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Questioning the Foundations Essay Contest (2012)
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The Paradigm of Kinematics and Dynamics Must Yield to Causal Structure by Robert W. Spekkens
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Author Robert W. Spekkens wrote on Sep. 7, 2012 @ 11:30 GMT
Essay AbstractThe distinction between a theory's kinematics and its dynamics, that is, between the space of physical states it posits and its law of evolution, is central to the conceptual framework of many physicists. A change to the kinematics of a theory, however, can be compensated by a change to its dynamics without empirical consequence, which strongly suggests that these features of the theory, considered separately, cannot have physical significance. It must therefore be concluded (with apologies to Minkowski) that henceforth kinematics by itself, and dynamics by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality. The notion of causal structure seems to provide a good characterization of this union.
Author BioRobert Spekkens is a faculty member at the Perimeter Institute for Theoretical Physics in Waterloo, Canada. His area of research is the foundations of quantum theory.
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John Merryman wrote on Sep. 8, 2012 @ 03:56 GMT
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.'
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Robert Spekkens replied on Sep. 16, 2012 @ 17:06 GMT
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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Stephen M Sycamore wrote on Sep. 8, 2012 @ 15:42 GMT
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
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DANIEL WAGNER FONTELES ALVES wrote on Sep. 8, 2012 @ 21:57 GMT
Dear Robert,
Definitely, very good arguments. Congratulations.
I would like to make one point.
''So we can change the kinematics from conguration 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
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Author Robert W. Spekkens replied on Sep. 21, 2012 @ 16:31 GMT
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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Daniel Wagner Fonteles Alves replied on Sep. 24, 2012 @ 00:12 GMT
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
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Member Benjamin F. Dribus wrote on Sep. 9, 2012 @ 08:23 GMT
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...
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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
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Jayakar Johnson Joseph wrote on Sep. 9, 2012 @ 18:09 GMT
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
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Phil Warnell wrote on Sep. 10, 2012 @ 00:29 GMT
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
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Travis Norsen wrote on Sep. 15, 2012 @ 11:52 GMT
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...
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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!
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Robert Spekkens replied on Sep. 16, 2012 @ 16:53 GMT
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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Travis Norsen replied on Sep. 16, 2012 @ 19:05 GMT
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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Author Robert W. Spekkens replied on Sep. 17, 2012 @ 15:55 GMT
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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Travis Norsen replied on Sep. 17, 2012 @ 17:01 GMT
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...
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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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Travis Norsen replied on Sep. 18, 2012 @ 01:35 GMT
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...
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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
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Helmut Hansen wrote on Sep. 18, 2012 @ 12:46 GMT
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
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Member Sean Gryb wrote on Sep. 20, 2012 @ 11:46 GMT
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...
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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.
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Author Robert W. Spekkens replied on Sep. 21, 2012 @ 16:41 GMT
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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Member Sean Gryb replied on Sep. 24, 2012 @ 12:17 GMT
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.
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Stephen M Sycamore replied on Sep. 26, 2012 @ 11:28 GMT
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
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Member Sean Gryb replied on Sep. 26, 2012 @ 15:59 GMT
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.
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Author Robert W. Spekkens replied on Sep. 26, 2012 @ 22:43 GMT
Steve,
The fact that it is possible to describe any such constraints within each of the possible choices of kinematics that one can make (i.e. any section of the fiber bundle) seems to me to support the notion these constraints are not part of the conventional distinction between kinematics and dynamics and rather something that is either part of the causal structure or something else that must supplement the causal structure, as Sean suggested. I think it’s a really interesting question and I probably need to learn much more about these anomalies to answer it properly.
Best,
Rob
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Peter Jackson wrote on Sep. 20, 2012 @ 17:01 GMT
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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Lidia del Rio wrote on Sep. 21, 2012 @ 07:11 GMT
[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:
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
(with the velocities), and not just the positions
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)?
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Anonymous replied on Sep. 21, 2012 @ 18:53 GMT
[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.
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Author Robert W. Spekkens replied on Sep. 21, 2012 @ 18:57 GMT
Oops, that last post should have appeared as mine, rather than anonymous.
Amanda Gefter wrote on Sep. 22, 2012 @ 06:18 GMT
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
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Anonymous wrote on Sep. 24, 2012 @ 19:04 GMT
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...
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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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Hou Ying Yau wrote on Sep. 25, 2012 @ 04:58 GMT
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
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Member Tobias Fritz wrote on Sep. 26, 2012 @ 20:09 GMT
This is a very insightful essay!
It might be worth mentioning that computer scientists have long recognized the fact that kinematics and dynamics do not have separate observational meaning. This can be formalized in terms notions like bisimulation. There ought to be a definition of bisimulation for theories of physics!
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Author Robert W. Spekkens replied on Sep. 26, 2012 @ 22:44 GMT
Tobias,
Can you tell me more about the notion of bisimulation? I'm intrigued.
Member Bob Coecke replied on Oct. 3, 2012 @ 19:24 GMT
It's the cornerstone to concurrency theory:
http://en.wikipedia.org/wiki/Bisimulation
The right mathematical context in which it lives is coalgebra. Next year in Barbados: coalgebra + quantum foundations. Both of you are of course invited!
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Anonymous replied on Dec. 7, 2012 @ 15:32 GMT
Robert Spekkens,
I recently made a comment on the viXra blog about bisimilation and its relevancy to your causal structure in the sense that it allows the incorporation of bi-directional causation! I made the comment before I read these comments here and as soon as I saw this comment I thought I would direct your attention to a good paper on bisimilation: http://www.cs.unibo.it/~sangio/DOC_public/history_bis_coind.
pdf. This paper examines the history of bisimilarity in the context of computer science, Modal Logic, and set theory.
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Author Robert W. Spekkens replied on Dec. 8, 2012 @ 06:56 GMT
Dear anonymous,
Thanks for the reference! It's clear that bisimulation is relevant to what I want to do. I'll definitely have a look at the paper.
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Hoang cao Hai wrote on Sep. 27, 2012 @ 05:08 GMT
Dear Professor Robert W. Spekkens
I very approval with the statement of Professor.
In my opinion: the Causal Structure is the principle of every problem.
Kind Regards !
Hải.Caohoàng of THE INCORRECT ASSUMPTIONS AND A CORRECT THEORY
August 23, 2012 - 11:51 GMT on this essay contest.
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Vladimir Rogozhin wrote on Sep. 27, 2012 @ 10:23 GMT
Dear Robert! Excellent in-depth analysis in your essay. But why not have the depth of the ontology? Modern physics and mathematics - science not ontologically grounded. Today dominate the operational theory without the necessary ontological foundation.
Correctly, you have to look deep first structure. Bourbaki is a good title "mother" or "generative". Now, as for the physics and mathematics necessary first structure-mother. The concept of "causality" - a category of relationship (Immanuel Kant) ... What are the most fundamental relationship that is unconditional?
There is a fine principle of "coincidence of opposites." Also there is another good old principle of the triunity, who was not Isaac Newton.
In my absolute generating structure to form the basis of dialectical triad only absolute (unconditional) state of matter. This structure, which Umberto Eco calls "missing." "The truth must be drawn ..." (A.Zenkin) ... and ontologically grounded .... There is no other way to truth... My rating-9. Sincerely, Vladimir
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Anonymous wrote on Sep. 28, 2012 @ 12:19 GMT
Robert,
Congratulations, your excellent essay is in the top 35 essays of this contest. I wish you good luck in the final evaluation too.
As a final conclusion of your essay, please summarize in a few sentences, which of our 'Basic Physical Assumptions' are wrong in your opinion?
Anonymous
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Author Robert W. Spekkens replied on Sep. 28, 2012 @ 15:13 GMT
My essay argues against the prevalent assumption that any proposal for a physical theory should separately specify kinematics and dynamics, that is, a space of physically possible states and a law describing how these evolve in time.
Member George F. R. Ellis wrote on Oct. 3, 2012 @ 12:21 GMT
Dear Robert
a deep and intriguing essay. The core about causal sets sounds right: I believe there are many indications that gravity is really described by conformal degrees of freedom, and I learned the other day that all of the Standard Model interactions except one term are conformally invariant. Causal set theory is surely a good way to explore. But one somehow has to introduce a scale too at some point.
Your arguments about not separating kinematics and dynamics are intriguing. Of course in a sense that is what Einstein discovered about gravity.
Best wishes
George Ellis
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Author Robert W. Spekkens replied on Oct. 5, 2012 @ 22:11 GMT
Dear George,
I agree that Einstein’s theory of relativity provides further evidence for the conventionality of the distinction between kinematics and dynamics. Concerning the question of introducing scale, you should have a look at Sean Gryb’s comment (posted above). Sean is working on shape dynamics, which posits global scale invariance. He points out that the information left in the metric after one does away with the conformal factor is entirely about the causal structure. As I mentioned to Sean in my response to his post (and also in my response to Daniel Alves), the motivation for considering scale to be unphysical is very similar to the motivation for considering the distinction between kinematics and dynamics to be unphysical. I’m certainly sympathetic to the project of formulating our physical theories relationally, as one does in shape dynamics.
Best,
Rob
Jonathan J. Dickau wrote on Oct. 3, 2012 @ 15:25 GMT
Hello Robert,
I have not read it yet, but your essay is on my reading list for today. However, your key point is one I have already given a lot of thought to. The notion that kinematic states and dynamic evolution are separable seems to carry over from the subject-object distinction in English and other European languages.
It is a peculiar left-brain dominated preoccupation, which necessitates measures like Korzybski's "the word is not the thing." In Chinese, by contrast; one cannot describe a thing apart from its process, and even the individual strokes in a character tell the story of how that pictogram evolved.
But causal structure is a subject I've been interested in for some time. The challenges posed by the recent Fermi and Integral probe results have called many promising theories like CDT into question, because of problems with achieving Lorentz invariance. And I had some interesting discussions about this matter with Gerard 't Hooft during FFP10, and with some loop quantum gravity folks during FFP11.
So it might be interesting to read what you have to say about this.
All the Best,
Jonathan
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Member Bob Coecke wrote on Oct. 3, 2012 @ 19:20 GMT
Hey Rob, nice thingy, but one thing confuses me a bit. As you well know since to told me this, causal discovery is an ill-posed problem and to even have a non-trivial causal structure a joint probability should be degenerate. So how can a causal structure underpin everything? This almost sounds a bit like the causal set paradigm, which you clearly refute in your introduction.
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Author Robert W. Spekkens replied on Oct. 5, 2012 @ 22:31 GMT
Hi Bob,
It's certainly true that causal discovery algorithms, if applied to finite sets of data, are really just heuristics for identifying likely causal structures. One kind of causal discovery algorithm actually returns a probability distribution over causal structures as its output. In that way, even if one's probabilistic data does not, strictly speaking, exhibit any conditional independences among the observed variables, if it is close to exhibiting such independence the algorithm will identify the most likely causal structure to be one that predicts such independences in the limit of infinitely large statistics. I don't see any problem with positing causal structure to be primitive while granting that we can never be 100% certain of the precise causal structure underlying finite data. Isn't it just like other idealizations in physics? The notion of an inertial observer might be critical to making sense of the special theory of relativity even if, strictly speaking, no observer is every truly inertial.
Best,
Rob
Anonymous replied on Oct. 12, 2012 @ 19:16 GMT
...causality 20 % 40 % 60 % - well half truth or half half falsehood....
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Cristinel Stoica wrote on Oct. 5, 2012 @ 04:53 GMT
Dear Robert,
I think you are right about the "relativity" of kinematics-dynamics. Originally, I wrote a completely different essay for this contest, in which I explained that the universality of the physical laws (its independence of position and time), as well as the principle of relativity, should not be considered as assumptions, because they can be ensured by extending the configuration space and modifying accordingly the evolution laws. This was based on something I wrote in an
older unpublished article, in which I discuss the theories of physics from the perspective of sheaf theory. At the end, I decided to write a completely different essay, about singularities in general relativity, where I have more concrete and published results (
Did God Divide by Zero?).
I find brilliant the idea of playing with the kinematics and dynamics to yield an equivalent theory, but which is local. You may be interested in Maxim Raykin's recent
Analytical Quantum Dynamics in Infinite Phase Space, who finds a more elegant dynamics for de Brogile-Bohm theory. I would also humbly suggest
my own view on QM, in which I try to interpret the quantum weirdness by using only the unitary evolution of the wavefunction, constrained by global consistency conditions (which are intrinsic).
Best wishes,
Cristi Stoica
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Jin He wrote on Oct. 5, 2012 @ 19:22 GMT
MAX PLANK:
An important scientific innovation rarely makes its way by gradually winning over and converting its opponents; it rarely happens that Saul becomes Paul. What does happen is that its opponents gradually die out and that the growing generation is familiarized with the idea from the beginning.
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Member Benjamin F. Dribus wrote on Oct. 13, 2012 @ 08:32 GMT
Dear Robert,
I thought you might be interested in the following idea I posted on George Ellis's thread. Since you also are interested in "nonmanifold models that emphasize the role of causality," I thought I'd copy the idea here.
**********
After initially struggling with the idea, I’ve been thinking a bit about how your [George’s] top-down causation idea might look...
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Dear Robert,
I thought you might be interested in the following idea I posted on George Ellis's thread. Since you also are interested in "nonmanifold models that emphasize the role of causality," I thought I'd copy the idea here.
**********
After initially struggling with the idea, I’ve been thinking a bit about how your [George’s] top-down causation idea might look from the perspective of nonmanifold models of fundamental spacetime structure that emphasize the role of causality. It seems that top-down causation might provide an interesting new perspective on such models. For definiteness and simplicity, I use Rafael Sorkin’s causal sets approach as an example.
Causal sets, as currently conceived, are by definition purely bottom-up at the classical level. Causality is modeled as an irreflexive, acyclic, interval-finite binary relation on a set, whose elements are explicitly identified as “events.” Since causal structure alone is not sufficient to recover a metric, each element is assigned one fundamental volume unit. Sorkin abbreviates this with the phrase, “order plus number equals geometry.” This is a special case of what I call the causal metric hypothesis.
In the context of classical spacetime, top-down causation might be summarized by the statement, “causal relationships among subsets of spacetime are not completely reducible to causal relations among their constituent events.” In this context, the abstract causal structure exists at the level of the power set of classical spacetime, i.e., the set whose elements are subsets of spacetime. Discrete models very similar to causal sets could be employed, with the exception that the elements would correspond not to events, but to families of events. Two-way relationships would also come into play.
Initially this idea bothered me because of locality issues, but such a model need not violate conventional classical locality, provided that appropriate constraints involving high-level and low-level relations are satisfied.
This idea is interesting to me for the following reasons.
1. The arguments for top-down causation presented by you [George] and others are rather convincing, and one would like to incorporate such considerations into approaches to “fundamental theories,” particularly those emphasizing causality.
2. One of the principal difficulties for “pure causal theories” is their parsimony; it is not clear that they contain enough structure to recover established physics. Top-down causation employed as I described (i.e. power-set relations) provides “extra structure” without “extra hypotheses” in the sense that one is still working with the same (or similar) abstract mathematical objects. It is the interpretation of the “elements” and “relations” that becomes more general. In particular, the causal metric hypothesis still applies, although not in the form “order plus number equals geometry.”
3. There is considerable precedent, at least in mathematics, for this type of generalization. For example, Grothendieck’s approach to algebraic geometry involves “higher-dimensional points” corresponding to subvarieties of algebraic varieties, and the explicit consideration of these points gives the scheme structure, which has considerable advantages. In particular, the scheme structure is consistent with the variety structure but brings to light “hidden information.” This may be viewed as an analogy to the manner in which higher-level causal structure is consistent with lower-level structure (e.g. does not violate locality), but includes important information that might be essential in recovering established physics.
4. As far as I know, this approach has not yet been explicitly developed.
I’d appreciate any thoughts you might have on this.
**********
I’d appreciate your thoughts on this too! Take care,
Ben
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Eckard Blumschein wrote on Oct. 15, 2012 @ 06:11 GMT
Dear Robert Spekkens,
Your essay argues against the prevalent assumption that there are two separate basics of physics, a space of physically possible states and laws describing how these evolve in time.
Doesn't the expression "in time" guess that the future is predetermined and just unseen? Doesn't "a space of physically possible states" also guess that the world is built like a combination of discrete elements? Maybe these assumptions are good or at least clever guesses. I prefer to not assume more than what seems to be indispensable: reality and causality.
I see any causal structure real only in the past if the world cannot be seen from outside as a closed system although most of our theories do so. Is my caveat acceptable? I designed five figures in order to illustrate it and its implications.
Eckard
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Vladimir F. Tamari wrote on Dec. 1, 2012 @ 10:40 GMT
Dr. Spekkens,
Congratulations on having your beautifully written essay winning the contest. I missed reading it before and have just done so. Your conclusion that kinematics and dynamics should be considered as one causal entity sounds to me very natural in both senses of the word.
I know you have waded in your scholarly way through the whole layers of various quantum theories and applied your intuition and methodical analysis to reach this conclusion. Also working intuitively but lacking your erudition, I invented my own theory (of a universal lattice of nodes interacting locally, linearly and causally with their neighbors), which I think a priori has the above characteristics without consciously seeking them out (see attached figure). I would be grateful if you or your students can check it out half-cooked as it is, but it is the best I could do. Here is my
Beautiful Universe Theory and here is
my fqxi essay Fix Physics! on which it was based.
Finally I wonder if you agree with me that
Eric Reiter's essay deserved a prize ? Perhaps the good people at Perimeter can check out his research and replicate his experiments if need be .
with warm regards
Vladimir Tamari
attachments:
bu_figure_5.jpg
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Vladimir F. Tamari wrote on Dec. 1, 2012 @ 10:44 GMT
sorry I meant the fqxi essay is based on the 2005 theory not the other way round!
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Paul Reed wrote on Dec. 3, 2012 @ 04:59 GMT
Robert
As this paper won, I read it.
You have correctly identified a false distinction in the depiction of physical existence, but not actually, I think, explained why this is so. That is because physical existence can only occur in one physically existent state at a time. In terms of what exists at any time, it is not physical substance that matters so much as the physically...
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Robert
As this paper won, I read it.
You have correctly identified a false distinction in the depiction of physical existence, but not actually, I think, explained why this is so. That is because physical existence can only occur in one physically existent state at a time. In terms of what exists at any time, it is not physical substance that matters so much as the physically existent state thereof. Physical existence is existential sequence, ie one state at a time. There is no change within it. Change concerns difference between physically existent states, not of them. So there is no ‘time’ in physical existence, it is a spatial phenomenon which alters over time.
Any concept which incorporates something occurring over time, ie more than one physically existent state, is therefore addressing physical change, ie the sequence, and not the existent state as such. That is cause and effect. And the important point about cause and effect, once sequence is understood, is that only certain specific existent states could be responsible for any given outcome (ie existent effect). They must be from amongst other previous states which, when existent, were adjacent both spatially, and sequentially, to that which occurred next (ie effect). Because physical influence cannot ‘jump’ physical circumstance. Cause and effect can only be considered in terms of direct physical interaction, otherwise it becomes ‘the butterfly flaps its wings’ syndrome.
In other words, notions such as oscillation, reaction, feedback, etc, are ontologically incorrect, unless they are expressed properly in terms of a sequence of occurrences. At most there is just a repetition of a previously physically existent state as the sequence progresses, but this is still different because it occurred separately. Although even that is likely to be superficial, ie due to the level of conceptualisation (but possibly correct at that level). Physically, it is probably impossible that a configuration of any given physically existent state, in its entirety, will re-occur.
All this stems from the fundamentally flawed way in which we conceptualise physical existence. We see it as ‘things’, but these are abstract concepts based on a conceptualisation of reality at a higher level than what actually occurs. So, we fail to differentiate the physical sequence down to its physically existential level. That is, most circumstances which we address as a state of existence, are not so. In fact they comprise several states. This results in the reification of time, and the type of false differentiation which you have identified.
Paul
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Tosin wrote on Dec. 3, 2012 @ 23:48 GMT
I usually wait for the announcement and read the winning paper.
Can't wait to enjoy this one.
Congrats.
X Bubbler
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Eric Brunhouse wrote on Mar. 26, 2013 @ 00:09 GMT
Robert,
It is practical to say we think everything we observe happens through some causality. This gives us some sense of time moving forward, therefore time is not fundamentally fixed like a map in the background. So while causality exists (at least in our thoughts) events move forward and each event has an explanation. Quantum mechanics posits there is a break in geometric causation...
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Robert,
It is practical to say we think everything we observe happens through some causality. This gives us some sense of time moving forward, therefore time is not fundamentally fixed like a map in the background. So while causality exists (at least in our thoughts) events move forward and each event has an explanation. Quantum mechanics posits there is a break in geometric causation via nongeometric processes which may not have any relation to position or time in the sense they have hitherto been defined mathematicaly: this is the geometric postulate of time and space going back to Zeno and beyond. Here is the clear paradox: If causality gives us the sense time is moving forward how may some causal events be occurring by moving backward in time? One idea is that space and time are just properties of phenomena thus freeing up phenomena to have other properties that may be explored independent of the geometric notion of them at all. This leads to a break in the concept of causality, our understanding of nothingness (the vacuum of space) and perhaps affects a host of other concepts that were developed with a more definite sense of causality. Now, the causality as we know it, cannot be used to reduce our understanding of physical truth or provide for fundamental understanding given current observations. Therefore substantial interaction (defined in my essay) while positing some correspondence between properties via the concept ‘interaction’ is not necessarily causal. Substantial interaction is not reductionist either. It relays a methodology where new kinds of hypothesis may be clarified. This is not the fundamental way we would have understood it with the presumptive explanation of our experience in a fixed space-time world. So substantial interaction is a concept free from the presumption of causality as causality has been widely understood.
Just as the Greek ancient natural philosophers could stray way off track by theorizing essential principles: the matter that results in the form of all things, for example, without first trying to develop the scientific method and the tools for experimentation, so my contemporary generation may ride off track by presuming a great deal about the essential concept of causation without focusing on new methods and tools that may lead to actual abilities to newly impact our environment. The inspiration to strike out at the truth with reason was only good up to a point back then as it is likely to be now. 300 years of Greek thought did not lead Aristotle (who was certainly capable) to the scientific method but only to a less agile way of thinking. It is possible Aristotle could not act with the required confidence to make such a stupendous contribution because Aristotle did not believe in his senses brazenly enough to develop it, for his contemporaries argued relentlessly his senses were not trustable to begin with. Perhaps the scientific method would not have been useful to such contemporaries anyways? I hope it would have been useful to someone.
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sridattadev kancharla wrote on Oct. 30, 2013 @ 18:53 GMT
Dear Robert,
Congratulations. I hope you will enjoy the following blog and videos in it.
Any Body Can Derive - Everything From GeometryLove,
Sridattadev.
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Richard L Marker wrote on Sep. 13, 2018 @ 13:44 GMT
Robert Spekkens
Your well considered case for moving from kinematics and dynamics to causal structure stirs one's imagination. The concept of causal structure befits the notion of finding the inner machinery that drives our physics.
Your approach might benefit from considering dynamics on two different levels. One level would be the dynamics of a system that yields our observed...
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Robert Spekkens
Your well considered case for moving from kinematics and dynamics to causal structure stirs one's imagination. The concept of causal structure befits the notion of finding the inner machinery that drives our physics.
Your approach might benefit from considering dynamics on two different levels. One level would be the dynamics of a system that yields our observed physics. The deeper level would be the dynamics of the causal structure itself.
The dynamics that yields observed physics depends on the dynamics of the causal structure. However, that dependency may be far removed.
Consider the fabric of space itself as the causal structure, albeit not fully understood. Our physics fundamentally relies on observations which develop from our interactions with the fabric. What about the physics of the fabric itself?
Our observations do not tell us directly how the fabric interacts with itself in order to maintain its underlying structure and behavior. Our observations may be so far removed from the mechanism driving the underlying causal structure that they provide no real suggestions as to the form and dynamics of the causal structure. They only provide evidence of expected results from the causal structure.
If we attempt to find a causal structure that supports that which we know and observe, then we can never know with certainty that any proposed causal structure is the machinery for which we truly search. Instead of starting with known physics and observations, I submit that one must start by determining the causal structure directly from logic.
In developing the logic that determines the causal structure one must consider dynamics that bear little relationship to our known laws of physics. Unfortunately, this does not receive the focus of our attention. It may not even receive the periphery of our attention.
This goes far beyond simply questioning the foundations of our physics. It requires that we start with a clean slate at the lowest conceivable level in order to determine the causal structure. Later, we can determine how the causal structure merges with our known physics. Our pillars may not be as solid as we consider them to be, but the answer does not come from speculating about alternatives to those pillars. Rather, it comes from understanding the causal structure.
Congratulations on winning the contest! Your win was well deserved.
Richard Marker
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