Do Bell and PBR together point toward nonlocal reality?

[DrChinese]

Could you post a concise statement of PBR, or a link to such a statement? I remember reading the paper and yawning, because it didn't seem like it said anything that I didn't already know (or suspect).

[edit]Never mind, I found a good discussion here:
http://mattleifer.info/2011/11/20/can-the-quantum-state-be-interpreted-statistically/

That is the same link I posted above.

The issue about PBR and dBB vis a vis that link is: can 2 dBB wave functions overlap as shown in the Probability Density diagram? To quote: "... the question is: should we think of it as an ontic state (more like a phase space point), an epistemic state (more like a probability distribution), or something else entirely?"

The idea being that if the dBB wave function is sharply defined (as I think Ilja is saying), there can be no overlap. But that in turn is in contradiction to statistical spread from our unknown initial conditions. So I think if the dBB pilot wave is to be considered real: then there is no spread of values, there are hidden variables, there is non-local determinism and QM is incomplete. While PBR would say that if there are hidden variables, there must be a spread of outcomes for a particular wave state, and there will be overlap (therefore placing the theory in Group 1 and being prohibited).

I realize to the Bohmian, they see PBR as either neutral or a plus for their position. But I see it as either neutral or a negative for their position. As more and more elements of dBB are developed and declared, I think there are more and more opportunities for Bohmian class theories to run afoul of PBR in a fashion that they would not with Bell.

In other words: I agree with you that demonstrating the equivalency of QM and Bohmian class theories is not trivial. I think the idea that Bohmian theories *automatically* reproduce all QM predictions is unjustified. Logically, there must be a lot of ways to formulate the interaction effects of particle positions - and they can't all be equivalent (and be equivalent to QM at the same time). The very fact that there are multiple versions of dBB would imply that as well. Again, I cannot say *exactly* what is wrong with the Bohmian reasoning on this, but it certainly raises a lot of questions in my mind.

 

[stevendaryl]

I might point out that entropy can increase from "now" in both time directions. Obviously most lab situations are special cases in which entropy is made to be unusually lower than the surroundings. If you sampled the entropy of a typical environment, in thermal equilibrium: wouldn't you expect it to be at a local minimum? Ie the number of states it could have evolved from and the number of states it can evolve towards are both greater than now? That would be the statistical view, I believe. In a film of that, I do not believe you could discern its direction as forward or backward in any way (in contrast to the usual idea of a film of a glass breaking being an example of the time direction being obvious).

Or alternately, think of decoherence: entanglement disperses and decreases as you go forward in time. Does that require a fundamental time asymmetric law to describe as well?

There is a time-symmetric model of the second law that applies to classical physics (and I assume that it can be extended to quantum mechanics, as well).

Imagine taking a human being--okay, for ethical reasons, let it be a guinea pig, instead--and putting it inside an impenetrable, eternal box. No energy or matter can go in or out. Now just wait--a billion years, a trillion years, $10^{100}$ years, however long it takes. After a while, the guinea pig will die, and decompose and will reach some kind of uninteresting equilibrium state, and its component atoms will remain in that state for an ungodly length of time. But there will always be a certain amount of random thermal motion of the atoms. Purely by chance, if you are willing to wait forever, the atoms will eventually arrange themselves to a configuration that is arbitrarily close to the original state of the guinea pig. In other words, the guinea pig will eventually come back to life, a reversal of entropy.

But over an enormous span of time, if you plot entropy as a function of time, what you will find is that:

1. By far, the most likely configuration is the maximal possible entropy.
2. Very rarely, the entropy dips down to a non-maximal value.
3. In almost all such cases, the entropy returns quickly to a higher value.

The picture shows a typical plot of entropy vs time. Situations of type A are vastly more likely than situations of type B, which are vastly more likely than situations of type C, etc. So whatever the entropy is, if it's not the maximal value, then you are overwhelmingly likely to have higher entropy in the future, even though the graph is completely symmetric between past and future.

So the guinea pig, looking forward in such a universe can assume the second law of thermodynamics. He will likely age, die, and decompose just as the second law predicts.

What's weird about this thought experiment is that while the guinea pig can safely assume that he will be older and more decrepit in the future, he can't assume that he will be younger and in better health in the past [edit: was 'future']. In this model, the most likely past for the guinea pig is one in which he is older than now. It's overwhelmingly likely that right now the guinea pig is youngest he has been for millennia and the youngest he will be for millenia to come.

 

[DrChinese]

So this film would show the evacuation of the chamber before the experiment and the flooding with air afterwards?

...

Puh, I think this really leads off topic.

Probably right about off-topic...

But as to the film: Consider a film of a volume of air in equilibrium. You cannot tell forward from backward (until you reach the boundary in which it is no longer in equilibrium).

Or: Why do we see the arrow of time as forward? Is that a requirement of (the fundamental law of) increasing entropy? Or is it just a coincidence? Or maybe it has something more to do with initial conditions.

 

[stevendaryl]

That there is an animal named mechanism for causality is new to me, as far as I know causality is fundamental, assumed as given from the start. But, I guess, we think about different things named "causality".

In this case, I'm using causality to mean the propagation of effects. You drop a pebble into a pool of water, and the ripples spread out away from where you dropped it. Someone seeing those ripples will likely conclude that there must have been some disturbance at the apparent source of the outgoing circular waves. But the equations describing the propagation of waves in water are time-symmetric. So it is consistent with those equations to have converging concentric waves as well as diverging waves. So how do you explain why you always see diverging waves, and never see converging waves? It has to do with boundary conditions. The outgoing waves are the only possibility that is consistent with the boundary conditions.

 

[DrChinese]

My point was not a logical proof, but that there is strong empirical evidence that there is no time symmetry in nature. That there is an animal named mechanism for causality is new to me, as far as I know causality is fundamental, assumed as given from the start. But, I guess, we think about different things named "causality".

How is causality fundamental? Measuring a non-commuting observable on a system in a known eigenstate always produces a random value. That doesn't sound like empirically fundamental anything.

So I say that causes (or influences) from the future would appear (to us) as randomness in the present. Again, I am imagining some kind of time symmetric formulation of QM. That doesn't seem to be more of a stretch then imagining a Bohmian formulation in which all particle positions everywhere are a part of the equation. At least in the TS formulation, your limit of things to consider resides in a nice Einsteinian time cone (albeit in 2 directions).

Of course, beauty is in the eye of the beholder.

 

[kith]

What's weird about this thought experiment is that while the guinea pig can safely assume that he will be older and more decrepit in the future, he can't assume that he will be younger and in better health in the future. In this model, the most likely past for the guinea pig is one in which he is older than now. It's overwhelmingly likely that right now the guinea pig is youngest he has been for millennia and the youngest he will be for millenia to come.

Yeah. In relation to the origin of the universe, this argument states that it is incredibly more likely, that all of the observable universe was created in a fluctuation just a moment ago, instead of in a fluctuation with a much lower entropy during the Big Bang. I think this goes back to Boltzmann and it is quite puzzling.

Or: Why do we see the arrow of time as forward? Is that a requirement of (the fundamental law of) increasing entropy? Or is it just a coincidence? Or maybe it has something more to do with initial conditions.

I see this more clearly now, thanks. I still have a gap in my understanding regarding the relation between coarse-grained entropy and microscopic theory, though.

 

[Jon_Trevathan]

Yakir Aharonov's time symmetric interpretation of quantum mechanics (TSQM) offers a way to explain the EPR paradox and preserve local realism. (A TSQM-based explanation of the EPR Paradox was the #18 post in this discussion.) Please note that Yakir Aharonov was a student of Bohm and was very familiar with the deBroglie–Bohm theory (dBB). TSQM replaces dBB and, as noted above, provides a way to explain EPR, where dBB does not. For an introduction to TSQM, see post #23. For a few of the experiments which confirmed results TSQM had uniquely predicted, see post #24. As to the "realism" question, see posts #25 and 26.

 

[DevilsAvocado]

Regarding the Arrow of time and the Second law of thermodynamics, as “QM freak” it’s easy to forget gravity:

Clearly the initial conditions in the early universe, is what gives the direction and destruction of exergy. Energy can’t be destroyed but exergy can, and exergy is the fuel that drives the universe.

My guess is that the perplexity regarding T-symmetry etc will be gone once we get a complete theory for QM gravity, hopefully...(The thing that tickles me is the question – What if gravity was “turned on” after “matter creation”?? – there you have the special initial conditions in a little box! ;)

 

[stevendaryl]

I see this more clearly now, thanks. I still have a gap in my understanding regarding the relation between coarse-grained entropy and microscopic theory, though.

The idea about how the Liouville Theorem is consistent with increasing coarse-grained entropy is illustrated with the following picture: Imagine a system starting out with an uncertainty given by a certain compact volume in phase space, as shown on the left. With time, that simple shape evolves to a much more complex shape, such as the one on the right. The shape has the same actual volume as it did previously. But if you do coarse-graining, and ignore the details of the shape, the shape on the right appears to have a larger volume of phase space than the one on the left. So coarse-graining (ignoring tiny details)

 

[Demystifier]

But it is essentially forbidden. String theory publishes thousands of articles without a single empirical prediction. Based on the alternative approach, you can be happy if you succeed to publish a single paper, if you succeed to derive the whole particle content of the standard model from simple principles applied to a quite simple model (arXiv:0908.0591), and you can be sure that nobody even looks at it - once this horrible approach requires a preferred frame.

This effect, well known to all of us working on less popular theories in physics, has more to do with sociology and psychology than with science. I was thinking a lot about it and concluded that scientists are just like all other "ordinary" people. Even if they are more intelligent than the average, they are not much more rational. But let me not enter into the details, because that would be off topic ...

 

[Ilja]

How is causality fundamental?

There is no explanation in terms of anything more fundamental.

Measuring a non-commuting observable on a system in a known eigenstate always produces a random value. That doesn't sound like empirically fundamental anything.

Different values of the probability have also some cause. Not? By the way, I'm not talking about "empirically fundamental". This sounds like a contradiction for me. Empirical predictions are always quite complex derived things.

So I say that causes (or influences) from the future would appear (to us) as randomness in the present. Again, I am imagining some kind of time symmetric formulation of QM. That doesn't seem to be more of a stretch then imagining a Bohmian formulation in which all particle positions everywhere are a part of the equation. At least in the TS formulation, your limit of things to consider resides in a nice Einsteinian time cone (albeit in 2 directions).

I don't follow. In dBB it depends on a 3-dimensional configuration, in your TS on two four-dimensional. By the way, if the future already exist, we need no causality at all. The future simply remains as it is, it does not have to change at all.

 

[Ilja]

Yakir Aharonov's time symmetric interpretation of quantum mechanics (TSQM) offers a way to explain the EPR paradox and preserve local realism. (A TSQM-based explanation of the EPR Paradox was the #18 post in this discussion.) Please note that Yakir Aharonov was a student of Bohm and was very familiar with the deBroglie–Bohm theory (dBB). TSQM replaces dBB and, as noted above, provides a way to explain EPR, where dBB does not. For an introduction to TSQM, see post #23. For a few of the experiments which confirmed results TSQM had uniquely predicted, see post #24. As to the "realism" question, see posts #25 and 26.

Seen them and answered in #28.

Anyway, causal influence from the future violates Einstein causality too, it allows only causal influences from the past light cone. Thus, Einstein causality would be dead even in your choice. If it is not about causal influence from the future (which is how I interpret the paper) then it is about something different and irrelevant as an explanation of the violation of Bell's inequality.

For me, causal influences from the future are mystical sci-fi nonsense not worth to be considered seriously. To take it seriously, one would need extremely strong empirical evidence. Something completely unexplainable with classical causality as in dBB. If you think otherwise, your choice.

 

[Demystifier]

But if you know the position of a particle at all times, then you know the velocity at all times (well, if the position is a differentiable function of time). Yet position and velocity are non-commuting.

Yes, but I think that's not what Dr Chinese had in mind.

 

[Demystifier]

Thanks, that's a nice point of view. I still don't understand something: both the quantum potential and the probabilities are derived from the wave function. The wave function and the potential are regarded as ontic in the PBR sense. So where does the epistemicity -which is reflected by the probabilities- come from? Or speaking in terms of classical mechanics: we seem to have an equation for a state of knowledge ρ which describes the motion of some particles in an ontic potential V(ρ). This is hard to reconcile for me.

Let me use a simple classical analogy. Suppose that you have lost your keys in your apartment, but you have no idea in which room have you lost them. What you know is that some rooms are bigger and others are smaller. The rooms themselves and their size are ontic properties. Now, do these ontic properties imply some epistemic (probabilistic) properties as well? Yes they do. You can easily conclude that the probability of finding the keys in a given room is proportional to the size of the room. It is more likely that you will find the keys in a bigger room than in a smaller one.

In Bohmian mechanics, instead of the room you have wave function, and instead of the room's size you have |psi|^2. The bigger |psi|^2 at a given point, the bigger probability that you will find the particle there.

 

[kith]

Thanks, stevendaryl and Demystifier. I have learned quite a bit from this thread. :-)

 

[DrChinese]

There is no explanation in terms of anything more fundamental.

Circular reasoning. You assume that which you conclude, which is that causality rules. That would more or less force you down the Bohmian path. And voila...

 

[Jon_Trevathan]

Seen them and answered in #28.
For me, causal influences from the future are mystical sci-fi nonsense not worth to be considered seriously. To take it seriously, one would need extremely strong empirical evidence. Something completely unexplainable with classical causality as in dBB. If you think otherwise, your choice.

You need to read the papers I cited.

 

[Ilja]

@Jon_Trevathan: I have read (and cited) one of them, what was interesting for me has been clarified, I have no interest in interpretations which use confusing time-symmetric notions to describe a time-asymmetric world.

@DrChinese: No circular reasoning because I have never claimed that I can somehow conclude that causality has to be fundamental. In my opinion it is, and I have never seen a meaningful approach where it has been non-fundamental, derived from something different. Feel free to introduce me to such an approach.

 

[bohm2]

An interesting paper that kind of relates to the topic of this thread:

Theorem 16 (PBR). For any preparation independent theory that reproduces(a certain set of ) quantum correlations, the wavefunction is ontic.Motivated by this, we present a weak version of Bell’s theorem [3], in which we additionally assume preparation independence. The proof here is similar to that of proposition 14 and striking for its simplicity. The theorem could also be regarded as a combination of the PBR theorem, and a result closely related to the following, proved in [8].

Theorem 17. Quantum mechanics is not realisable by any preparation independent, local theory. Proof. If quantum mechanics is realisable by a preparation independent theory then, by the PBR theorem, the wavefunction is ontic with respect to that theory. We proceed by showing that there exist quantum correlations that cannot be realized by any local model for which the wavefunction is ontic...

On the Reality of Observable Properties
http://arxiv.org/pdf/1306.3216.pdf

If I'm interpretating this correctly, this is the reason why Leifer argued that using PBR we can now "infer nonlocality directly from EPR":

As emphasized by Harrigan and Spekkens, a variant of the EPR argument favoured by Einstein shows that any psi-ontic hidden variable theory must be nonlocal. Thus, prior to Bell's theorem, the only open possibility for a local hidden variable theory was a psi-epistemic theory. Of course, Bell's theorem rules out all local hidden variable theories, regardless of the status of the quantum state within them. Nevertheless, the PBR result now gives an arguably simpler route to the same conclusion by ruling out psi-epistemic theories, allowing us to infer nonlocality directly from EPR.

PBR, EPR, and all that jazz
http://www.aps.org/units/gqi/newsletters/upload/vol6num3.pdf

 

[DrChinese]

@DrChinese: No circular reasoning because I have never claimed that I can somehow conclude that causality has to be fundamental. In my opinion it is, and I have never seen a meaningful approach where it has been non-fundamental, derived from something different. Feel free to introduce me to such an approach.

Umm, Quantum Mechanics?

Perhaps you know of *something* where indeterminism (raw chance) does not play a part. Anything actually. How about human behavior? Ever seen the slightest indication that A causes B there? Structure of the universe, what caused the sun to be where it is and the Earth to be where it is. Anything...?

And if you even bother to mumble something about initial conditions, you will really bring a smile to my face. In fact you already have...

 

[Ilja]

Umm, Quantum Mechanics?

How does QM derive causality?

Perhaps you know of *something* where indeterminism (raw chance) does not play a part. Anything actually. How about human behavior? Ever seen the slightest indication that A causes B there?

?? Suggests that you seem to think that indeterminism somehow is in contradiction with causality.

Structure of the universe, what caused the sun to be where it is and the Earth to be where it is. Anything...?
And if you even bother to mumble something about initial conditions, you will really bring a smile to my face. In fact you already have...

As I said, it seems that your notion of causality is very different from my ideas about causality.

 

[stevendaryl]

How does QM derive causality?

I can let Dr. Chinese answer for himself, but I thought the point of quantum mechanics is that causality isn't fundamental. There is no causality at the level of microscopic physical laws, so the appearance of causality at the macroscopic is some kind of emergent phenomenon.

 

[Ilja]

This is one position. But I doubt it is well justified, because it depends on the interpretation.

Essentially, independent of the physical theory, it is always possible to use a more solipsistic, positivistic interpretation which remains silent about causality at all. In QM such a positivistic interpretation - the minimal interpretation - is quite popular, that's all.

In the Copenhagen interpretation, there are at least some elements of causality, or at least I think so: The measurement is the cause of the collapse of the wave function. The dBB interpretation is a classical causal interpretation.

The key point for me is that a positivistic interpretation cannot derive any causality at all. It can compute, and derive from more fundamental assumptions, probabilities and correlations. That's all. Observation can give only correlation, and theories which allow to compute only observables, that means, probabilities and correlations, are in a similar situation, they can give only correlations.

You need a theoretical hypothesis to go beyond correlations. Causality is something about the underlying reality.

 

[stevendaryl]

The key point for me is that a positivistic interpretation cannot derive any causality at all. It can compute, and derive from more fundamental assumptions, probabilities and correlations. That's all. Observation can give only correlation, and theories which allow to compute only observables, that means, probabilities and correlations, are in a similar situation, they can give only correlations.

That's certainly right. You can't derive causality from mere correlation. However, the phenomena that gave rise to our notions of causality can be understood without actually using causality. In this case, causality would be an effective theory, rather than fundamental, in the same sort of way that thermodynamics is an effective theory, while the more fundamental theory is the physics of many interacting particles.

I don't think it's accurate to describe non-causal theories as "solipsistic". I would almost go so far as to reverse that. It's human nature to prefer causal theories, but there is no reason for the world to try to work in a way that is intuitively understandable to humans.

 

[stevendaryl]

You need a theoretical hypothesis to go beyond correlations. Causality is something about the underlying reality.

I'm not convinced that there is a non-fuzzy notion of causality that goes beyond correlations. People typically are satisfied with a theory that predicts future states of the world in terms of past states, usually described with differential equations. But a differential equation is simply stating a correlation between future states and past states. It doesn't actually say that the past causes the future. What additional thing do you need to get causality?

I'm not sure.

 

[Ilja]

What you need is a theory. A theoretical hypothesis.

A deterministic equation can be considered, of course, as a particular example of a causal theory. You have the equation of the theory, and the initial state, the result follows with certainty. But, of course, the causal theory is a little bit more: It also presupposes a direction of time (causal influence is from past to future).

But there may be, of course, also causal theories which are not deterministic. Something like the initial conditions A cause B, but we do not observe B but instead B' which with some probability 5% differs from B. Or A and B and C together causes D, but unfortunately we cannot prepare A and B and C with certainty, and A and B, together with some null assumption about C, gives D with probability 95% or so.

That causality goes beyond correlation is obvious. Correlation gives us p((A and B) or (not A and not B)) = 1.
Causality gives us A causes B, or B causes A, or C causes A and C causes B, already three different theories, in fact an infinity because for different C we have different causal explanations.

 

[halfrealist]

What is the status of measurement problem in the light of PBR theorem?

 

[eloheim]

Does considering a specific scenario, like the one presented below, help any in sorting out the differing notions of causality (and implications thereof) discussed in this thread?

Quantum correlations with no causal order

Here's a popular article describing the research. I know these things tend to be sloppy but I had the bookmarks together so please don't hate me:

Quantum causal relations: A causes B causes A

 

[stevendaryl]

What you need is a theory. A theoretical hypothesis.

But how does the theory predict that a correlation is actual a causal relationship? I'm not convinced that the word "cause" plays any role in physics that can't be played by "correlation".

 

[stevendaryl]

Does considering a specific scenario, like the one presented below, help any in sorting out the differing notions of causality (and implications thereof) discussed in this thread?

Quantum correlations with no causal order

Here's a popular article describing the research. I know these things tend to be sloppy but I had the bookmarks together so please don't hate me:

Quantum causal relations: A causes B causes A

Thanks for the references.

 

[DrChinese]

I can let Dr. Chinese answer for himself, but I thought the point of quantum mechanics is that causality isn't fundamental. There is no causality at the level of microscopic physical laws, so the appearance of causality at the macroscopic is some kind of emergent phenomenon.

Well said. I do not think any notion of causal influences is really necessary for orthodox QM. Does a unique set of initial (quantum) conditions always produce a unique outcome? No, and certainly not as far as anyone knows.

So I guess that the appearance of causality is much like the appearance of a thermodynamic arrow of time.

 

[bohm2]

What is the status of measurement problem in the light of PBR theorem?

PBR has no effect on the measurement problem but, since you brought it up, others do argue that the issue of causality/probability/randomness/time direction discussed in above threads do depend on how the quantum measurement problem is resolved:

In quantum theory, the statistical move plays no particular role: the results of quantum statistical mechanics arise from the quantum dynamics of individual states and do not depend on any additional probabilistic postulate. As a consequence, debates about the nature of classical statistical-mechanical probability are not of direct relevance to our understanding of the actual world as described by contemporary physics. Probability in contemporary physics arises from the probabilistic nature of quantum theory itself, not from any additional posit.

That `probabilistic nature' depends on how the quantum measurement problem is resolved. According to dynamical-collapse theories, it is a fundamental stochasticity, analogous to pre-quantum stochastic mechanics. According to (deterministic) hidden-variable theories, it is a consequence of a probability distribution over the hidden variables, analogous to pre-quantum statistical mechanics. According to the Everett interpretation, it is something new, not analogous to either; it is controversial whether this means that Everettian probability is more or less well understood than pre-quantum probability.

The direction of time in the probabilistic macrodynamics of quantum theory is also dependent on the resolution of the measurement problem. In dynamical collapse theories, it is a consequence of the fundamental time-asymmetry of the dynamics. In the Everett interpretation, and in hidden-variable theories, it is a consequence of a non-probabilistic constraint on the initial quantum state.

Probability in physics: stochastic, statistical, quantum
http://philsci-archive.pitt.edu/9815/1/wilson.pdf

 

[Ilja]

But how does the theory predict that a correlation is actual a causal relationship? I'm not convinced that the word "cause" plays any role in physics that can't be played by "correlation".

There is a correlation between IQ and race. A lot of people care about explanations for such a correlation. Genes? Environment? Which environmental influence?

Of course, this example may be an unfortunate choice, because the various causal theories used to explain this correlation have a strong ideological background, so one may doubt that they are scientific theories. At least in some completely objective, idealized science, one may argue, these theories should be rejected as unscientific.

But even if these theories may be attractive to people with certain ideological backgrounds, they remain scientific. Because they allow to make predictions. The theory that some C is the cause of the correlation can be tested by considering various constellations where C is absent or present. Ok, this part is reducible to correlations: The theory leads to predictions about other correlations.

But this is not the only way to decide if C is a reasonable cause. There should be, in this case, a reasonable causal explanation, that means, a mechanism which explains why C, say more books at home, can lead to a higher IQ.

And, sorry, this part is much more interesting at least for me. If I find a way to replace a claim about A correlates with B by C correlates with A as well as with B, this does not really sound like a scientific progress. But if we find a causal explanation for something where initially there was only a strange correlation, we have a different situation.

It is, of course, not an accident that I have chosen an example from everyday life and not from fundamental physics. The point is that the everyday life example makes the difference more clear. Instead, the interpretations of fundamental physics I consider as distorted by the influence of positivism.

 

[stevendaryl]

There is a correlation between IQ and race. A lot of people care about explanations for such a correlation. Genes? Environment? Which environmental influence?

But isn't it true that what we're really worried about is how robust the correlation is? Here's an example that's a little less controversial. Suppose we notice a correlation between the length of a tree's shadow and the position of the sun in the sky: In the morning and evening, the shadow is very long, and the sun is low in the sky. At noon, the shadow is very short, and the sun is high in the sky. So can we control the sun by manipulating the length of the shadow? Of course not, but the failure to be able to do that doesn't actually require causality, but can be seen through correlations alone. If you make the shadow shorter by cutting off the top of the tree, the position of the sun doesn't change. The correlation disappears.

It seems to me that most of the time that we are interested in causality, we can re-express our interests in terms of correlations.

 

[Ilja]

It seems to me that most of the time that we are interested in causality, we can re-express our interests in terms of correlations.

This may be indeed possible, but is it helpful?

There is, so to say, a subtype of correlations we can name "causal correlations". These causal correlations have, first, a particular sequence in time, A->B means t(A)<t(B) in a fundamental notion of time. Second, they have realistic explanations, some mechanism which explains it, which, in terms of correlations, may be described as a sequence of other causal correlations, such that A->C₁->C₂->C₃...->C_n->B. Is that all? No, there is also that the smallest causal connections C_k->C_k+1 in this sequence which we are able to find out have more elementary character, they are usually of an especially simple type, say, some bodies simply moving inertially or so, and usually much more universal.

Note also that this explanatory sequence requires that all of these correlations are of the special causal type, thus, t(C_k)<t(C_k+1). And than there is the additional hypothesis that for every intermediate t t(A)<t<t(B), there has to be yet another C_t between them, A->C_t->B. And that this explanation has to be complete, that means, after controlling for the correlations which are explained by this sequence, there is no remaining correlation between A and B, else the explanation is not complete and one has to look for other causal explanations.

Thus, looking for causal connections means looking for especially simple correlations with some special properties. It is, so to say, a guidance for our research, which of the correlations are really interesting and helpful and which are more of less accidental, like all those correlations studied by astrology.