I Carroll interviews Barandes on Indivisible Stochastic QM

[gentzen]

The ontological and nomological commitments are straightforward: The system is in a classical configuration, and evolves stochastically along a trajectory in configuration space, with dynamics given by directed conditional probabilties. Stochastic doesn't mean arbitrary.

The directed conditional probabilities by themselves don't yet specify (or commit to) a dynamics for the classical configuration between two division events. This is because the directed conditional probabilities are from a division event to some time in between division events.

If we look at a time $t_m$ exactly in the middle between two division events (say at $t_0 < t_1$), and take your "I read this to mean" seriously, then we have two probability distribution that both describe the classical configuration at $t_m$. Without further clarification, it is ambiguous what this means. (My guess is that Barandes would prefer the probability distribution from the division event at $t_0$.)

The clearest solution for you and me (i.e. people who are not Barandes himself) is probably to accept that his theory has not (yet) made ontological commitments to any dynamics or evolution of the classical configuration between division events. Its only ontological commitment is that the system is always in a unique classical configuration at each point in time.

The correspondence is exact, so there is exact agreement with experiment.

Let us look at the correspondence in detail:
1) For simplicity, we start with an unistochastic matrix which smoothly depends on time.
2) We choose an unitary matrix suitably, that reproduces the given unistochastic matrix, and also depends smoothly on time.
3) We choose a Hamiltonian which generates the time dynamics of the unitary matrix.

This correspondence allows us to exactly reproduce the predictions of non-relativistic QM, by running those steps backwards, i.e. starting with a Hamiltonian and the identity matrix in Hilbert space, get the time dependent unitary matrix that this dynamics generates, and compute the unistochastic matrix from that unitary matrix.

The question whether this correspondence (or quantum reconstruction) is predictive arises for me, because the description of the physical situation and how QM makes predictions about it are missing here. So my question is: Have quantum reconstructions (including the one by Barandes) focused too much on complex numbers and Hilbert spaces, and missed the actual empirical content of QM?

However, I realized that it is good that you try to defend Barandes' proposal, because Barandes himself "lacks the time" to do it. This gives people like me the opportunity to present their quibbles as clear as possible. I still try to bring across two concrete "fixable"/"doable" things.

By the way, my other "doable" thing (i.e. quibble) is that in step 2) above, Barandes has not yet shown that the smooth dependence on time of the unistochastic matrix translates into a smooth dependence on time of the unitary matrix. I guess this will be true, but as a mathematician I still have to insist that Barandes has not shown this yet.

 

[Fra]

So my question is: Have quantum reconstructions (including the one by Barandes) focused too much on complex numbers and Hilbert spaces, and missed the actual empirical content of QM?

Good question, and I think this ia very often true!

Taking the empirical content - in context - serious is what lead me to the inference perspective and the insight that both the inference process and its context are constrained physically, just like real physics llmit computational power etc. But exactly how isnt clear.

/Fredrik

 

[Morbert]

The directed conditional probabilities by themselves don't yet specify (or commit to) a dynamics for the classical configuration between two division events. This is because the directed conditional probabilities are from a division event to some time in between division events.

If we look at a time $t_m$ exactly in the middle between two division events (say at $t_0 < t_1$), and take your "I read this to mean" seriously, then we have two probability distribution that both describe the classical configuration at $t_m$. Without further clarification, it is ambiguous what this means. (My guess is that Barandes would prefer the probability distribution from the division event at $t_0$.)

The two distributions are answers to different questions: One distribution answers what the configuration is likely to be, given an initial distribution at $t_0$. The other answers what the configuration was likely to have been, given a later distribution at $t_1$. Since distributions are epistemic rather than ontological, I don't see the issue with two distributions.

I will admit though that I do not see this explicitly addressed in the papers so far, so this is indeed my reading. At the very least I don't anticipate issues so long as the premises laid out in the paper are taken seriously.

Let us look at the correspondence in detail:
1) For simplicity, we start with an unistochastic matrix which smoothly depends on time.
2) We choose an unitary matrix suitably, that reproduces the given unistochastic matrix, and also depends smoothly on time.
3) We choose a Hamiltonian which generates the time dynamics of the unitary matrix.

This correspondence allows us to exactly reproduce the predictions of non-relativistic QM, by running those steps backwards, i.e. starting with a Hamiltonian and the identity matrix in Hilbert space, get the time dependent unitary matrix that this dynamics generates, and compute the unistochastic matrix from that unitary matrix.

The question whether this correspondence (or quantum reconstruction) is predictive arises for me, because the description of the physical situation and how QM makes predictions about it are missing here. So my question is: Have quantum reconstructions (including the one by Barandes) focused too much on complex numbers and Hilbert spaces, and missed the actual empirical content of QM?

Pointer expectation values, response rates etc. make up the empirical content of QM and, by extension, unistochastic processes.

 

[gentzen]

Since distributions are epistemic rather than ontological, I don't see the issue with two distributions.

I just thought that the two distributions nicely illustrate that without further clarification, it remains ambiguous whether there is an evolution of the classical configuration between two division events, or which type of evolution is intended.

However, I realized that it is good that you try to defend Barandes' proposal, because Barandes himself "lacks the time" to do it. This gives people like me the opportunity to present their quibbles as clear as possible.

I think I now presented my quibbles as clear as I wanted. (Of course, others are free to present their quibbles even more clearly, or to refute my quibbles to their satisfaction.) Thanks for providing me with that opportunity.

As for

Pointer expectation values, response rates etc. make up the empirical content of QM and, by extension, unistochastic processes.

I will have to study other quantum reconstructions first to get a better picture of "the empirical content of QM" they try to capture, and how well they succeed.

 

[Fra]

I just thought that the two distributions nicely illustrate that without further clarification, it remains ambiguous whether there is an evolution of the classical configuration between two division events, or which type of evolution is intended.

My personal opinion on this, is it seems to me most conceptually consistent view is that the actual "configuration" which consists of a number of distinguishable states, which in the generaly case, hardly has form a continuum - does change stochastically step by step.

So while we can imagine a continous probability that changes continously, this would just be some prospensity, but the actual configuration space should not a priori allow uncountably many small steps.

If if you picture a random walk, where each step implies information update and a division event, I think there is conceptual way to distinguis the intermediate state. Either the configuration is distinguished to change or is didn't.

Of course, one can imagine the actual steps beeing "small enough" to effectively form a continuum from some perspective, but that I see as some limiting case. Is the continuum itself not only real valued, but "REAL", or is it just a limiting case of a fictional high complexity limit?

This detail will IMO get critical in a reconstruction, the way limits are manipulated in physics is a well known tragedy, although it has nothing specificalyl to do with Barandes,

I will have to study other quantum reconstructions first to get a better picture of "the empirical content of QM" they try to capture, and how well they succeed.

For me, the "empirical picture" should involve also the "empirical inferece/fitting" of parameters of hamiltonian and state spaces, or equivalentnyl the transition matrix. The limit fallacy is again always done, and we picture "perfect, infinite, ideal" statisitcs. Which is fine for normal subatomic physics. But what about cases where the empirical processing is taking seriously, and the processing capacity timescale is slow, as comapare to the empirical testing. Then what happens can't be described by models constructed taking not fictional limits (fictional as is not empirically and practicaly realizable).

/Fredrik

 

[iste]

I just thought that the two distributions nicely illustrate that without further clarification, it remains ambiguous whether there is an evolution of the classical configuration between two division events, or which type of evolution is intended.

Yes, in https://arxiv.org/pdf/2302.10778 he seems to acknowledge that there is no meaning to trajectories without constructing higher-order conditional probabilities which he says he leaves to future work:

"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. In particular, probabilities assigned to whole trajectories, as constructed from higher-order conditional probabilities in the sense of (10), are then left unspecified as well. The higher-order conditional probabilities of an indivisible stochastic process could, in principle, vary contingently from one set of instantiations or runs of the process to another. 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."

But my belief is that these higher-order probabilities are already specified by quantum mechanics and they are due to measurement disturbance and so make it impossible to make a logistically sensical picture of these trajectories. The nonsensical picture is in fact already implied by the fact that translating the quantum evolution into any generic unistochastic system means the measurement device pops up (e.g. https://philpapers.org/rec/BARADA-16, pg. 15). He also says in the above arxiv reference:

"indivisible quantum theory is a manifestly contextual theory, with a
given quantum system’s beables belonging to a specific measurement context"

They cannot have a meaning without measurement. Beables in Bohmian mechanics and stochastic mechanics are non-contextual and they freely move without the measurement device present. Explicitly including the measurement device then re-introduces contextuality in these pictures so that you get definite trajectories when the system isn't being measured, that are then subsequently perturbed if one were to involve the measurement device at some point in time. The problem with Barandes is that the measurement device is always there; constructing trajectories with the measurement device there at every time-step is just a bizarre picture. I think you can make an argument that the unistochastic transition probabilities conditioned on initial time describe behavior that would have occurred without measurement; because after all, the unmeasured Bohmian and stochastic mechanical probabilities are the same as one-time measurements probabilities in QM. But there is no way that conditional probabilities for intermediate times can be seen as describing the system independently of the measurement device, because the measurement device is what causes indivisibility in orthodox quantum mechanics, and I don't think this is a matter of interpretation. Or I think, maybe a more accurate way of saying it is that there can be no transition probabilities that are not conditioned on a potentially disturbing measurement using a device - or else there would be no indivisibility.

 

[Morbert]

"indivisible quantum theory is a manifestly contextual theory, with a given quantum system’s beables belonging to a specific measurement context"

They cannot have a meaning without measurement. Beables in Bohmian mechanics and stochastic mechanics are non-contextual and they freely move without the measurement device present.

You cut off the important part:

"indivisible quantum theory is a manifestly contextual theory, with a given quantum system’s beables belonging to a specific measurement context, and various classes of emergeables belonging to other measurement contexts, as detailed in Subsection 4.2."

From subsection 4.2

"Moreover,if indeed $\tilde{A}^S$ is an emergeable, then the measurement result obtained by the measuring device is an emergent effect of the interaction between the subject system and the measuring device rather than transparently revealing a physical aspect of the configuration of the subject system alone."

I.e. What is contextual is the observable as an emergeable vs as a beable. But beables themselves are properties of the subject system, not brought into existence by an interaction with the measurement device. Emergeables are what emerge from measurement device interaction.

 

[iste]

You cut off the important part:

"indivisible quantum theory is a manifestly contextual theory, with a given quantum system’s beables belonging to a specific measurement context, and various classes of emergeables belonging to other measurement contexts, as detailed in Subsection 4.2."

From subsection 4.2

"Moreover,if indeed $\tilde{A}^S$ is an emergeable, then the measurement result obtained by the measuring device is an emergent effect of the interaction between the subject system and the measuring device rather than transparently revealing a physical aspect of the configuration of the subject system alone."

I.e. What is contextual is the observable as an emergeable vs as a beable. But beables themselves are properties of the subject system, not brought into existence by an interaction with the measurement device. Emergeables are what emerge from measurement device interaction.

But positions at different times is also clearly contextual. Either way, if beables are always belong to a specific measurement context, the theorydoes not talk about them outside of a specific measurement context.

 

[Morbert]

But positions at different times is also clearly contextual. Either way, if beables are always belong to a specific measurement context, the theorydoes not talk about them outside of a specific measurement context.

A system (no measurement device) has, say, a variable $A(t)$ with a spectrum of magnitudes $a_1(t),\dots,a_N(t)$ depending on the system's configuration $i = 1,\dots,N$. No measurement device is needed for this to obtain.

 

[Fra]

This easily sounds a conceptually confusing I think. As I choose to view this, I think it makes no sense to speak about the configuration/beables as not requiring a mesurement device. I rather think of it all, that the beables are more like a kind of special trivial case of "self measurement" sort of made from the the unique "basis" of the self.

Ie. the beables, which we think of as "real", is the configuration that defines the system itself, relative to itself. It represents like the "state" of what the system can encode.

So I wouldnt sayt it's non-contextual as in objective beables or Bohmian, but it's more self-contextual. A subtle distinction but one that is important to me when thinking about it, otherwise it gets confusing. But I agree that "no external measurement device" is needed, as it's a sort of "self-reading" or self-nmeasurement of internal state.

Emergables I like to view more as a kind of "processed" or transformed information, where the input is beables or histories to beables. This is then "more contextual", as it adds a processing step, than is for ME (interpreting Barandes) is best understood not as internal processing of the observing system. And indeed this capability requires more complexity than the original system I think. But further interpreting this gets unavoidably leads to deeper interpretations of what it means, so I'll stop there.

/Fredrik

 

[gentzen]

I think I've only ever understood about two or three of Fra's posts!

Fra‘s frequent typos, word omissions, and grammar mistakes contribute a lot to making his posts hard to decipher:

This easily sounds a conceptually confusing I think.

This is then "more contextual", as it adds a processing step, than is for ME (interpreting Barandes) is best understood not as internal processing of the observing system.

But further interpreting this gets unavoidably leads to deeper interpretations of what it means, so I'll stop there.

Fra may believe that it is easy to deduce the intended text from this. But it is not, at least not for me.

 

[Fra]

Fra‘s frequent typos, word omissions, and grammar mistakes contribute a lot to making his posts hard to decipher:

My wife tells me the same, so its not just about physics

Fra may believe that it is easy to deduce the intended text from this. But it is not, at least not for me.

Im aware of this sorry. I should spend more time editing and explaining properly.

/Fredrik

 

[gentzen]

I should spend more time editing and explaining properly.

For me, checking your texts for omitted words and unnecessary typos before posting would be enough.

 

[iste]

A system (no measurement device) has, say, a variable $A(t)$ with a spectrum of magnitudes $a_1(t),\dots,a_N(t)$ depending on the system's configuration $i = 1,\dots,N$. No measurement device is needed for this to obtain.

Yes, but I would be assuming this anyway if we are talking about beables. And the emergeable / beable distinction isn't necessarily relevant either because a beable is an emergeable when the system is viewed from a different perspective, e.g. position vs. momentum basis.

 

[Morbert]

Yes, but I would be assuming this anyway if we are talking about beables. And the emergeable / beable distinction isn't necessarily relevant either because a beable is an emergeable when the system is viewed from a different perspective, e.g. position vs. momentum basis.

Remember that the underlying ontology here is the system's classical configuration, and so variables represented by a diagonal matrix in a configuration basis are what are considered beables. (see time stamp below).



It might be possible to construct a unistochastic reformulation based on momentum space instead of configuration space, where the sparse directed conditional probabilities that make up your dynamics (or the standalone probabilities make that make up your epistemic distributions) are over possible momenta vs possible configurations. QM doesn't privilege one basis over another, but I suspect it would be at the very least peculiar to interpret momenta as more fundamental than configurations. And Barandes has constructed his formalism around configurations.

 

[Fra]

I'll try to avoid missing words in this post. But it's nevertheless not trivial to explain, but comment again, using the logic of post#70 how I view all this.

And the emergeable / beable distinction isn't necessarily relevant either because a beable is an emergeable when the system is viewed from a different perspective, e.g. position vs. momentum basis.

Remember that the underlying ontology here is the system's classical configuration, and so variables represented by a diagonal matrix in a configuration basis are what are considered beables. (see time stamp below).

It might be possible to construct a unistochastic reformulation based on momentum space instead of configuration space, where the sparse directed conditional probabilities that make up your dynamics (or the standalone probabilities make that make up your epistemic distributions) are over possible momenta vs possible configurations. QM doesn't privilege one basis over another, but I suspect it would be at the very least peculiar to interpret momenta as more fundamental than configurations.

The question is how to understand the "preferred basis" that is sort of implicit i Baranders picture. But to avoid confusion with hilbert space basis, I think of it as a kind of "inferential basis" - ie the perspective from inferences are made, and the results encoded.

Different perspectives are conceptually analogous to different processing and encoding algorithms. A configuration space with beables, central to Baranders view requires that one holds only commuting codes. I think is the picture in which the information is encoded in the simplest possible, and sparsest way, it is in a sense distinguished as its optimal.

So while other encodings are possible, they may not be as efficient in the evolutionary context of predicting the future, in the local environment. So, the environment, would "select" the optimal representation. I think one can even form a mathematical question out of this in terms of optimal predictive encoding.

So how to understand the emergeables vs beables? I think of them conceptually as requiring a kind of active transformation of the internal structure of the "agent" or observing system. Ie. a litteral physical change in internal microstructure (although exactly how is a harder question).

So the unistochastics IMO must someone presume that all subsystem already attained their optimal internal equilibraration. And which each internal microstate sytem there is a natural configuration space. But these are subjective beables, not objective beables like in bohminan mechanis.

The problem i had and hinted all the time, with Barandes view is that - i find it HARD to really understand this system of unistochastic transition matrices, unless we can go geeper and understand how they come about, or how they evolved. But that process of evolution, necessarily need to be described outside unistochastic picture.

So I think of it like this, while the representation basis mathematically is arbitrrary, they are not equally fit in a given environment, so they are not physicall arbitrary, or say equally likely to be seen.

So I am still at the position that to further understand this deeper, the "explanation" to the unistochastic picture, must be found by first relaxing it, and then understand why it's some kind of attractor.

Edit: This indeed open another can of worms, as to argue for a physical selection among algoritms and representations of different effiency, some contraints on information capacity and memory is required. So then on needs to interpret what this menas physically, is it related to mass? or something else?

/Fredrik