How valid is the indivisible interpretation of quantum mechanics?

[Fra]

And I really do think Barandes is stronger realist than you think, and he even says stuff like this in that last Albert interview and others before. You can have something be not inferrable but objective if you just don't have epistemic access to measuring it properly. A star ligt years away will have objective properties I don't have any access to because its too far away and I don't have appropriate technology to bridge the gap sufficiently.

For me, realism concerns the ontological elements of a paradigm: what the theory treats as currently instantiated facts, defining the context itself. Those facts may have a connection to inferential or evolutionary history, but they are real relative to the context in which they occur.

Objectivity, on the other hand for me at least, concerns whether different inferential perspectives are mutually consistent and converge on the same claims. This is because inferential perspectives is central to my preferred paradigm.

So in this sense something can be real, without beeing objective, precisely because its out of empirical reach for other perspectices. Barandes IMO replaces the hypothetical "inside observer" with "subsystems". In my view the configuration of the subsystems in Barandes views are "real", but not "objective". In my personal view, "reality" is necessariy contextual. Objectivity OTOH, is about consistnecy in between contexts. This is in the sense which he removes the observer, but the subsystems implictly takes its role, and this is in a way good as it emphasising that an observer is of course simply a subsystem of the universe, not a human or a brain.
In Barandes’s view, I would say the configurations of subsystems are real, but not automatically objective. This is exactly the sense in which they may constitute a new kind of hidden variable: real relative to their native context, but not necessarily invariant across all contexts.

The decomposition of the whole system into subsystems is itself not unique, so a “subsystem configuration” is real relative to a particular decomposition or context. But it is the contexts that interact. What becomes objective is the stable transition structure, Gamma.

/Fredrik

 

[Morbert]

Sure, but the quantum dictionary and the Born rule basically have the same form. The difference is kind of trivial, and I think that can be used to make point. No one interprets the Born rule as giving you a stochastic process, only a probability. And so how can the dictionary give you anything more than just a probability either. But a stochastic process needs more than that.

The dictionary terms give you the elements of the transition matrix, which plays the role of dynamics in an indivisible stochastic process. Does an indivisible stochastic process need to specify more than that? From Calvo's paper:

This is not the first stochastic approach to quantum theory; but it is the first indivisible approach with a satisfactory underlying philosophy (ontology) which is based on quantum theory, as opposed to classical dynamics.

Sure, but if you want the other multi-time probabilities then they are going to have to be related to those conditional probabilities by marginalization and the product rule. The point I am trying to make is that the correspondence says absolutely nothing about some additional stochastic process. Sure, no stochastic process is ruled out, but the point is you can't actually know what is ruled out or not unless you actually try to produce a model of this stochastic process behavior. You have no idea whether what you envision a good underlying description to be is actually possible or not.

If you want to model quantum systems as a stochastic process with specified multi-time probabilities then godspeed. A motivation for this indivisible stochastic correspondence is the difficulties with the alternative (see the timestamped video below):

Well as far as the latest formulation is concerned, all the other major historical objections with regard to this question have been solved: https://arxiv.org/abs/2301.05467 e.g. pg. 8 . But the theory almost certainly still has this non-locality feature in analogy to Bohm.

I sometimes use "quantum mechanics" and "quantum theory" interchangeably. Is Nelsonian mechanics generalizeable to other quantum theories like quantum theories of fields, or of many-body systems with spin? When I get a chance I'll have a look at that paper.

 

[iste]

Does an indivisible stochastic process need to specify more than that?

I would say that an "indivisible stochastic process" is not a stochastic process. It doesn't have the multi-time joint probabilities to be interpreted as such and has nothing to say about those things. It is just a set of conditional probabilities which has nothing to say or even entail about trajectories.

If you want to model quantum systems as a stochastic process with specified multi-time probabilities then godspeed. A motivation for this indivisible stochastic correspondence is the difficulties with the alternative

Okay, but the reason these views have had issues is that they are putting their neck out to specify the trajectories. Not specifying trajectories does not ameliorate this problem but avoids it. If you had many attempts at specifying trajectories that either fail or are undesirable for one reason or another, then this should actually make you skeptical of a perspective that postulates trajectories but doesn't want to specify them ... until they actually do specify some laws or something like that which is informative about their properties. If you don't view the indivisible approach in terms of trajectories then obviously this is an alternative to those other failed or undesirable trajectory approaches contingent on some interpretation of what the conditional probabilities mean metaphysically (that doesnt involve trajectories).

I sometimes use "quantum mechanics" and "quantum theory" interchangeably. Is Nelsonian mechanics generalizeable to other quantum theories like quantum theories of fields, or of many-body systems with spin? When I get a chance I'll have a look at that paper

Yes, but obviously with the preferred spacetime foliation caveats.

e.g.

https://scholar.google.co.uk/scholar?cluster=15973777865898642687&hl=en&as_sdt=0,5&as_vis=1

https://arxiv.org/abs/2307.03188

 

[iste]

For me, realism concerns the ontological elements of a paradigm: what the theory treats as currently instantiated facts, defining the context itself. Those facts may have a connection to inferential or evolutionary history, but they are real relative to the context in which they occur.

Objectivity, on the other hand for me at least, concerns whether different inferential perspectives are mutually consistent and converge on the same claims. This is because inferential perspectives is central to my preferred paradigm.

So in this sense something can be real, without beeing objective, precisely because its out of empirical reach for other perspectices. Barandes IMO replaces the hypothetical "inside observer" with "subsystems". In my view the configuration of the subsystems in Barandes views are "real", but not "objective". In my personal view, "reality" is necessariy contextual. Objectivity OTOH, is about consistnecy in between contexts. This is in the sense which he removes the observer, but the subsystems implictly takes its role, and this is in a way good as it emphasising that an observer is of course simply a subsystem of the universe, not a human or a brain.
In Barandes’s view, I would say the configurations of subsystems are real, but not automatically objective. This is exactly the sense in which they may constitute a new kind of hidden variable: real relative to their native context, but not necessarily invariant across all contexts.

The decomposition of the whole system into subsystems is itself not unique, so a “subsystem configuration” is real relative to a particular decomposition or context. But it is the contexts that interact. What becomes objective is the stable transition structure, Gamma.

/Fredrik

What is it about the indivisible approach that attracts you though; i would have thought to our kind of perspective doesn't necessarily need this kind of indivisible view?

 

[Morbert]

I would say that an "indivisible stochastic process" is not a stochastic process. It doesn't have the multi-time joint probabilities to be interpreted as such and has nothing to say about those things.

And other people say an indivisible stochastic process is a stochastic process because it concerns a system modeled with a configuration space and a stochastic dynamical law. Our disagreement should be more substantive than definitional alignment.

It is just a set of conditional probabilities which has nothing to say or even entail about trajectories.

Just because probabilities over trajectories aren't specified doesn't mean nothing at all is said about them. The transition matrix as a stochastic dynamical law imposes constraints on trajectories. I can be confident, for example, that my trajectory will not involve a trip to the moon.

Okay, but the reason these views have had issues is that they are putting their neck out to specify the trajectories. Not specifying trajectories does not ameliorate this problem but avoids it. If you had many attempts at specifying trajectories that either fail or are undesirable for one reason or another, then this should actually make you skeptical of a perspective that postulates trajectories but doesn't want to specify them ... until they actually do specify some laws or something like that which is informative about their properties. If you don't view the indivisible approach in terms of trajectories then obviously this is an alternative to those other failed or undesirable trajectory approaches contingent on some interpretation of what the conditional probabilities mean metaphysically (that doesnt involve trajectories).

Not sticking its neck out is the gambit: Distilled dynamics with no commitment as to whether they are realized by some compact conceptualizeable process like Bohmian mechanics or some arbitrarily complex process specified by towers of probabilities known only to God. This is metaphysically compatible with an actually-existing microphysical trajectory

Yes, but obviously with the preferred spacetime foliation caveats.

e.g.

https://scholar.google.co.uk/scholar?cluster=15973777865898642687&hl=en&as_sdt=0,5&as_vis=1

https://arxiv.org/abs/2307.03188

I won't comment further on this project until I bring myself up to speed on it.

 

[PeterDonis]

I can be confident, for example, that my trajectory will not involve a trip to the moon.

How do you know?

 

[iste]

And other people say an indivisible stochastic process is a stochastic process because it concerns a system modeled with a configuration space and a stochastic dynamical law. Our disagreement should be more substantive than definitional alignment.

You can call an indivisible stochastic process anything you want, it doesn't change anything about the fact it has no necessary connection to stochastic trajectories.

This is metaphysically compatible with an actually-existing microphysical trajectory

You don't actually know that if you're not going to actually demonstrate it. And the only examples that do exist, mainly Bohmian and Nelsonian mechanics, are going to be rejected by this perspective. In a theory that eludes classical explanation, there is a burden to prove that a realistic process can reproduce quantum behavior in ways you find acceptable.

 

[danieltanfh95]

One way to read this argument is that particles are emergent instead of fundamental. Barandes shows that if we take particles to be fundamental, we pay costs (non-Markovian indivisible dynamics, the three structural gaps David Albert names in his 2025 PhilSci notes at item 26777, the whole “distilled dynamics with no commitment about trajectories” texture), which are what particle-preservation approaches have been paying for a hundred years.

Modern QFT is already effectively wave-realist in its mainstream reading, with fields as fundamental and particles as Fock-space labels of field states. Barandes’ theorem, on this reading, gives structural evidence for a direction that has been developing since Schrödinger’s 1926 wave mechanics to treat the matter-wave as real.

 

[PeterDonis]

Modern QFT is already effectively wave-realist in its mainstream reading, with fields as fundamental and particles as Fock-space labels of field states.

Quantum fields aren't waves, they're operators. So I don't think "fields as fundamental" is the same thing as "wave-realist".

 

[danieltanfh95]

Quantum fields aren't waves, they're operators. So I don't think "fields as fundamental" is the same thing as "wave-realist".

Sure, my point is that the canonical wave-particle duality picture is challenged on this reading of Barandes' work. QFT already treats fields as fundamental and particles as derived, so this reading points toward wave-realism even if the full derivation isn't in yet.

 

[PeterDonis]

my point is that the canonical wave-particle duality picture is challenged on this reading of Barandes' work.

But you're claiming more than that:

QFT already treats fields as fundamental and particles as derived

Ok so far, but...

this reading points toward wave-realism even if the full derivation isn't in yet.

...this is an additional claim which, as I've already said, is not implied by QFT, because quantum fields are operators, not waves.

 

[PeterDonis]

QFT already treats fields as fundamental and particles as derived

I would say QFT also treats waves as derived--they're coherent states, just as particles are Fock states. The fundamental entities in QFT are operators, since that's what quantum fields are.

 

[danieltanfh95]

I would say QFT also treats waves as derived--they're coherent states, just as particles are Fock states. The fundamental entities in QFT are operators, since that's what quantum fields are.

Operators are mathematical objects, no? Are you describing more of an instrumentalist reading of QFT?

 

[PeterDonis]

Operators are mathematical objects, no?

Everything in a theory of physics is mathematical objects.

Are you describing more of an instrumentalist reading of QFT?

I'm not describing any particular reading of QFT. I'm just pointing out that QFT doesn't imply what you claimed it implies.

 

[Morbert]

How do you know?

Equation (5) from the paper: $p(t) = \Gamma(t\leftarrow t_0)p(t_0)$. Given some initial distribution $p(t_0)$, the dynamics $\Gamma(t\leftarrow t_0)$ give us future distributions $p(t)$. No realistic dynamics will give a nonvanishing probability that I am on the moon anytime soon.

 

[Morbert]

You don't actually know that if you're not going to actually demonstrate it. And the only examples that do exist, mainly Bohmian and Nelsonian mechanics, are going to be rejected by this perspective. In a theory that eludes classical explanation, there is a burden to prove that a realistic process can reproduce quantum behavior in ways you find acceptable.

This is too close to ground we've covered in other threads. Not sure there's value in rehashing it.

 

[PeterDonis]

No realistic dynamics

What restrictions are there on the dynamics in the actual theoretical model under discussion that would ensure that they are "realistic"? Note that in standard QM, as pop science articles from people like Brian Greene are fond of pointing out, there are tiny but nonzero amplitudes for all kinds of outlandish things happening, like you being transported through a wall--or to the moon.

 

[iste]

Sure, my point is that the canonical wave-particle duality picture is challenged on this reading of Barandes' work. QFT already treats fields as fundamental and particles as derived, so this reading points toward wave-realism even if the full derivation isn't in yet.

Wave realism is exactly the opposite of what Barandes is going for, and his formulation can be applied to fields such that you have a perspective of fields based on classical-like configurations, and which is not wave-realist (or operator-realist aa such). I also give a link to another formulation of QFT which is like this, but further along than what stage of development the Barandes view of QFT is at, in post #93 of this thread.

 

[danieltanfh95]

Everything in a theory of physics is mathematical objects.


I'm not describing any particular reading of QFT. I'm just pointing out that QFT doesn't imply what you claimed it implies.

Theories of physics study physical invariants in reality. There has to be some mapping between the mathematical objects a theory uses and physical reality, otherwise the theory gets falsified by the experiments we run on that reality. I can't specify the full mapping here (nor do I have one), but I want to point at one direction the argument opens onto.

Wave realism is exactly the opposite of what Barandes is going for, and his formulation can be applied to fields such that you have a perspective of fields based on classical-like configurations, and which is not wave-realist (or operator-realist aa such). I also give a link to another formulation of QFT which is like this, but further along than what stage of development the Barandes view of QFT is at, in post #93 of this thread.

I agree that Barandes' own view isn't wave-realist. He extends his reverse-derivation of QM-with-particles to an ontology reading that 'reality is made of non-Markovian indivisible processes'. What David Albert and I push back on is that reading. The empirical structure of physical reality is Markovian at the fundamental level. Schrödinger evolution is Markovian in the wave function, and quantum field equations of motion (Dirac, Klein-Gordon, Yang-Mills) are Markovian in the field. Non-Markovianity appears when we project these Markovian dynamics onto particle-configuration variables and condition on them.

That's what leaves waves as fundamental (under the traditional wave-particle duality). Waves are what evolves Markovianly, particles are what shows non-Markovian conditional probabilities upon projection. The full derivation isn't in yet, sure, on how to specify what the wave-content is physically and how detector-side particle discreteness emerges from wave-only ontology, but the direction is clear, imo.

 

[PeterDonis]

There has to be some mapping between the mathematical objects a theory uses and physical reality

Of course. But that doesn't mean the mathematical objects are reality. Nor does it mean that the mapping in question has to be simple.

Waves are what evolves Markovianly

In QFT, which is what we've been discussing, it would be quantum fields that evolve Markovianly, yes? As I've already pointed out, quantum fields are not waves.

 

[danieltanfh95]

Of course. But that doesn't mean the mathematical objects are reality. Nor does it mean that the mapping in question has to be simple.

Perhaps there was a misunderstanding. I wasn't claiming that mathematical objects are reality. I was noting that since waves and particles are real (or emergent from some underlying reality) and mathematical operators are abstract, mathematical operators can't be what waves and particles physically derive from. There might be something else that is fundamental. I don't know what that is, but the framing lets us explore what that might be.

In QFT, which is what we've been discussing, it would be quantum fields that evolve Markovianly, yes? As I've already pointed out, quantum fields are not waves.

On QFT Markovianity: wave-realism identifies 'waves' with the quantum state, not the field operators. In the Schrödinger picture this is the wave functional Ψ[φ] over field configurations, which evolves Markovianly under the QFT Schrödinger equation. Field operators act on the state to give expectation values. This can be characterized as a question of 'interpretation of QFT', but my view is that we do need to specify (or explore) what physical structure the mathematical objects represent.

Additionally, I suspect we can explore this via empirical anchoring, looking for specific physical facts that force the formalism into place, similar to how cosmological and experimental data forced upgrades from Newton's gravity and Schrödinger's wave equation.

 

[PeterDonis]

which evolves Markovianly under the QFT Schrödinger equation

But this throws away relativity, since the QFT Schrodinger equation forces you to pick a particular frame, which makes your definition of "wave" frame-dependent. And one of the central lessons of relativity is that things that are physically real can't be frame-dependent; physical reality has to be contained in invariants. (I believe you yourself used the word "invariant" in this connection in a previous post.)

Field operators act on the state to give expectation values.

In the particular formulation of QFT you refer to, yes. But as noted above, this formulation, as you're using it, isn't really consistent with relativity. And there are other formulations of QFT, such as the path integral formulation, that don't require any notion of "state" at all--all you need to compute probabilities are the starting preparations and the final measurements.

 

[Fra]

What is it about the indivisible approach that attracts you though; i would have thought to our kind of perspective doesn't necessarily need this kind of indivisible view?

My motivation is rooted in a different paradigm - ABM-like rather than ordinary system dynamics, so I am not sure I can convety this out of context. I will just give a few short statements as hints.

In my view dynamical laws are emergent and replaced, or at least grounded, by stochastically driven decision-making based on an evolving predictive encoder. This changes the fine-tuning problem into an evolutionary stability problem: stable effective laws are those that survive and equilibrate under the constraints of interaction, prediction, memory, and "computation". So instead of starting from “one state space” with a fixed law that are manually fine tuned to fit experiment, understanding interactions for me means understanding how subsystems interact, stabilize, and constrain each other.

I associate Barandes unistochastic transition structure with a limiting case of such an encoder in a steady state. In that sense the stochastic-quantum correspondence functions as a correspondence principle for me: if the effective process approaches a unistochastic structure, then I know it can reproduce ordinary quantum theory.

A stochastically evolving predictive encoder does not have access to unlimited external memory or computation. It is constrained by its own configuration, its own encoding capacity and the stochastic constraints imposed by its context. Ie. the "system IS the dice".

Now the appeal if indivisibility

I think indivisibility is what physically constrained prediction looks like from inside a finite-capacity predictive context interacting with a larger environment.

The intrinsic question is P(next transition|now)

Here (P) is associated with the subsystem itself. It is intrinsically evolved within the subsystem’s predictive context, not merely obtained by marginalizing over some fictive God’s-eye environment. The latter may be mathematically possible, but it corresponds to an externalized perspective that the subsystem itself does not physically possess.

By contrast, P(future path|now) is the wrong question IMO

where the first element of the path is the next transition, is a more expensive construction. It requires specifying much more representational structure, but it does not necessarily add predictive value for the next move! Whatever the future path turns out to be, the system still evolves one transition at a time. Barandes also raises the issue that this requires specifying alot of information, and we dont want what. Thius is not a practical matter for me, I see it as as a constraint of effiency of a subsystem can possible encode and process. And my default assumption is that nature has evolved to be pretty efficient.

And in the general case after each transition, the predictive context changes. You effectively get a new dice. So a fixed path measure constructed at the initial time is not the natural primitive. Not updating the predictive engine in light of the latest information would not increase fitness, it would be dynamically suboptimal.

So I have issues with the value/meaning of thes higher order probabilities; specifically from the perspective of decision making under constraints.

/Fredrik

 

[Morbert]

What restrictions are there on the dynamics in the actual theoretical model under discussion that would ensure that they are "realistic"? Note that in standard QM, as pop science articles from people like Brian Greene are fond of pointing out, there are tiny but nonzero amplitudes for all kinds of outlandish things happening, like you being transported through a wall--or to the moon.

If quantum mechanics describes me (a subsystem heavily coupled to my environment) as evolving according to a quantum channel $\Phi_t(\rho)$, then the corresponding theory of me as an indivisible stochastic process will have dyanmics $\Gamma(t)$ where the chance of transitioning from configuration $j$ to configuration $i$ is $$\Gamma_{ij}(t) = \mathrm{tr}P_i\Phi_t(P_j)$$ The chance of me transitioning from here $h$ to the moon $m$ is $$\Gamma_{mh}(t) = \mathrm{tr}P_m\Phi_t(P_h)\approx 0$$The usual caveats about this being effectively 0 rather than exactly 0 apply.

 

[danieltanfh95]

But this throws away relativity, since the QFT Schrodinger equation forces you to pick a particular frame, which makes your definition of "wave" frame-dependent. And one of the central lessons of relativity is that things that are physically real can't be frame-dependent; physical reality has to be contained in invariants. (I believe you yourself used the word "invariant" in this connection in a previous post.)


In the particular formulation of QFT you refer to, yes. But as noted above, this formulation, as you're using it, isn't really consistent with relativity. And there are other formulations of QFT, such as the path integral formulation, that don't require any notion of "state" at all--all you need to compute probabilities are the starting preparations and the final measurements.

The Schrödinger picture in QFT is Lorentz-covariant. Tomonaga (1946) and Schwinger (1948) generalized the functional Schrödinger equation to arbitrary spacelike Cauchy surfaces.

The Markovian character of fundamental dynamics doesn't hinge on picking that formulation. Markovian at the field level means the future field is fixed by the present field and its conjugate momentum, with no history dependence, which lives in the equations of motion rather than in the picture, like how the Dirac equation is first-order in time in any Lorentz frame and the Heisenberg equations are first-order commutator dynamics. The path integral inherits the semigroup property from locality of the Lagrangian. Every fundamental formulation has the generator depending only on the current field, not on the history. The non-Markovianity in Barandes' correspondence comes from projecting this onto particle-configuration variables, which makes it a marker of a projected description, not of a fundamental one.

 

[Sambuco]

I would like to participate in the discussion, as I have an objection to Barandes' formulation (we already talked a little about that in other threads), and I'm not sure if it's related to the one @iste is pointing out.

My objection to Barandes' interpretation lies in the fact that he postulates the existence of "things" that are not physical, in the sense that they play no role in his own theory. To understand what I mean, it's worth noting that, given the stochastic-quantum correspondence, Barandes' formalism could be described by saying that, between division events, the position of a particle at each instant in time is a well-defined variable whose probability is given by the square of the wave function. As we've already discussed in another thread, this allows for cases like a particle entering through one slit and exiting through the other in the two-slit experiment. This doesn't have to be a problem in itself, the issue is that these values for the position of a particle are not physical, in the sense that they don't appear in the equations of the theory!

Another way to look at it is by examining how this same issue is addressed in other $\psi$-epistemic interpretations. For example, in RQM, it's argued that, in general, $P(c|a) \neq \sum_i P(c|b_i) P(b_i|a)$. Since assigning a value to $b$ has no physical meaning, it is assumed that it does not (physically) exist. In contrast, what Barandes does is start from the fact that it is possible to define the probabilities of a variable taking one value or another at time $t$ and, from this, conclude that that variable must take some value at that moment.

In a way, this might seem to contradict well-known no-go theorems, such as Bell's and/or Kochen-Specker's. One way to see how Barandes' interpretation is able to overcome this type of no-go theorems is to think that these implicitly assume a divisible temporal evolution, but the truth is much simpler: Barandes's interpretation assigns a value to the variables at each instant in time, but these values are not physical, they play no role in the theory, and they aren't even mentioned in it!

Lucas.

 

[Fra]

Perhaps i misunderstand the core of your objection, but here is a comment on what I think you might mean.

the issue is that these values for the position of a particle are not physical, in the sense that they don't appear in the equations of the theory!
...
Barandes's interpretation assigns a value to the variables at each instant in time, but these values are not physical, they play no role in the theory, and they aren't even mentioned in it!

In a game of expectations, which I think we have at hand, the stochastic constraint of one one subsystem, must not be dependent on the "true values" of configuration of other subsystems. That is the beauty. There should not be an instantaneous influece here, this is guaranteed by the fact that only the stochastic constraints of the various subsystems are tuned/relational - not their stochastics itself.

The real configuration spaces are hidden to other subsystems. The stochastic evolution of each subsystem are tryly independent, it's only the constraints that are related. So the fact that the hidden configurations are not explicitly entering the dynamics is not a flaw to me, it is the soluton.

In this sense the configuration can be real, and have a real history, as seen from the subsystem itself. I'd say the role the configuration plays is that it represents the evolution of the stochastic process.

/Fredrik

 

[Sambuco]

the stochastic constraint of one one subsystem, must not be dependent on the "true values" of configuration of other subsystems

The issue is that the "true value" of the configuration of a subsystem plays no role, even in the temporal evolution of the same subsystem.

In this sense the configuration can be real, and have a real history, as seen from the subsystem itself.

This is not true for the reasons I explained above. Of course, this is something Barandes is aware of. In his work 10.31389/pop.186 (arxiv.2302.10778), he wrote:

"To the extent that quantum theory is empirically adequate, the higher-order conditional probabilities are then unobservable in experiments and will be left unspecified in this paper (...) Whether there exists some theoretical principle that picks out one set of higher-order or whole-trajectory probabilities from all the various possibilities is a question that will be left to future work."

Lucas.

 

[Morbert]

The non-Markovianity in Barandes' correspondence comes from projecting this onto particle-configuration variables, which makes it a marker of a projected description, not of a fundamental one.

Are you saying a stochastic process modeled with field configurations would be Markovian?

 

[danieltanfh95]

Are you saying a stochastic process modeled with field configurations would be Markovian?

No. For example, Bohmian QFT (Struyve-Westman or Dürr-Goldstein-Tumulka-Zanghì) constructs stochastic processes where field configurations are the state variables, and the process is Markovian only in the extended (φ, Ψ[φ]) space and non-Markovian in the field configurations alone.