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  • Post #10

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.

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  • Post #11

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

Some follow-ups to your follow-ups.

* Re: Ptolemy and Copernicus. It seems to me that simply because one choice of coordinate system may be especially perspicuous or useful for making theoretical progress, as the coordinate system with the sun at the origin helped Galileo and Newton in a way that the earth-centered coordinate system did not, this does not imply that formulations of a theory that differ only in their choice of coordinate make different physical claims about the world. It is often the case that one choice of convention is more perspicuous and useful than another. I agree that the Copernican system did a better job of providing qualitative and intuitive explanations of astronomical phenomena. In fact, my impression is that the Ptolemaic system only described the phenomena and didn't really seek to explain them. Still one can imagine a proponent of the Ptolemaic picture trying to provide such explanations and doing a worse job of it than the Copernicans. But the point would remain that an elegant solution to a problem and a proper understanding of how to explain it often requires a good choice of conventions. So yes, it was the model of Copernicus that ultimately led to Newtonian mechanics but even by the lights of this final product, there is no physical significance to the coordinate system in which the sun is at the origin - only the *relative positions* of the planets to the sun are relevant for the Newtonian explanation of their motion. This is the sense in which I think that the methodological principle is right when it asserts that the choice of coordinate system is only conventional. The same sort of history might repeat itself in the sphere of the interpretation of quantum theory --- a particular choice of convention might provide more insight than other such choices. Nonetheless, I still think that we benefit from understanding which elements of our physical theories are merely conventions and which are not and that we stand a better chance of making progress when we don't mistake conventional differences for physical differences.

Let me also say something about the great debate over GRW, dBB, MWI and other comers. GRW makes different empirical predictions from dBB and MWI, so one needn't appeal to my methodological principle to decide between them. Even in comparing dBB and MWI, given that they each lead to different extensions or modifications of quantum theory - I'm thinking here of Valentini's nonequilibrium modification of dBB for instance - we also needn't appeal to my methodological principle. However, for the sake of argument, let's consider two models that do make precisely the same operational predictions. Let me take the example of GRW and a version of MWI wherein the anomalous decoherence postulated by GRW is reproduced by virtue of there being additional hitherto-unknown degrees of freedom that couple unitarily to the known degrees of freedom. Simulating the predictions of GRW in this way is always possible by virtue of the Stinespring dilation theorem, as I describe in the article. What should one say regarding these two models? Let's leave aside the stories that Everettians and collapsicans tell for a moment and consider someone who adopts a purely operational interpretation of quantum theory. The operational difference between the two views is that in one, the extremal set of allowed transformations corresponds to a set of nonunitary but linear dynamics, while in the other the set of allowed preparations includes additional degrees of freedom while maintaining unitarity of the extremal transformations. I take the view that this equivalence of operational statements teaches us something about the correct ontological interpretation of quantum theory. I suspect that neither the Everettian nor the collapsican would agree with me. They don't draw any ontological lesson from that equivalence. I'm saying that they're mistaken not to do so. The phenomenology of the purely operational version of the theory is, I think, our best guide to the correct ontology. So my view on the great debate over realist interpretations of quantum theory is that the existing camps are not likely to be the correct story, and to find the correct story we will probably need to focus more on the operational version of the theory.

* Re: spin in dBB. Looking at Holland's book again, I see now that in fact the evolution of the particle position in the BST model *does not* depend on the orientation of the particle, so the error was mine. Therefore, I now agree with you that the orientation in the BST model seems, relative to Bell's minimalist model, to be like the colour of the objects in the colour-and-shape model relative to the shape-only model for Plato's cave. Given this, I agree that this example does not do a good job of making the point that I want to make. Nonetheless, I think that my point can still be made using other examples of underdetermination in dBB. For instance, whether we use the electric or magnetic field strengths as our supplementary variables in a pilot-wave version of QED seems to be an example of a distinction in kinematics where neither variable seems to be like the colour in the Plato's cave example (but perhaps you can convince me otherwise). These cases are meant to demonstrate that while the combination of kinematics and dynamics has explanatory power, the fact that we can achieve empirical adequacy using different choices of kinematics and dynamics demonstrates that some aspect of the pair is purely conventional, purely colour-like. Perhaps my use of the Plato cave analogy has been a bit misleading. Given that the colour and the shape of the objects in Plato's cave are part of the kinematics of the prisoners' theories (nothing has been said about dynamics), the analogy might suggest that the methodological principle should be used only to decide among competing choices of kinematics, such as the kinematics in the BST model and the Bell model. But my argument is really that there are conventional elements that are a part of the pairing of kinematics and dynamics without being a part of the kinematics alone or the dynamics alone and to eliminate these conventional elements we must adopt a framework that doesn't take the distinction between kinematics and dynamics to be fundamental.

* Re: kinematical locality. I've been using the term "locality" in "kinematical locality" in a general sense, not wedded to spatial separation, but I'm happy to talk about kinematical locality in the case of spatially separated systems. I think I now understand the sense in which you accuse me of presupposing the notion in its definition. Let me see if I've got it right. I'll start with the background to my definition. It is common to make a distinction between systems and the attributes/properties of those systems. Often, the systems are taken to be primitive and the attributes are assigned to these. This, I think, is how one usually makes sense of claims about holistic properties. There is a system A, a system B, and a system which is the composite of these, call it AB. Each of these systems is assigned a set of properties. There exist holistic properties when some of the properties of AB cannot be understood as supervening upon properties of A and properties of B. My sense is that you want to say that systems are not primitive, that somehow they are defined as the locus of a set of properties. In this case, if a set of properties cannot be "factorized" into sets of properties of a pair of components, then we simply aren't warranted in saying that we have a pair of systems rather than a single indivisible system (interestingly, the only other person I've heard make such an argument for the incoherence of holism is Chris Fuchs). I have been assuming that we can make sense of claims of holism in the standard way. But, in the end, I think that the notion of kinematical locality is not really well-formed, so if you want to put more nails in its coffin by criticizing the standard way of making sense of it, please do so! Unfortunately, I'm not familiar with Albert's "marvelous point" theory, so you'll have to explain it to me.

* Re: Bell's formulation(s) of locality. You say "one can and should understand the second of the two formulations/diagrams as following from the first." I disagree. In the first formulation, the variables that screen off region 1 from region 2 are entirely confined to the backward lightcone of region 1. If Bell had wanted to define a region that both screened off 1 from 2 and screened off 2 from 1, then he should have taken a union of regions, one within the backward lightcone of regions 1, and the other within the backward lightcone of region 2. The fact that he included regions of space-time outside either backward lightcone implies, I think, that one cannot derive his second formulation from his first. I agree with what you say in the second half of your comment, namely, that Bell's second formulation does yield a notion of locality that does not presume kinematical locality.

*On the last point. I guess our intuitions simply diverge here. Still, I look forward to seeing what you come up with in the department of theories of exclusively local beables. The issue of kinematical locality is an important one that has not yet received the attention it deserves.

Thanks once again for your thoughtful and informed responses.

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  • Post #13

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

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  • Post #14

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

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    • Post #18

    [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)?

      Dear Daniel,

      Thanks for your comments and apologies for taking so long to reply.

      I'm very much in agreement with you that Newtonian kinematics, with its background of absolute space and time, is inferior to a relational kinematics, of the sort that Julian Barbour has espoused, following Leibniz and Mach. Indeed, I would say that the reasons that have traditionally been given in favour of relational kinematics are very similar to the methodological principle to which I have appealed in my essay (that one should not assign physical differences where there are no observational differences). For instance, in his criticism of the Newtonian notion of absolute space, Leibniz argued that it would make no difference if the entire universe were translated rigidly in absolute space, consequently the original universe and the translated universe should be taken to describe the same physical state of affairs. If we take no difference to mean no *observational* difference, then this can clearly be understood as an application of the methodological principle. I've often thought that this principle needs a snappy slogan to go along with it. The best I've been able to come up with is: empirical indiscernables are physically identical. This has been crafted to be reminiscent of Leibniz's principle of the identity of indiscernables, which was part of his motivation for relationalism I think.

      I also agree with you that it is best to understand spatio-temporal claims as claims about the behaviour of physical objects. As I mentioned in my response to Travis Norsen's comments on my essay, my own view is that the notions of space and time supervene upon notions of causal structure. That is to say, rather than taking temporal succession to be part of the definition of a cause-effect pair, we take cause-effect relations as more fundamental and assert that one event precedes another in time only if it is a potential cause of the other. Space and time are also derived concepts in this approach.

      So to summarize, I'm a big fan of shape dynamics and Barbour's research program (which you did a very nice job of summarizing in your essay by the way). I think the motivations behind that research program are very similar to the motivations I've outlined for abandoning kinematics and dynamics in favour of causal structure.

      Good luck with the contest!

      Hi Sean,

      Always good to hear from you!

      I'm intrigued that you've reached a similar conclusion about the primacy of causal structure from a completely different starting point. That being said, I think that there is a bit of similarity in our starting points: we have both been guided by the same philosophical motivations I think. As I mentioned in my response to Daniel Alves's comment, the methodological principle that does all the work in my essay --- no physical difference without an empirical difference - is arguably what motivates seeking a relational dynamics. Indeed, I read your essay (a really beautiful piece of work by the way!) and in it you argue that scale is unphysical on the grounds that there is no observational consequence of a global change of scale (Did Leibniz also make this argument?). So you have implicitly appealed to the notion that any change that does not yield an observational difference should not correspond to a physical difference.

      You mentioned that there's a theorem stating that if we 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. Can you point me to the reference?

      Finally, I really like your point about gauge theories providing a way of varying over choices of kinematics and dynamics without changing the observational predictions. The fact that there are global properties of the fibre bundle that can show up in the physics suggests to me that these features need to be part of whatever conceptual framework replaces kinematics and dynamics. I should mention, however, that from the perspective of "quantum states are states of knowledge" one might be able to accommodate certain apparently-holistic effects, like the Aharonov-Bohm effect, without requiring nonlocality or holism. Indeed, I suspect that a standard ontology of electric and magnetic field strengths but with a restriction on how much we can know about these may be sufficient to get phenomena analogous to the AB effect. Mind you, I have not yet examined the question carefully because I haven't yet extended my work on classical theories with an epistemic restriction to the domain of field theories. In any case, I agree that I should definitely have a look at the topics you mention, in particular the chiral and Weyl anomalies. I'm certainly open to the idea that we might need something more than causal structure to replace kinematics and dynamics.

      Thanks for the thoughtful comments!

      • [deleted]

      • Post #21

      [also adapted from our email exchange]

      Hi Lydia,

      Nice to hear for you, and thanks for the comments.

      1) This is a confusion of terminology, which I'm sorry I didn't clarify in the paper. The term "separability" is used by quantum information theorists to describe quantum states that are convex combinations of product states. In quantum foundations, the same term is sometimes used to describe an assumption about ontological models, namely that the ontic state space satisfies kinematical locality. You're right that lambda_AB is just the ontic state for AB. The consequences of kinematical locality on the epistemic states is just that we can write P(lambda_AB) = P(lambda_A,lambda_B) and we can therefore talk about whether lambda_A and lambda_B are correlated or uncorrelated, etcetera. Kinematical locality does not imply the quantum information theorists' notion of separability.

      2) The information that needs to be specified to make predictions is certainly the positions and the velocities, but I don't think one should consider the velocities to be part of the kinematics. Maybe this argument will clarify why I think so: in a variational approach to classical mechanics, one could specify the initial position and the final position and deduce the trajectory followed by the particle in the intervening time. But one would not thereby conclude that the kinematics included the initial and final positions (at least, that's not how people usually talk about kinematics). So one shouldn't, I think, identify the variables used for boundary conditions with the kinematics.

      3) The bit where I present the causal diagrams for Hamiltonian and Newtonian mechanics shows that one can easily translate a theory from the kinematical-dynamical paradigm into the causal paradigm. Deterministic dynamics is represented by a conditional probability distribution which is a point distribution on the conditioned variable for every value of the conditioning variable. For instance, in the Hamiltonian scheme, the conditional probability P(p2|q1,p1) is just delta(p2,f(q1,p1)) where delta(.,.) is the Kronecker delta and f(q1,p1) is just the function that defines p2 in terms of the earlier phase space point. That being said, these causal diagrams don't yet capture all and only the nonconventional bits. I'm not exactly sure what mathematical formalism does this. People in machine learning have introduced the notion of an equivalence class of causal diagrams, and this strikes me as promising.

      4) As I see it, an operationalist is a kind of empiricist. Empiricism in the philosophy of science is the idea that the goal of science is simply to "reproduce the phenomena", for instance, to provide an account of what we experience. We should not ask "why", according to the empiricist, only "how". Empiricists were motivated to build knowledge on top of statements about experience because they thought that in this way it would be immune from error. This motivation was later convincingly shown to be misguided by people like Popper and Quine but in physics we still have a strong empiricist streak in our attitude towards quantum theory. The operational brand of empiricism is that the primitives in terms of which experience is described are experimental operations.

      So, yes, "not about the underlying reality" is a good description of operationalism. If you look at any of the recent work on operational axioms for quantum theory, you'll get a feeling for the operational interpretation. Basically, an operationlist talks about preparations, transformations and measurements of systems, not about properties of systems or evolution of those properties. Your example of shadow growth is spot on.

      The first couple of sections of this short paper that I wrote with Lucien Hardy describes in more detail the difference between realism and operationalism.

      Oops, that last post should have appeared as mine, rather than anonymous.

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      • Post #23

      Hi Robert,

      I really enjoyed your essay. It's a fascinating idea that kinematics and dynamics might be two aspects of a more fundamental causal structure. It leaves me wondering *why* causal structure should be so fundamental?

      As I touch on in my essay, theoretical developments in understanding black hole physics, such as the holographic principle and horizon complementarity, seem to suggest that reality is radically frame-dependent, where frames are delineated in terms of causal structure. Do you suspect that this frame-dependence might shed light on the foundational role of causal structure?

      Thanks, and again, I really enjoyed reading your work!

      All best,

      Amanda

      • [deleted]

      • Post #24

      Dear Robert

      I agree we´re being drived by the same motivation. Thanks for reading my essay and for the comments.

      ''Empirical indiscernables are physically identical''

      Something very nice may happen if we impose that. One of the puzzles of QM is the nature of observation: why is observation so different from other physical phenomena? Observation makes wave functions collaps, but how can we classify a physical process as an observation? If we impose that two configurations of the universe MEAN the same if they are OBSERVED to be the same, the observation can be given a precise mathematical meaning... something like ''observation is that thing that identifies any two configurations of the universe as being the same''. In the last section of my essay I propose a way to express this more concretely using category theory. Maybe something similar could be done in your approach.

      Best regards,

      Daniel

      Hi Rob,

      Always good to hear from you too! Thanks for your detailed comments.

      It's encouraging to hear that we seem to be coming to similar conclusions from the same philosophical motivations but different physical problems. I think it points to the strength of the principle that: "empirical indiscernables are physically identical" (not that "snappy" I have to admit!!). I've often thought of this as the core idea in Mach's principles but haven't been able to come up with a catchy slogan either. Regarding Leibniz, I don't think he explicitly mentions scale (or Mach either) but you should really check with Julian, who could tell you for sure.

      The theorem I mentioned is one of the primary motivations for Causal Set theory, so Rafael could probably give you an exhaustive list of references (and he could probably explain the theorem more carefully than me). However, I think the original result was in: Journal of Mathematical Physics, July 1977, Volume 18, Issue 7, pp. 1399-1404. There are probably more modern versions though. I think there is a discussion and proof of this in Hawking and Ellis.

      Regarding global structures like anomalies, boundary terms, and the AB effect. It would be interesting to see if one could reproduce these effects through a restriction of knowledge. Maybe this is naive, but wouldn't this restriction itself be just a kind of replacement for holism in the sense that it acts as a kind of global restriction on the system? In any case, I am coming to think more and more that these kinds of effects might be very fundamental.

      Cheers,

      Sean.

      • [deleted]

      • Post #26

      I just read your essay. I need to read it again for greater depth. I usually give these a couple of readings. I am pondering what you are saying. I think it comes down to the Bell statement

      P(XY|ST) = sum_λP(X|Sλ)P(Y|Tλ)P(λ),

      where the ontic variable is ultimately a summation or dummy variable. This means that what ever the analyst assigns to λ it is independent of the constituent subsystems. Your further implication is that any assignment of ontic variables for the constituent systems is then observer dependent and physically irrelevant.

      In my essay I conclude something related to this. I remove the notion of locality from field theory. This is different from the statndard notion of locality, where in QFT this is commutivity of fields on a spatial amplitude fixed by a coordinate condition. However, for noncommutivative spacetime, say quantized spacetime or fine grained detail on a D-brane, quantum nonlocality occurs with gravity and this QFT construction is no longer afforded. The result, based on a reference of mine in this essay, is that the configuration variables of particles are gauge-like dependent. This means the universe consists of only one of each type of elementary particle, such as there is only one electron. The multiplicity of electrons, from the electron kicked up in energy by photosynthesis of one of my tomato plants, one electron in your computer passing through a logic gate, or one in a white dwarf exerting its degenerate pressure to hold the star up, and all the others, are due to a gauge dependent holographic projection of that one electron onto what we think of as local configuration variables.

      In this setting the standard QFT approach to assigning field variables φ(x_i,t) at points on a spatial manifold is an observer dependent procedure which is not fundamentally correct. Consequently what you appear to advocate may have deeper implications with quantum gravity.

      I am not well read on the subject of causal sets. However, this does suggest that the ontic variable is a sort of gauge-like "processor" that structures a network between nodes of events in the universe.

      Cheers LC

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      • Post #27

      Dear Robert,

      In related to the hidden variable theories you mentioned in the essay, I have a different thinking that I hope you may find it interesting. Nothing mathematical fancy, I find that the bosonic quantum field can be reconciled from a system with vibrations in space and time. The model has some unique features that seem to be extendable to gravity and non-locality of quantum theory.

      Is there really no reality in quantum theory

      Your feedback will be valuable.

      Hou Yau

      Dear Sean and Robert,

      When you make that important statement (Sean):

      "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."

      Does it follow that dynamics is to be preferred to kinematics where there is that departure? In other words, kinematics has a larger set of constraints and may not be as malleable in conforming to global properties and boundary terms. A case in point is the Aharonov-Bohm effect you mention which is not readily modeled by U(1) topologies. Relativistic kinematics seems to require a force fit into any even marginal compliance with SU(n) topologies.

      Steve Sycamore

      Hi Steve,

      That's a good question. I don't have a good answer but I will think about it.

      It may be that these global things - like global anomalies, boundary terms, and the non-trivial topology of the gauge bundle - should have their own status in a theory. In my view they play an important but mysterious role in physics. It may also be that Rob is right: that we can just accommodate them through a restriction on knowledge. My guess is that this restriction would have to be of a slightly different nature but I could easily be wrong!

      Cheers,

      Sean.