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...

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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!

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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,...

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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!

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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...

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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

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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...

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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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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...

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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!

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