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.

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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.

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I'd appreciate your thoughts on this too! Take care,

Ben

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  • Post #47

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

2 months later

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 TamariAttachment #1: bu_figure_5.jpg

sorry I meant the fqxi essay is based on the 2005 theory not the other way round!

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  • Post #50

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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  • Post #51

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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  • Post #52

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.

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.

4 months later

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  • Post #54

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.

7 months later
5 years later

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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