The Paradigm of Kinematics and Dynamics Must Yield to Causal Structure by Robert W. Spekkens

Robert,

What if you treat time as effect of action, rather than measure of events. Not a progression from past to future, but the process by which future becomes past. Not the earth traveling a fourth dimension from yesterday to tomorrow, but tomorrow becoming yesterday because the earth rotates?

That way, cause and effect is not sequence, but energy exchange. Yesterday doesn't cause today, any more than one rung on a ladder causes the next. It is the sun radiating on a rotating planet that causes the sequence of events called 'days.'

Hello Robert,

From a practical standpoint it does seem that an over-reliance on kinematics in quantum theory and practice does result in a very static picture, leaving us little to say about even essential processes such as emission and absorption.

The limitations of space-time kinematics are studied from a classical perspective in the essay Is Kinematics Compatible With Field Symmetries? The investigation there shows that space-time kinematics can be replaced by dynamics using a 3-vector expression of de Broglie's wave mechanics. Does that help or hinder your arguments?

Steve Sycamore

Dear Robert,

Definitely, very good arguments. Congratulations.

I would like to make one point.

''So we can change the kinematics from conguration space to phase space and maintain the same empirical predictions by adjusting the dynamics accordingly. It's not possible to determine which kinematics, Newtonian or Hamiltonian, is the correct kinematics. Nor can we determine the correct dynamics in isolation. The kinematics and dynamics of a theory can only ever be subjected to experimental trial as a pair.''

Apart from mathematical manipulations, there is another way to produce ''new'' kinematics: conceptual questioning. For instance, classical mechanics kinematics is specified with a background space/time structure. If one asks the seemingly purely philosophical questions ''what is space?'',''what is time?'' we could indentify something different then the space/time structure to describe physics. For instance, we could perceive that we never measure displacements against the fixed invisible background, we measure relative displacements between visible objects. Also we never measure an invisible time parameter t, we measure the motion of a visible object we call a clock. So by constraining the MEANING of space/time statements to the behaviour of physical objects we get a completely different kinematics where the background is a derived concept.

Actually these thougts can be extended to field theries, and particularly to a 3-D metric field, and the result is GR! That is, GR is almost uniquely signed out by finding a more reasonable kinematics. This is Barbour´s research, shape dynamics.

I invite you to read my essay

, where I explore how different conceptions of motion, thus different kinematics, originated from conceptual questioning may lead to new and known physics.

Good luck in the contest,

Best Regards

Daniel

Dear Robert,

I really enjoyed your essay. It is clearly expressed, rich in context, and advocates a view with which I have great sympathy. I have a few remarks and questions.

1. Since dynamics in conventional physics involves time evolution, and since causal graphs incorporate their own notion of "time" given by the directions on the edges, how would you characterize the kinematics and dynamics of causal graphs themselves?

It seems to me that there are three separate things to specify: the class of causal graphs allowed (one might impose local finiteness, for instance), the class of "transitions" considered (one might use Sorkin's sequential growth, or alternatively one might add maximal antichains; this would be analogous to relativistic frames of reference), and the weights assigned to the transitions. The choice of class of graphs might be quite restrictive depending on what one is trying to model. However, it seems there might be many choices for the class of transitions, of which the two above are examples. Personally, I refer only to the specification of weights as dynamics; a different choice of transition class requires a different dynamics to describe the same physics, and I call the configuration space together with the choice of transition class a kinematic scheme. I describe this further in my essay here: On the Foundational Assumptions of Modern Physics.

2. Your comparison of the Hamiltonian and Newtonian formulations of mechanics raises the general question of when and if it is necessary to distinguish between direct and indirect causation. It appears the answer is that it is not necessary in this particular context, but it seems that you are allowing for different weights on the edges of the causal graphs themselves, rather than only at the higher level of transitions. In my own work on causal theory, with a view toward quantum gravity, I do not weight the relations of each classical universe, but only the transitions between, and I can see no reason to restrict to transitive graphs; i.e., it seems the distinction between direct and indirect causation is a priori important. What is your view on this?

Causal theory is the most promising viewpoint I know of from which to discuss the topics you raise, and you do a marvelous job of analyzing them. Take care,

Ben Dribus

Dear Robert Spekkens,

In Coherently-cyclic cluster-matter model of universe, dynamics and dimensionality coexists in time; in that the kinematics of macro objects includes disjunction and conjunction of string-matters on their Tribology and thus the union of dynamics and kinematics is predicted.

With best wishes,

Jayakar

Dear Dr. Spekkens,

This not is just to have you know I found your essay quite interesting and thought provoking, that is if for no other reason as perhaps suggesting a way of having the formalisms of physical theories be found to be more consistent and less ambiguous as they relate to their corresponding interpretations. However I'm also cautious when theory is to be restricted to such bare bones foundational limits that those elements not suggested by observation or consistent with existing or proposed theory would become as a consequence at risk to being totally ignored. That is I find it difficult to imagine how if such restriction if rigidly adhered to would allow intuition to continue to play as an important as it currently does respective of the expansion of physics, or lend the inspiration required to having it pursued.

In such regard I'm reminded of what Einstein warned about developing physical theory when he said, "The supreme goal of all theory is to make the irreducible basic elements as simple and as few as possible without having to surrender the adequate representation of a single datum of experience". That is I'd contend he would also have included experience as to take in what one could imagine how the physical world might be and not only as it's able to be observed or what our conceptualizations relating to theory would have them found needed to be. That is in short I find your argument to be a good one in the sense that we need examine new perspectives as to explore all the possibilities, yet not at the exclusion of the ones which have thus far proven to have served us so well.

Regards,

Phil

Here is an email I sent to the author before the essay was posted here. He suggested moving the discussion here.

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Hi Rob, [...] I thought I'd share some thoughts I had while reading it. In no particular order...

* Despite your attempt to distinguish your basic methodological principle ("any difference between two physical models that does not yield a difference at the level of empirical phenomena does not correspond to a physical difference and should be eliminated") from operationalism, I don't quite see how they're different. Or more precisely, I'm worried that your principle, if applied consistently, is just a sort of anti-realism that (while not exactly the same as operationalism) has a lot of overlap with operationalism's bad points. Concretely, it's not clear to me how, according to your principle, Ptolemy's and Copernicus' models of the solar system are different theories. Or how ordinary QM and dBB are different theories. Yet, I think, clearly, they are. Or, in terms of your Plato's cave example, I don't understand what it means to say that the shape hidden variable

(unlike color) has "explanatory power". Isn't the idea that there is also a third candidate theory on the table, namely the one that posits *neiter* of these hidden variables? And if this third theory predicts the same empirical phenomena as the shape hidden variable theory, wouldn't your principle force us to regard these as somehow equivalent, i.e., not take even shape seriously?

* Re: your discussion of the two versions of dealing with spin in dBB, the situation to me seems closely analogous to the theories with and without color in the Plato's cave example. The extra stuff that Bohm/Schiller/Tiomno posit (Holland also does a lot of this in his text) is really truly irrelevant to the empirical predictions, so long as one keeps in mind what you mention - that we humans become aware of experimental outcomes through the positions of pointers. So then I'm

confused why, again according to your guiding principles here ("constrain our model-building in such a way that every aspect ... has some explanatory function") I think the B/S/T version of spin simply fails that test, and so we aren't left with an example of two otherwise passable theories with different kinematics/dynamics but the same empirical implications.

* While (as you know) I definitely agree that it is important to distinguish what you call "kinematical locality" and "dynamical locality", I have the feeling that your description of "kinematical locality" doesn't sufficiently emphasize how strange its violation would be. It's not just that the physical state fails to factorize, but that the "physical stuff" posited by the theory doesn't live in 3+1 spacetime at all. The way you describe it makes it sound like "kinematical nonlocality" would be rather inocuous. But I think it would be extremely radical, perhaps even almost incomprehensible. With a violation of "dynamical locality" on the other hand, it's

perfectly clear what it means - faster than light influences - even if it's surprising from the point of view of relativity. But before relativity nobody had any particular idea that there should be some speed limit for causal influences, and indeed many people thought instantaneous action at a distance really existed. But as far as I know no serious scientist ever even dreamed of the idea that there might be physical stuff that doesn't live in ordinary space-time. Indeed, I really don't even know what that would mean. So this, I think, is the point of my "theory of exclusively local beables". Your description of it is perfectly sound, but again it seems unclear from what you write why anybody should care about a mere "proof of principle that kinematical locality can indeed be achieved". Maybe the particular model in question is indeed so silly that nobody should care, but I think people should care a great deal about trying to achieve a plausible TELB. Just as an illustration of how basic the assumptions here are, note that your very explication of "kinematical

locality" really presupposes the very notion in question: "if, for any two systems A and B, every ontic state lambda_AB of the composite is simply a specification of the ontic state of each component". But strictly speaking it isn't "any two systems" that need this property - it's specifically any two *spatially separated* systems. For example, I don't think it would be a violation of "kinematical locality" if, say, the spin and the color degrees of freedom for a single quark were entangled. But for two spatially separated particles to be in a spin singlet state does involve a violation (assuming quantum states are ontic). My point here is just that you can't even really say what would constitute a violation of "kinematical locality" without in some sense presupposing that there is a physical space with objects or systems or stuff of some kind that lives in it. That is, basically, the assessment of "kinematical locality" sort of presumes that we're

talking about a TELB but then relaxes just one relatively minor aspect of a theory's being a TELB. Taking the bull by the horns and accepting nonlocal beables on their own terms (and this is

*especially* the case for theories like MWI with *only* nonlocal beables!) is so unfamiliar and weird that it's really not even clear any more what one is talking about. Certainly it is then a severe

understatement to say something like "the ontic states of spatially-separated subsystems fail to factorize"; the real truth is that, if you just go by what the theory in question is positing and don't bring in outside "common sense" notions (like that the theory is "obviously" about particles, which "obviously" have positions in 3-space) there *are* no spatially-separated subsystems!

* What you say about what Bell said about kinematical locality and local beables seems not quite right: Bell refers "to models satisfying kinematical locality as theories of 'local beables'." In

my terminology, a model satisfying kinematical locality would be a theory of *exclusively* local beables, a TELB. Bell never insisted on any such thing - he only insisted that a theory must have *some* local beables, in order to make sense of empirical predictions (which after all come down to things like pointer positions) and in order to provide a meaningful formulation of ideas like locality. I think you are right that there are hints that his formulation of (dynamical) locality in some ways presupposes what you call kinematical locality, but strictly speaking he never insists on this and indeed assess various theories (ordinary QM, dBB) as (dynamically) local/nonlocal

even though they are not TELBs.

* Finally, I haven't thought about this nearly as much as you, but I have a vague and preliminary sense that your proposed "causal structure" alternative to kinematics/dynamics - as pictured in the happy little flowchart diagrams - kind of involves kinematical/dynamical notions. What are the bubbles if not statements of the (kinematical) state of something, and what are the arrows if

not statements of (dynamical) law? Clearly it is possible to characterize all of this without explicitly using these terms, but I worry that it nevertheless presupposes the kinematics/dynamics

distinction and so isn't really any kind of genuine alternative.

That's all I've got. Despite all of these quibbles, I really enjoyed reading the paper, which definitely made me think about new things in new ways, so thanks!

Thanks for your thoughtful comments. Let me try to respond to each in turn. (By the way, I'm sorry for the delay in replying to your email -- I've been on holiday for the last two weeks.)

* Concerning the methodological principle and operationalism. A longer paper would be required to properly answer questions about the kind of scientific realism I'm espousing here. First, let me try to express what I think is the difference between realism and operationalism. Here's an excerpt from a short article I wrote with Lucien Hardy (http://arxiv.org/pdf/1003.5008v1.pdf):

"But operationalism is not enough. Explanations do not bottom out with detectors going 'click'. Rather, the existence of detectors that click is the sort of thing that we can and should look to science to explain. Indeed, science seeks to explain far more than this, such as the existence of human agents to build these detectors, the existence of an earth and a sun to support these agents, and so on to the existence of the universe itself. The only way to meet these challenges is if explanations do not bottom out with complex entities and everyday concepts, but rather with simple entities and abstract concepts. This is the view of the realist. Without adopting some form of realism, it is unclear how one can seek a complete scientific world-view, incorporating not just laboratory physics, but all scientific disciplines, from evolutionary biology to cosmology. It is true of course that all of our evidence will come to us in the form of macroscopically observable phenomena, but we need not and should not restrict ourselves to these concepts when constructing scientific theories. For the realist, then, we need an interpretation of quantum theory."

My other beef with operationalism is just a beef with empiricism in general. The empiricist tradition promotes the notion that "why" questions are somehow inappropriate and that we should only ask "how" questions. That's fundamentally wrong in my view. Science is really about providing good explanations. That's why I think that a mere description of the shadows in the cave is not really good science, while an attempt at explaining their various forms in terms of the 2D projections of a 3D shape is good science. But I haven't said what counts as a good explanation. Hopefully, your realist intuitions align with mine and we can agree that certain accounts constitute better explanations than others. I see my methodological principle as a consequence of more general principles about what counts as a good explanation. For instance, one characteristic of a good explanation is that it should be difficult to vary. This kind of consideration is what makes "it was the will of the gods" a bad explanation. (This account of explanation has been promoted by Deutsch in his book "The beginning of infinity"). Any element of an explanation that can be varied without empirical consequence clearly doesn't pass the "difficult to vary" test. So my methodological principle can, I think, be motivated by this deeper principle. I haven't really thought too carefully about trying to formalize the notion of explanation, but hopefully this gives you an idea of what I'm after.

So to summarize, I think that with Plato's cave, colour should be excluded because it has no explanatory role to play. Similarly, the third option of neither shape nor colour should be excluded because it doesn't really provide any sort of explanation at all. I should have made it clearer in my article that the methodological principle is meant to help narrow down the options among approaches that espouse scientific realism. It was not intended as an argument for realism against operationalism. More general sorts of arguments suffice for that.

* Concerning Ptolemy and Copernicus. I'm not sure I have enough knowledge of the historical details of these two models to answer adequately. Nonetheless, from what little science history I've read, I have the impression that they did not make the same predictions, in which case the conditions for the applicability of my methodological principle are not met. But let me consider the case of a Ptolemaic-like model which makes precisely the same predictions as the Copernican model. It is really just a redescription of the Copernican model within a coordinate system that puts the earth at rest at the origin (adding whatever epicycles are required to achieve this). Given the way I've defined it, this model must now make precisely the same predictions as the Copernican model. The conditions of my methodological principle are now met. Because the object one puts at the origin (sun or earth) can be varied without empirical consequence, what the principle asserts is that this difference does not correspond to a physical difference. That seems right to me. The difference between the two models is purely a conventional one having to do with the choice of coordinate system.

* Concerning spin in deBroglie-Bohm. The orientation variable in the BST model is not like the colour property of the objects in Plato's cave because the outcome of a measurement does depend on the value that this variable takes prior to the measurement. Suppose that the Stern-Gerlach setup is such that the interaction between the spin and motional degrees of freedom begins at time t and that the location of the particle is measured at time t'. Although the measurement outcome is independent of the orientation at time t', it is not independent of the orientation at time t. This is because the dynamics of the Bohmian position depends on the Bohmian orientation during the interval between t and t'. So I think it is correct to say that the Bohmian orientation of the particle *does* have an explanatory role to play in the BST model. We would only have a good analogy with the colour variable in Plato's cave if we supplemented Bell's model with a Bohmian orientation that was irrelevant to the dynamics of the Bohmian position and irrelevant to the outcomes of any measurement.

* Concerning the distinction between kinematical and dynamical locality. I didn't mean to suggest that a violation of kinematical locality would be innocuous. I share your intuition that it is hard to even make sense of a theory that presumes a background space-time but which posits objects that have holistic properties, i.e. which don't "live" in space-time. However, unlike you, my view is that holistic properties are bizarre for any composite degrees of freedom, even if the components are not spatially separated (like your spin and colour example). I'm not sure exactly what you mean by "your very explication of 'kinematical locality' really presupposes the very notion in question." Are you arguing that one needs to specify a way of separating the whole into components before one can ask about kinematical locality relative to that notion of separation? If so, I don't agree. My own view is that we should require kinematical locality with respect to *every* decomposition of a system into independent degrees of freedom.

Consider psi-ontic models of quantum theory. One might say that one needs a preferred factorization of the Hilbert space into a tensor product of Hilbert spaces to define a notion of separation and thereby assess whether one has kinematical locality relative to this notion of separation. But actually, regardless of the factorization one uses, one finds that there are entangled states relative to this factorization, so one has a failure of kinematical locality for every choice of factorization. On the other hand, one has kinematical locality for the ontic state space of two classical bits regardless of the factorization. Suppose the "natural" factorization is into two bits, denoted a and b. One can also factorize the state space into a and the parity (a+b)mod2 . Or one can factorize into b and (a+b)mod2. In all cases, the ontic state space of the composite is the Cartesian product of the ontic state spaces of the components.

You also say that "as far as I know no serious scientist ever even dreamed of the idea that there might be physical stuff that doesn't live in ordinary space-time." I'm not sure about that assessment. Many physicists have suggested that space-time is not fundamental, but rather is an approximate and emergent description of something more primitive that does not live in space-time. My own view is that causal structure is more primitive than space-temporal structure. What I mean by this is that whereas it is usually assumed that part of the definition of a causal relation is that the cause precede the effect in time, one could rather assume that part of the definition of what it is for one event to precede another in time is that one event is a potential cause of the other. Similarly, for two events to be spatially separated means that they cannot be potential causes of one another.

* Concerning Bell's notion of local beables. I'd like to understand better precisely what Bell had in mind. I've always found it odd that in explaining his assumption of locality, he sometimes draws one diagram and sometimes another. In the first sort he draws space-like separated regions, labelled 1 and 2, and refers to a full specification of local beables in a space-time region 3 that screens off region 2 from the intersection of the backward lightcones of 1 and 2. This is the diagram he uses to describe his general notion of local causality. In the second sort of diagram, he draws a squiggly line extending across both backward lightcones, labels it by lambda and makes the comment that lambda need not be a local beable. This is the diagram he uses to explain the notion of locality applicable in the two-wing experiment. It seems to me that only the second diagram avoids assuming kinematical locality. Indeed, I argue that it transcends the kinematics-dynamics distinction. My sense is that Bell's "standard" definition of local causality, the one that refers to the first diagram, assumes kinematical locality, i.e. exclusively local beables. As you know, the definition is this: "A theory will be said to be locally causal if the probabilities attached to values of local beables in a space-time region 1 are unaltered by specification of values of local beables in a space-like separated region 2, when what happens in the backward light cone of 1 is already sufficiently specified, for example by a full specification of local beables in a spacetime region 3..." If there were some nonlocal beables, then these could not be part of the full specification of local beables in region 3. Nonetheless, such nonlocal beables could be correlated both with beables in region 1 and in region 2 so that by specifying the values of beables in region 2, one would update the probabilities attached to values of the nonlocal beables and this would in turn lead one to update the probabilities attached to the values of beables in region 1. So conditioning on region 2 *would* lead to an update in region 1 even though the beables in region 3 are fully specified. Given Bell's discussion of the second sort of diagram, it seems to me that he would like to consider this case as *satisfying* locality, and yet it clearly fails to satisfy his standard definition of local causality. So I conclude that his standard definition of local causality folds in a notion of kinematical locality and it is this which fails in the example provided. It is only the definition of locality that accompanies the second diagram which avoids the assumption. Unfortunately, I don't have my copy of Bell's "La Nouvelle Cuisine" with me at the moment, so I can't review precisely what he says. I suspect that he did not have complete conceptual clarity on these distinctions. Maybe you can convince me otherwise.

* Concerning causal structure versus kinematics and dynamics. It is true that one can convert models with different kinematics and dynamics into the different causal diagrams. That's what I did for Newtonian and Hamiltonian mechanics, for instance. My claim is that the nonconventional aspect of causal structure is specified by certain features that are common to these causal diagrams, that is, by an equivalence class of causal diagrams. In the case of Bell's notion of locality for Bell-type experiments, the question of whether the ontic state of the pair of quantum systems factorizes or not simply doesn't arise. We just assign a variable lambda to the pair of quantum systems and specify its causal relations to the other variables. The real advantage of causal diagrams is that we don't need to specify where any given variable "lives" in space-time. Indeed, it is better, I think, to infer spatio-temporal relations from the causal relations. That being said, I think more work needs to be done here to properly answer your question.

>That's all I've got. Despite all of these quibbles, I really enjoyed reading the paper, which definitely made me think about new things in new ways, so thanks!

Thanks again for the comments!

John,

I agree that cause and effect should not be considered a sequence. I would put it this way. Whereas many philosophers have thought that the definition of a cause-effect relationship should include the fact that the cause must precede the effect in time, it is better to take the view that causal relations are more primitive than spatio-temporal relations and what it means to say that one event is earlier than another is that the first is a potential cause of the second. In this view, time is inferred from the partial order relation on events induced by cause-effect relationships. (Of course, I'm not the first to propose that time is emergent from causal structure.) I must admit that I don't really understand what it means to say that a cause-effect relationship is defined by energy exchange.

Thanks for the interesting replies. Some follow-ups:

* Re: Ptolemy and Copernicus, my understanding is that Copernicus only made distinct predictions because he updated a few of the empirical parameters using the data that had come in since Ptolemy's time. But Ptolemy -- had he still been around -- could have updated his parameters in an exactly parallel way, such that the differences in predictions should not really be understood as in any way inherent to the two theories. Instead, I think the two theories should be understood as empirically/observationally equivalent, basically as you describe. You say this renders them physically equivalent and that this seems right. I don't agree; I think it sounds quite wrong. My view is that, despite making equivalent predictions, the two theories provide radically different explanations of the underlying physics and hence should be understood as physically distinct theories. And I think the subsequent history supports this: Copernicus' proposal led to Galileo and Kepler, which led to Newton. In the same way, I expect some one particular version of quantum theory (dBB or MWI or GRW or something you invent, say) will lead to future revolutionary advances and future historians will look back and laugh at the stupidity of contemporary operationalists for thinking of all these as physically equivalent. Probably you agree there. In any case, the real issue here is not Copernicus, but why by your expressed methodological principles you wouldn't regard all extant "interpretations" of QM as physically equivalent. I gather you want to say: because, like shape in Plato's cave, the stuff those "interpretations" posit plays an actual role in explaining the phenomena in the context of the theory. But then, so does Copernicus' assumption that the earth rotates. So I remain slightly confused about how your views square with realism, operationalism, etc.

* Re: spin and BST/dBB, I guess I don't know the details of the model you're thinking of. I was assuming that it's like the model in Holland's book. In any case, here I think is what's true. We know that, in dBB, there is a set of possible guidance formulas that all produce "equivariance" and hence give rise to the same empirical predictions. Evidently the BST model you are talking about involves one of these guidance formulas with an extra term involving the "actual spin direction". (I was, evidently erroneously, thinking that you'd still use the same "vanilla" guidance formula, in which case the "actual spin direction" would certainly be like color in Plato's cave.) Anyway, I'd want to make two points here. First, just on standard Ockham type grounds, it seems rather silly to consider the doubly-more-complicated dBB model, when you can get exactly the same empirical predictions by jettisoning the "actual spin direction" beable *and* the extra term in the guidance formula. Second, by your professed standards, wouldn't the observational equivalence of these different formulations of dBB render them anyway, for you, physically equivalent? Either way, it doesn't seem like a helpful example for your cause.

* Re: kinematical locality, yes, I agree that an "entangled" or "holistic" connection between spin and color would be bizarre. My point was that insofar as the "entangled" degrees of freedom do not pertain to "spatially separated subsystems" I don't think the bizarreness has anything to do with a violation of any sort of *locality*. That is, I don't think a violation of "kinematical locality" should be understood as just any sort of "holism" among properties. It pertains specifically to a "holism" between spatially separated systems. That's what I meant in saying that the explication of kinematical locality presupposes the notion in question: even its failure, in this formulation, presupposes the ability to identify spatially separated subsystems. You start by assuming that it is possible to associate degrees of freedom with regions of space or spacetime; then you check to see if those degrees of freedom factorize. But the *real* failure of "kinematical locality" is if you can't even do the first part (e.g., in David Albert's "marvellous point" theory).

* Re: Bell's formulation(s) of locality, a couple of points. First, surely one can and should understand the second of the two formulations/diagrams as following from the first. That is, the second is definitely not a novel or alternative definition of locality: the slice that cuts across both back light cones is just an example of a region that satisfies all of the criteria described in the first formulation, for *both* of the two regions of interest. I suspect you already get that, but the way you put certain things suggests that there are two distinct formulations here, which I think is wrong. Second, I see evidence for more "complete conceptual clarity" then you seem to see. For example, I think it's crucial that, in formulating his notion of locality (in the context of the first diagram you mentioned) Bell describes the "complete specification of local beables in region 3" as merely an *example* of the required sort of description of goings-on there. I also don't have the paper in front of me, but the grammar is something like "probabilities for events in 1 should be independent of goings on in 2 when events in 3 are sufficiently specified, for example by a complete specification of local beables in 3". This is important to two issues: leaving room for the "free variables" assumption (which, in addition to locality, is needed to get the inequality) and (the one that's relevant here) figuring out whether Bell meant to *require* "kinematical locality" as a necessary precondition to assessing dynamical locality. Anyway, it's clear that he is at least open to the possibility that there could exist theories with nonlocal beables and that they can be assessed as nonlocal using his formulation. The mechanism for doing this seems pretty straightforward: if you include (in the description of region 3) some relevant nonlocal beables (such as a QM wf) as well as info about local beables and the condition is *still* violated, you're clearly dealing with a dynamically nonlocal theory. The evidence for this is simply that he makes exactly this argument. These issues are discussed some in my recent "Bell's concept of local causality" (American Journal of Physics) and in the Scholarpedia.org article on Bell's Theorem that I wrote with Goldstein, Tausk, and Zanghi.

* I don't have much to say about the last point, about the causal structure diagrams in some way being still based on the kinematics/dynamics distinction. Your comments, though, make me feel slightly queasy in a new direction. I don't think I'm going to be a fan of any novel approach to physics in which it's considered a virtue that "we don't need to specify where any variable lives in space-time". You know that I'm a staunch defender of Bell's claim to have proved that full dynamical locality cannot be maintained. But I feel equally strongly about the importance and fundamentality of (something like) kinematical locality. In particular, what you write here suggests that it would be an advance to work at a level of abstraction where the distinction between local and nonlocal beables cannot or need not be made. But I think this distinction is crucial and indeed think that a good way to weed out theories that are too crazy to take seriously is to abandon ones with nonlocal beables. I just wish I had in hand an example of a theory that isn't too crazy to take seriously by these standards!

Thanks again for the interesting thoughts,

Travis

Thanks Rob. I'll reply to the rest later, but the one I am most certain and passionate about is also the one where you seem to think it is the most unambiguous that I am wrong, so let me start there with the few minutes I have now before my next class...

It's the issue of Bell's formulation of "local causality" and basically what the relation is between Figures 4 and 6 in "la nouvelle cuisine". Several points about this:

1. Bell explicitly and carefully describes the first thing as a formulation of the principle of local causality. Then, in the derivation of CHHS in the later section, in particular in passing from his equation (9) to his equation (10), he writes explicitly that he is "Invoking local causality". So perhaps you think he was wrong, but he clearly took himself to be *applying* the earlier formulation to this case, as opposed to introducing some kind of new/alternative formulation for the case at hand.

2. Now let me try to convince you that he is not wrong in doing so. I again appeal to his careful wording of the original formulation (surrounding Figure 4). The idea is that specification of events in 2 should be irrelevant/redundant for probabilities in 1 "when what happens in the backward light cone of 1 is already sufficiently specified, for example by a full specification of local beables in a space-time region 3 (fig. 4)." As you know, the region 3 depicted in the figure lies exclusively in the back light cone of 1. The important point here is that, as he formulates things, this is merely an *example* of a region that will play the necessary role. In particular, there is nothing like an insistence that region 3 could not spill somewhat outside of the back light cone of 1; indeed it should be clear that region 3 could be a space-like hypersurface and everything would still work fine. In the discussion immediagely following the figure, Bell is quite careful and explicit about what criteria region 3 must satisfy: "It is important that region 3 completely shields off from 1 the overlap of the backward light cones of 1 and 2. And it is important that events in 3 be specified completely." Do you agree that a modified region 3 -- the one he shows in the figure, but squeezed temporally and stretched spatially into a space-like hypersurface -- satisfies these requirements? Thus, I think it's clear that a "sufficient specification" of the beables on such a hypersurface also "makes events in 2 irrelevant for predictions about 1 in a locally causal theory". Nothing at all hinges on region 3 being confined to the back light cone of 1 -- it's just that it must *cover* the back light cone of 1 in the way he describes, and the region 3 pictured in the figure is merely the simplest example of the way to do this. The specific spatial extent of 3 is no part of the formulation.

3. But then it's clear that the region cutting across the back light cones of 1/2 in the later figure -- which region is not labeled in figure 6 but is apparently referred to as "region 3" in the text! -- can play the necessary role for *both* regions 1 and 2 in that later figure. That I think is the whole point. In his terminology, if c and \lambda jointly specify the state in that (spatially infinite) region, then ipso facto they jointly satisfy all the conditions needed (by appeal to the earlier formulation) to make A independent of b and B -- and they *also* satisfy all the conditions needed (again by appeal to the earlier formulation) to make B independent of a and A.

So... it seems clear to me that Bell intended the derivation of his equation (10) to *use* the earlier formulation. Indeed, he writes: "very often such factorizability is taken as the starting point of the analysis. Here we have preferred to see it not as the *formulation* of 'local causality', but as a consequence thereof." And it also seems clear to me that he has not made a mistake, i.e., that the factorization condition does indeed follow logically from the original formulation of "local causality" under the assumed conditions.

OK, gotta run to class. More later on the other threads.

Travis

Hi again. Quick(er) replies on the other points...

* Ptolemy/Copernicus. The idea that these models only differ as to choice of reference frame is a very contemporary perspective. Certainly that is not how Copernicus saw what he was proposing. He instead thought he was proposing a distinct physical explanation for observable phenomena, and I think he was right to think that. But I feel like this thread is taking us farther away from the main issue you raised. I only raised it as a simple talking point contra operationalism, and it's become clear we're not as far apart there as I initially thought.

* The example of GRW vs (modified) MWI reminds me of the discussion about the "free will theorem" between Conway/Kochen and Tumulka/etc. I think that, if these extra degrees of freedom being posited in the modified MWI theory are considered beables, then the two theories posit different ontologies and (hence) should really be understood as physically distinct theories. Or if instead the extra degrees of freedom are not beables, then evidently this would be merely a different mathematical way to express the GRW evolution law. I think you want to say, on the contrary, that even if the extra degrees of freedom are beables, since they remain in some sense "hidden", the theories should be considered as members of the same equivalence class. Maybe. It's an interesting suggestion. My worry would be, though, that as in the "free will theorem" case, certain other properties (e.g., locality) could actually differ. But I should think about all this more.

* It seems strange to me to use the word "locality" to denote something that need not relate to spatially separated systems. No point arguing about terminology, though. Your different usage is noted.

* You've basically got what I was trying to suggest vis a vis the formulation of "kinematical locality" in some sense already presupposing it. It's not, though, exactly that I "want to say that systems are not primitive". I'm rather just trying to point out that, with the usual sort of formulation of kinematical locality, you *presume* the existence of identifiable spatially separated systems. But if you aren't already neck deep in knowing about QM, and somebody just comes up to you on the street and hands you a random two-particle wave function and asks you to figure out what kind of physical system it might describe, I don't think you'd ever come up with "well, obviously it's describing two particles, each of which exists in 3-space, but there are certain properties of the 2-particle system that don't supervene on the properties of the individuals." You'd just never find that there unless somehow you already knew that's what you were supposed to find. Thus, with standard formulations of "kinematical locality", I think it's a gross understatement (if not just an outright lie) to say that one of the weird things about QM is that it violates kinematical locality. No, what's weird is that the wave function, if a beable, is a nonlocal beable -- and worse, if the wf is all you've got in the theory, you have no local beables! But no ontology in 3-space at all is far, far weirder than "holism" or a mere violation of kinematical locality. These latter terms suggest (wrongly in this case) that we've got a basically sensible ontology of particles (or some elementary "subsystems") in ordinary physical space, but then there are properties of joint systems that aren't reducible to the properties of the individual systems composing them. Anybody who thinks ordinary QM is only that weird should have to explain in detail what the ontology is, exactly.

* This is a complete tangent now, but "marvellous point" is a slightly-barbed name for Albert's idea that the way to correctly understand dBB is in terms of everything playing out in 3N-dimensional configuration space: the ontology is a wave in this space and a single particle (the "marvelous point") being pushed around by the wave in this space. So the idea is that "really" or "fundamentally" reality is just a single particle being pushed around by a wave but in a very high-dimensional physical space. The appearance of many particles in 3-space is then somehow emergent from this. Now I think all other dBB fans think this is crazy (though Valentini seemed to endorse it once...??) -- it being considered crucial to a correct understanding of dBB that there are many particles in 3-space, whose configurations can account for our perceptions of trees, cats, pointers, planets, etc. My point in bringing it up was just that, despite disagreeing with Albert that this is a good way to understand dBB, I think he takes "kinematical locality" bull by the horns in a way that most don't. The wave function of a many particle system really just cannot sensibly be understood as describing stuff in 3-space, but with some surprising kind of "holism". The actual situation is much worse/weirder than that, I think.

I find Bell's terminology, distinguishing local from nonlocal beables, to be much more clarifying here than trying to think in terms of kinematical locality (and whether or not it is violated). I think these are in some sense two different attempts to get at the same basic issue, but the latter doesn't do it very effectively because, so to speak, it cuts too far from the joint. It presumes that the "worst case scenario" is far more benign than the actual situation we are confronted with in QM, and hence actually prevents people from grasping what is bizarre in QM.

Travis

Dear Robert,

I think you are right: There is an ambiguity about how to make the separation between kinematics and dynamics.

A somehow dramatic case is the relativistic kinematics. It is not only compatible with the wave-like version of the constancy of light as it is stated in the second postulate of SRT, but it is also compatible with a particle-like version of the constancy of light c.

Reference: Stachel, John. Einsteins Light-Quantum Hypothesis, or Why Did not Einstein Propose a Quantum Gas a Decade-and-a-Half Earlier? (Einstein. The formative Years, Einstein Studies 2000, p. 240)

In his 1905b-paper Einstein has noted that the velocity of light V cannot be altered by composition with any subluminal velocity.

This kinematical notion - if connected with the particle model of light - implies a far-reaching consequence : Even if the speed of light depends on the speed of the emitting source, the speed of light is always measured of being constant.

Consequently, all measurements concerning the second postulate of SRT are not unambiguous. There is - at least in principle - the possibility that something different has been measured - a sort of a particle-like version of the constancy of light.

Good Luck for your Essay.

Kind Regards

Helmut

Hi Rob!

I was happy to see that you've also entered this competition. The last time we saw each other I didn't get time to hear about your new insights. Now I get a chance to read about them!

Very thought provoking essay. I must say that I endorse the idea that causal structure should be fundamental. In fact, in shape dynamics we've reached the same conclusion through different reasoning. The argument is simple: we question the physical meaning of scale which forces us to do away with the conformal factor of the metric. The information that is left can be mapped one-one with the causal structure of spacetime (there is a theorem for this). However, the problem that we've been facing is that causal structure alone doesn't seem to be enough to recover the dynamics of gravity. I believe that something similar happens in the causal set approach.

So what could be wrong? I find your statement about the interchangeability of kinematics with dynamics persuasive but to difficult to make rigorous in general. However, in gauge theory one has complete control over this. Gauge theories are defined on a fibre bundle but the physics is only described on a particular section of this bundle. Each section represents a different kinematics but the dynamics can be accommodated in a precise way in order to describe the same physics. However, even in this rigorous setting there is a problem with the interchangeability of kinematics and dynamics: there can be global properties of the fibre bundle itself that can show up in the physics. An example of this is the Aharonov-Bohm effect that would be relevant to your model of the electromagnetic fields vs potentials. Similar things, like boundary terms, can appear during Legendre transforms which imply real differences between the Lagrangian and Hamiltonian. The chiral anomaly is yet another example relevant to the Standard Model.

Thus, I am sympathetic to your general argument but I wonder how these global effects, which are ultimately holistic, may also be important. One thing I have in mind, in particular, is the Weyl anomaly, which occurs when you try to gauge the conformal factor of the metric (i.e., when you try to remove all but the causal structure). I'm starting to believe that this may ultimately be related to origin of, let's call it "succession". In any case, I think there is some evidence that there might be some subtle structure in addition to causal structure that may be necessary to fully describe reality. Don't get me wrong, I would prefer it if this wasn't the case!

Take care,

Sean.

Robert

I applaud causal structure denouncing distinctions between kinetics and dynamics. But you must forgive me for already testing this unknowingly and proving it's worth, the results reported my essay.

I agree and indeed show the consequences of lambda (but also its derivative frequency) changing and the wave function being conserved with causality on all transformations. I'm not a quantum physicist so my language is different (even theatrical!) but the emergent causal structure of reality is self apparent, deriving classical relativity from a causal quantum mechanism. I hope you can read and comment for me. The physics is flooding out rather uncontrollably at present and needs help. My essay (to mix metaphors) is the tip of the iceberg.

Have you looked at the structure of truth functional logic with respect to compound systems. I only refer to dynamic logic (PDL) in my own essay but it is based on the hierarchical structure of 'nested' kinetic states with similarities to the infinite multiple components of ontic states, each only initially definable wrt the 'next state up' (local background state)?

As for your own essay I found it excellent. Clear, well argued, well written and correct, so a good score certainly coming. I hope you may feel the same of mine, if very differently presented.

Very best wishes for the contest.

Peter

[adapted from an email exchange with the author]

Hi Rob,

I just read your paper, and I found it beautiful.

I presented it in our group seminar, and some questions arose:

1) Your notion of kinematic locality on page 4: [math]\lambda_{AB} = (\lambda_A , \lambda_B).[/math]

You say that this is the same of separability, but it looks an awful lot like product states.

2) Newtonian physics.

Some people insisted that the kinematics, as they learned it, should be [math]\{q_i, \dot{q}_i\}_i[/math] (with the velocities), and not just the positions [math]\{q_i\}_i.[/math]

3) Practicability.

Is it always clear how to compute the causal-statistical parameters of a theory? For instance, how are they in your two examples (Hamiltonian and Newtonian physics) ? An expansion of the equations of motion?

4) Second page, your methodological principle vs operationalism

The definition of operationalism here wasn't super clear to me. After re-reading, I'd guess you take it to mean:

"make only claims about the outcomes of experiments, and not about the underlying reality."

Is this correct? The Plato Cave example illustrates what you mean by your principle very well, but I was left without understanding what kind of theories would fit operationalism in the example.

I have a guess:

The claim "shadows grow in the afternoon" (assume there is a concept of time and they call the hours before the dark "afternoon") respects operationalism.

The claim "shadows grow in the afternoon because there is a source of light sinking" does not respect operationalism, because it makes a claim about something (the source of light) that you cannot measure. It would however fit your methodological principle, because it helps explain something empirical.

Is this right? Is that why the 3D shape theory is not operational(ist)?