what you mean by "the stochastic map is now [...]". The stochastic map of the universe $\tilde{\Gamma}(t\leftarrow 0)$ is indivisible. The stochastic map of the quasiclassical subsystem $\Gamma(t\leftarrow 0)$ is divisible, as the subsystem is regularly imprinting on environmental degrees of freedom in the universe. If, in the future, some speculative process like a superobserver or Poincare recurrence renders $\Gamma(t\leftarrow 0)$ unreliable, it will have still have been reliable for the timescales of human history Albert brings up. I.e. We can use this divisible stochastic map to reliably infer Napoleon from his records, even if in the very very very distant future it might no longer be a reliable stochastic map.

Maybe I'm misunderstanding you. Marginalizing over environmental degrees of freedom produces the transition map $p_i(t) = \sum_j \Gamma_{ij}(t \leftarrow t') p_j(t')$. Are you also saying something like "What this statistical mixture means is that the system is constrained to a single branch, we just don't know which one it is"? If that is the case, I agree.

I probably agree with the spirit of your quoted statement, but a transition map is not a statistical mixture. What you have posted above is a linear marginalization relation. The marginalization that yields a divisible transition map is equation (50) in Barandes's paper. In that section, he derives the subsystem transition map $\Gamma^\mathcal{S}$ from the subsystem + environment transition map $\Gamma^\mathcal{SE}$.

A transition map says nothing about what state the system is in. It is instead the dynamical rule by which the system will evolve, whatever configuration it is in.

[edit] - I'm not saying you disagree. I'm just trying to tighten up the language.

 

[Morbert]

@Sambuco Maybe the conversation can be refocused by telling me which statement you disagree with.

i) The transition map of the entire universe (under appropriate assumptions about the universe) is indivisible.

ii) Following Barandes's procedure 3.7, we can write down a candidate transition map of the Earth that is divisible.

iii) Until we are at recurrence times, or until a superobserver imposes their will on the universe, the transition map from ii) will reliably describe the dynamics of Earth. So much so that it is effectively exact across human timescales.

iv) This transition map will constrain the configuration of Earth from "jumping across quasiclassical branches". I.e. It will ensure the Earth evolves quasiclassically.

v) Therefore, humans can use the transition map from ii) to reason about the past state of the Earth based on present-day observations (e.g. infer Napoleon existed based on records of his campaigns).

 

[Sambuco]

@Sambuco Maybe the conversation can be refocused by telling me which statement you disagree with.

I agree with your last two posts. Thanks @Morbert!

As an aside, it seems to me that Barandes's formulation does not necessarily imply an ontology where the configuration of the system is defined at every instant. Therefore, I believe the formulation is compatible with an interpretation based on sparse events, such as relational quantum mechanics. I think something like this could alleviate the difficulties some may have with the fact that, although the configuration takes a defined value at every instant, there is no continuity, so particles could "jump" between division events, as we have already discussed in relation to the double-slit experiment.

(edit): I just noticed that in the last section of this recent paper, Barandes says:
"This interpretation has a thoroughly realist orientation, and does not entail parallel universes, nor does it involve perspectival or relational notions of ontology."

Lucas.

 

[Fra]

As an aside, it seems to me that Barandes's formulation does not necessarily imply an ontology where the configuration of the system is defined at every instant.

I think it explicitly does!

But this ontology is understood differently, the same thus goes for that there is a definitey history also.

But there exist no global realist phase space that can encode the union of all subsystem histories consistently without destroying interference. The "realist perspective" of Baranes is more that the world can be understood as a union of "real" subsystems, that are as real as anything gets, and have definite histories - BUT when you put these things together in a causally local way you arrive at a system exhibiting quantum interference, but it seems to give a new understanding to causation. There is no univeral causation in terms of initial state -> future state. Barandes formulation suggest that there is only a universal stochastical constraints that determines how parts of the sytem interact stochastically with other parts.

So I think Barandes moves the "weirdness" of an entagled system, like we ask what IS IT, to saying that all the entagled parts are not "complex" they are just real stuff, but he suggest new dynamical laws, that constrain the stochastics of the parts.

And of course that this is equivalent to the simple dynamics in hilbert space, but instead we get a "werid ontology" because noone understands what a hilbert space is.

(edit: On re-reading the last paragraph I see it seems to add nothing not already said above, so i removed it, no need to rephrase. )

/Fredrik

 

[gentzen]

And of course that this is equivalent to the simple dynamics in hilbert space, but instead we get a "werid ontology" because noone understands what a hilbert space is.

Can you please read your sentence carefully yourself, and then fill in the missing words? Maybe then I have a chance to understand it.