Chapter 11: Is Connectivity Entailed by the Physical?

[hypnagogue]

With the basic concepts of the theory of causal significance in place, an important issue to address is how physical theory fits into the picture. Does a complete physical theory already encompass all the details of a theory of causal significance, or does it only describe a subset of it? If the latter, what aspects of causation belong to the domain of physics, and what aspects are beyond its scope?

In order to better frame these questions, Rosenberg identifies three basic levels of description of the world, in ascending order of metaphysical richness. The first is the Humean mosaic, which is a rather bare description of property instantiations across space and time. If we imagine the trajectory of a ball that is tossed upwards and then falls back to the ground, a description of this event on the level of the Humean mosaic would just include facts about the ball's spatiotemporal coordinates along the trajectory and its properties (mass, elasticity, etc.) at each such coordinate. The next level of description is the nomic mosaic, which introduces counterfactual supporting natural laws to account for observed patterns in the Humean mosaic. For instance, an account of our tossed ball on the level of the nomic mosaic would describe its trajectory in terms of dynamic laws of motion. This richer account introduces modal facts above and beyond the facts about the Humean mosaic, such as, "had the ball been thrown with a different force F, it would have taken trajectory T₂ rather than the observed trajectory T₁." Finally, the richest level of description of the world is a complete account of the causal mesh, including facts about receptive properties and causal laws. An account on this level of description would specify the receptive connections, effective properties, and causal laws that create a constraint structure on the ball's possible effective states and spatiotemporal locations. (In this case, the constraint structure would be such that it would filter out all possible states and locations of the ball except those which correspond to its actual, observed properties and trajectory through space and time.)

The basic form of Rosenberg's main argument in this chapter is

1. The facts about the nomic mosaic do not entail all the facts about the causal mesh.
2. Physics describes only the nomic mosaic.
3. Therefore, the causal mesh contains facts above and beyond the physical facts. (pg.223)

Facts about the nomic mosaic do not entail all the facts about the causal mesh

Note that the facts about the Humean mosaic do not strictly entail the facts about the nomic mosaic. Given a Humean mosaic H, it is not the case that the facts about H alone are sufficient to fix a unique set of nomic facts, because there are multiple kinds of nomic mosaics that are logically consistent with H. For instance, there could be two sets of natural laws whose predictions are in agreement with all events that actually occur in the history of a universe, but nonetheless disagree about what would have happened had some conditions been different.

Similarly, Rosenberg argues that the facts about the causal mesh are not completely entailed by the facts about the nomic mosaic, since a single set of dynamic laws is logically consistent with multiple kinds of causal constraint structures. Revisiting the toy physics of the Life world introduced in chapter 2, he explicitly details two distinct sets of receptive structures and causal laws, each of which reproduces the same dynamic Life world law describing the state of a cell at time t as a function of its state and the state of its neighboring cells at time t-1. Rather than reproduce Rosenberg's example, I will use a somewhat simpler case study here which should suffice to demonstrate the same general principles and results.

Suppose, as in chapter 10, that there is a world whose only elementary effective property is charge, which can take on a value of either + or -. (Charge is meant to refer to a novel, imaginary effective property, rather than the property called charge in physics.) Further suppose that time is quantized in this world, and that there is a dynamic law describing the behavior of charge over time as follows: the value of an instance of charge at time t is the opposite of its value at time t-1. Call this the law of charge oscillation. In order to show that the facts about this nomic mosaic do not entail the facts about its causal mesh, we need only demonstrate two distinct sets of causal facts which are consistent with the law of charge oscillation.

One set of causal facts (call it C1) consistent with the law of charge oscillation has already been presented in chapter 10. The receptive structure of C1 consists of a regular series of overlapping, two place, asymmetric level 1 receptivities binding instances of charge at each time slice. The causal law on these receptivities states that only an odd number of +s and -s, respectively, may be bound together in the same causal nexus. So, for a temporal sequence of charge instantiations ..., +_0.1, -_0.2, +_0.3, ... occurring at successive times t₁, t₂, and t₃, respectively, the receptive structure looke like the following:

..., [+_0.1 => -_0.2], [-_0.2 => +_0.3], ...

The causal law described above, when operating on two-place receptivities, forces two bound instances of charge to take on opposite values. The regularity of two-place receptivities binding every pair of temporally adjacent instances of charge ensures that every instance of charge at a time t will have an opposite value from its temporal neighbors at t-1 and t+1. Thus, the causal processes described in C1 create a world that supports the dynamic law of charge oscillation described above.

We can readily draw up other sets of causal facts that are equally consistent with the law of charge oscillation, even though they feature different receptive structures and causal laws. For instance, suppose we have the following causal conditions:

Causal law on level 1 nexii: There must be an even number of + charges bound within a level 1 nexus.
Causal law on level 2 nexii: There must be an odd number of + charges bound within a level 2 nexus.
Receptive structure: There is a regular pattern of receptive connections on levels 1 and 2, such that instances of charge are bound by overlapping, three-place receptivities into level 1 causal nexii. These level 1 individuals are bound by overlapping, two-place level 2 receptivities.

The receptive structure and causal law on level 1 allow three possible effective states for level 1 individuals: [-.+.+], [+.-.+], and [+.+.-]. Independently possible dual joint states of these individuals, given that they overlap at the endpoints, are:

1. [-.+.+_0.n], [+_0.n.-.+]
2. [-.+.+_0.n], [+_0.n.+.-]
3. [+.-.+_0.n], [+_0.n.-.+]
4. [+.-.+_0.n], [+_0.n.+.-]
5. [+.+.-_0.n], [-_0.n.+.+]

These independently possible joint states present a prior possibility space for the effective states of the level 2 individuals. Joint state (5) is ruled out directly by the level 2 causal law, since it has an even number of + charges. Furthermore, note that level 2 nexii featuring joint states (1), (2), and (4) entail the existence of another level 2 nexus featuring joint state (5), due to the stipulated regular, overlapping level 2 receptive structure. These joint states all have at least one level 1 member individual X featuring a - charge at one of its 'endpoints,' and this individual X must be receptively bound into another level 2 individual Y, due to the regular, overlapping level 2 receptive structure existing in this world. But because of the regular, overlapping receptive structure on level 1, Y can only have joint state (5).

For instance, suppose we have a level 2 individual I_2.1 with joint state (4), i.e. [[+_0.1.-_0.2.+_0.3]_1.1.[+_0.3.+_0.4.-_0.5]_1.2]_2.1. Because of the stipulated regularity of overlapping receptivities at levels 1 and 2, the existence of I_2.1 entails the existence of another individual I_2.2 of the form [[+_0.3.+_0.4.-_0.5]_1.2.[-_0.5.?_0.6.?_0.7]_1.3]_2.2. The level 1 causal law forces I_1.3 to take the form [-.+.+], which in turn requires that I_2.2 takes on joint state (5), but this is not permitted by the level 2 causal law.

Because joint state (4) logically entails an impossible situation given these causal conditions, it follows that it is impossible for joint state (4) to instantiate in the particular kind of level 2 individuals discussed here. Similar reasoning applies to states (1) and (2); essentially, joint states (1), (2), and (4) are inconsistent with the total constraint structure enforced by the conjunction of causal laws and receptive structures in place in this world, so joint state (3) is the only possible configuration left for level 2 individuals. Because the level 2 individuals are all forced to take on joint state (3), the instances of charge are forced to take on a regular, alternating pattern of oscillating values, in agreement with the dynamic law of oscillating charges described above.

The alternate causal conditions described here and in the text are fairly complicated, and even have an air of strangeness or superfluity, in order to demonstrate more forcefully the point that a single set of dynamic laws can be consistent with a large range of causal circumstances. The general idea is that dynamic laws describe regularities of effective state instantiations that result from the operation of causal laws on existing receptive structures. Different receptive structures and causal laws can implement the same pattern of effective state instantiations, and so there could exist substantially different worlds that nonetheless instantiate identical nomic mosaics. Thus, it is not the case that facts about the nomic mosaic entail all the causal facts, but rather it is the other way around; a complete specification of the causal facts will already subsume all the facts about the nomic mosaic.

Physics describes only the nomic mosaic

In section 9.7, Rosenberg set out a lower bound for what aspects of the causal mesh physical theory describes: He argued that physical theory at least designates the low-level effective properties, and that its physical laws at least describe the regularities of effective property instantiations. In other words, physics is at least a theory of the nomic mosaic. I summarized this argument in the thread for chapter 9 as follows:

Effective properties are those properties that have the capacity to place causal constraints on the space of possible ways the world could be. These are precisely the kind of properties studied by physics. Physics is ultimately an empirical endeavor driven by observation, and we only observe things (either directly or indirectly) by means of the roles they play in a causal chain of events that culminates with the systematic activation of our biological senses. In other words, all phenomena that can be the objects of objective empirical study must be effective properties or complexes thereof, because such effective causal properties are precisely the things that subserve objective observation in the first place.

The guiding theoretical concern of physics is to explain and predict experimental results, and by a simplicity constraint, physical theory encompasses the least set of properties needed to explain these experimental results; to posit any properties superfluous to the explanation or prediction of possible experiments would be to posit properties beyond the guiding concern of physics, and thus ultimately beyond its scope. But in principle, an exhaustive theory of the nomic mosaic would already be sufficient to predict and explain the outcome of any experiment-- such a theory would tell us, in the context of the experimental design, how the effective properties of the target phenomena systematically covary with the effective properties of the measuring devices, and ultimately, with those of our own biological senses. In other words, any prospective facts to be added to physics above and beyond the level of the nomic mosaic would come with the cost of added complexity, and without the payoff of added experimental content-- by the simplicity constraint, such facts should not belong to the domain of physics. This amounts to saying that physics is at most a theory of the nomic mosaic, and in conjunction with the lower bound introduced above, we arrive at the view that physics simply is a theory of the nomic mosaic.

Because facts about receptive connections and causal laws are facts above and beyond the level of the nomic mosaic, they are thus beyond the scope and concerns of physics as well. In short, the effective face of causation is precisely the aspect of causation studied by physics, and connectivity, the receptive face, is not entailed by the physical; physics studies only one aspect of causation, allowing the others to reside implicitly in the background because they are beyond its guiding theoretical concerns. This is not to say, however, that the receptive face of causation is entirely opaque from the physical perspective. Studying the effective aspects of causation could very well suggest facts about receptivity, if not directly and explicitly entail them (and presumably, studying the effective side in the context of a research program specifically designed to garner clues about the receptive side could be especially fruitful in a way that retrofitting receptive concepts to established physical theory is not).

Additionally, although facts about the receptive face of the causal mesh would not add experimental content to physical theory, we should not take this to be indicative of a failure of a complete theory of the causal mesh to add any empirical content to the sciences. The receptive face of causation is nonphysical, which in turn implies that not all the causal facts about the world are physical facts. If true, this implication opens up new vistas of theoretical and empirical study, and begins to lay the groundwork for scientific theories that can explain and predict nonphysical facts about subjective experience on the naturalistic basis of both physical and nonphysical causal facts.

 

[Tychic]

Is space an individual?

I agree that (natural) individuals are not fixed by the nomic mosaic. There are concepts of individuals used by chemistry or biology and also by physics themselves. I would say that the same physical/chemical/biological effects could be explained by supposing other individuals in the sciences. You, Hypnagogue, show this with the toy world example, Rosenberg with his Live world example.

Nonetheless I’m interested whether space (or space-time) is or could be an individual. From § 10 I follow that it is no primitive receptive or effective property. In § 9.8 (p.155) Rosenberg suggests that “Einstein added receptivity to space.” Although the terminology is not technically fixed at this point of the discussion I would follow that space is a receptivity.
If it is an individual, it has to be a completed receptive connection. In this case I ask: Are all effective properties of this individual determined and or is space(time) an undetermined/abstract individual?
If space is an uncompleted receptivity, what could fill the open slots?

 

[hypnagogue]

According to the proposal Rosenberg put forth in chapter 10, spacetime is not a natural individual, but rather the causal infrastructure enforced by receptive connections in the causal mesh. But according to General Relativity, spacetime is warped by mass, and Rosenberg's model does not seem to provide any explicit mechanisms whereby this could happen, i.e. whereby the structure of receptive connections could change systematically in response to an effective property like mass.

Your idea about spacetime itself being a natural individual might be one way to solve this problem, although as you mention, it introduces new problems itself: What would the effective properties of spacetime be? Shape? Certainly, whatever they might be, they would seem to be strange and abstract in a way that the other natural individuals are not.

The general problem here in reconciling Rosenberg's tentative model of spacetime with GR seems to be one of providing a detailed account of how receptive structures tend to become introduced to, or change with respect to, a given causal situation. Rosenberg doesn't propose such a detailed account, but he does propose some principles that could be the basis for such an account. For instance, he mentions an important point somewhat paranthetically in chapter 11: realistically speaking, in a world with regular, reliable dynamic laws, the underlying receptive structures themselves would also have to instantiate in a regular manner. Given that this is the case, what could be guiding the regularity of receptive structures? The discussion in section 9.12, "Laws of Emergence for Higher Level Individuals," proposes some basic candidate principles that might shape the topology of the world's receptive structure, particularly the principle of maximal completeness and the principles of thermodynamics. Also, in figure 10.14, a toy physics example is demonstrated wherein the introduction of a new instance of charge changes receptive structures at two levels of nature.

So if we need a story about how receptive structures (Rosenberg's proposed spacetime) can be systematically responsive to the distribution of an effective property (mass), we might be able to form one based on general principles like those suggested above, wherein something like the principle of maximal completeness figures into how receptive structures are preferentially 'constructed,' and how the introduction of new receptive structures in this manner can have ripple-like effects for other receptive connections. e.g., something like, "when mass is distributed in such-and-such a way, so-and-so receptive structures offer the greatest degree of completeness to their member individuals, because of causal laws X, Y, and Z; therefore, by the principle of maximal completion, so-and-so receptive structures are, in fact, instantiated given a such-and-such distribution of mass." Such a model would give the illusion that spacetime is an individual with effective and receptive properties, but strictly speaking, that would not be the case.

 

[antfm]

Well, surprisingly I think I've no big problems with this chapter.

Perhaps some considerations about individuals come to my mind. Individuals we usually assume in science, seem to me dependent on the context of the particular theory we might be using at that moment. I mean, in some contexts, say biology for instance, we could be taking cells sometimes, organs in other moments, or organisms, etc. We could be handling atoms or mollecules, in some contexts in chemistry or physics, and eletrons or any other kind of elementary particles in other occasions
They all share some sense of individuality, but i'd say it is a sort of contextual individuality. As some authors say, we have different ontic realities and corresponding epistemic realities, depending on the level at which we are applying our instruments or our theories.

But I think they all act more like pseudoindividuals than as actual individuals (individuals as completions of causal nexi) as they are defined by Rosenberg.
In fact, as scientific theories evolve, sometimes the boundaries of these individuals become fuzzy or not well defined. In field theories of physics, for instance, many physicists seem to abandon the concept of particle in favor of the more general concept of field. In that case, I guess, it would be the field which would approach better Rosenberg's concept of individual.

But I don't think these side considerations affect my general understanding of the chapter. Thanks again, Hypnagogue, for the helpful summary.

 

[Tychic]

Hypnagogue,
thank you for your courageous last post. A main thesis is the following:

According to the proposal Rosenberg put forth in chapter 10, spacetime is not a natural individual, but rather the causal infrastructure enforced by receptive connections in the causal mesh.

General Relativity is not ruled out if you think the causal structure of the world (and especially the gravitational field) is the supervenience base for the warped spacetime.

antfm thinks that fields could be individuals in Rosenberg's sense. He is confronted with the same problem as my theory of spacetime as an individual.

What would the effective properties of spacetime be? Shape? Certainly, whatever they might be, they would seem to be strange and abstract in a way that the other natural individuals are not.

I accept that the regularity of individual constitution is no trivial thesis even if the regularity of the causal mesh is conceded. You remember of

the principle of maximal completeness and the principles of thermodynamics. Also, in figure 10.14, a toy physics example is demonstrated wherein the introduction of a new instance of charge changes receptive structures at two levels of nature.

What do you want to say with the hint to figure 10.14?

In the last paragraph you are proposing an model of the coherence of receptive structure with spacetime.

e.g., something like, "when mass is distributed in such-and-such a way, so-and-so receptive structures offer the greatest degree of completeness to their member individuals, because of causal laws X, Y, and Z; therefore, by the principle of maximal completion, so-and-so receptive structures are, in fact, instantiated given a such-and-such distribution of mass." Such a model would give the illusion that spacetime is an individual with effective and receptive properties, but strictly speaking, that would not be the case.

I agree. But is General Relativity relevant for your proposal? Does your proposal not also work if space is Newtonian?

 

[Tychic]

Theses: It is likely that there are chemical and biological individuals

Perhaps some considerations about individuals come to my mind. Individuals we usually assume in science, seem to me dependent on the context of the particular theory we might be using at that moment. I mean, in some contexts, say biology for instance, we could be taking cells sometimes, organs in other moments, or organisms, etc.

But I think they all act more like pseudoindividuals than as actual individuals (individuals as completions of causal nexi) as they are defined by Rosenberg.

I disagree. If there is a receptive structure it is also necessary that there are individuals. Perhaps it is empirically impossible to identify these individuals, but they have to exist. Each effective binding takes part on the constitution of an individual, as far as I see.
In Hypnagogue's toy example (chapter 11) the question is whether there are individuals with two or three charges. One can widen this example so that much more charges are parts of higher level individuals. And if one higher individual is known it could be possible (together with the assumption of regularity of individual constitution) to make the implication that there exist no level-one individuals with 2 charges but only level-one individuals with 3 charges.

 

[antfm]

Hi Tychic,

I disagree. If there is a receptive structure it is also necessary that there are individuals. Perhaps it is empirically impossible to identify these individuals, but they have to exist. Each effective binding takes part on the constitution of an individual, as far as I see.

Perhaps we don't disagree so much. You admit that it could be difficult that we identify those individuals. I am saying that I'm not sure that the individuals we usually manage as such (particles, cells, etc) are actual individuals in Rosenberg's sense. I'm not denying that they could be, but that from our empirical, moving standpoint is is not easy to afirm they are. But as soon as we are working in a particular epistemic level of description we can consider them as individuals (though that is why I said pseudoindividuals).

I think this derives from the fact that individuals instantiate effective properties, objects of empirical sciences, bounded by receptive properties, which are only partially known by science.

Hypnagogue's toy example could also serve to see that it is difficult, in general, to say where an empirical description can be finally stopped in a determinate level, establishing a determinate level of individuation. I gave the example of elementary particles, because in some levels of epistemic description they can play the role of individuals, but in other levels (field theories, for instance) it might happen that they were not those individuals.

In any case, Tychic, thanks for disagreeing. It is thought provoking, and that's what we try, don't we?

 

[hypnagogue]

antfm thinks that fields could be individuals in Rosenberg's sense. He is confronted with the same problem as my theory of spacetime as an individual.

Well, I suppose we could create a theory where fields are individuals, just as we could perhaps create one where spacetime is an individual. That is to say, there do not appear to be any logical or empirical considerations that rule such a thing out, at least prima facie. I'm still not sure how to even conceptualize spacetime as an individual though-- it could just be a failure of my imagination, but I find Rosenberg's proposal more intuitive.

What do you want to say with the hint to figure 10.14?

Just to point out another general mechanism/condition Rosenberg offers by which a pattern of receptive structures can change.

I agree. But is General Relativity relevant for your proposal? Does your proposal not also work if space is Newtonian?

The problem I was trying to address is that according to GR, mass warps spacetime-- i.e. in some sense the structure of spacetime is sensitive to the presence of mass. Rosenberg proposes that the structure of spacetime is nothing but the receptive structure of the causal mesh. So putting these together, we would need an account whereby the receptive structure of the mesh could be responsive to the presence of an effective property-- mass-- in a systematic way. In other words, we would need a more explicit theory of the principles by which the receptive structure of the world is patterned, and it would need to be in such a way that it could be responsive to the presence and magnitude of certain kinds of effective properties. In my last post, I was trying to sketch a very skeletal and general account of how we could build such a thing using the conceptual materials Rosenberg has provided thus far.

Sorry for the delays as of late-- I've been a bit too preoccupied recently to be as dedicated to this as I need to be. I'm going to work over this weekend to get a thread up for chapter 12, which is where the real fun begins.

 

[selfAdjoint]

The problem I was trying to address is that according to GR, mass warps spacetime-- i.e. in some sense the structure of spacetime is sensitive to the presence of mass. Rosenberg proposes that the structure of spacetime is nothing but the receptive structure of the causal mesh. So putting these together, we would need an account whereby the receptive structure of the mesh could be responsive to the presence of an effective property-- mass-- in a systematic way. In other words, we would need a more explicit theory of the principles by which the receptive structure of the world is patterned, and it would need to be in such a way that it could be responsive to the presence and magnitude of certain kinds of effective properties. In my last post, I was trying to sketch a very skeletal and general account of how we could build such a thing using the conceptual materials Rosenberg has provided thus far.

It is momentum, momentum-stress, and energy which modify the value of the Einstein tensor, and indirectly warps spacetime in GR. Mass is of course a form of energy, but it is really better not to zero in on the metaphysics of mass when it is kind of a stepchild to the things that really matter.

Note also that according to the Standard Model of particle physics, most of the mass we encounter in this world, and base our philosophy of matter upon, is really the binding energy of the gluons within the protons and neutrons. Only a minor amount is due to the masses of the quarks, which in the current model are due to the interaction of those particles, the underlying nature of which is massless, with a Higgs particle, which gives them a nonzero mass.

Of course you may doubt these theories, but I don't think you can overthrow them with historical considerations of what our smartest ancestors thought mass was.

 

[antfm]

How interesting all this is, SelfAdjoint. And how amazing and beautiful that us, human beings, can try to get some understanding of it.

...the underlying nature of which is massless, with a Higgs particle, which gives them a nonzero mass.

If so, and if this Higgs particle that gives mass to the rest is itself a nonzero mass particle, does it obtain its mass from some kind of 'arising' from a ¿vacuum? structure?
But this, of course, I know, would be more amenable to a mathematical description than to a intuitive one.
Which do you think, SelfAdjoint, are "those things that really matter"?
Some underlying 'field', 'math', 'structure'...?

 

[selfAdjoint]

How interesting all this is, SelfAdjoint. And how amazing and beautiful that us, human beings, can try to get some understanding of it.


If so, and if this Higgs particle that gives mass to the rest is itself a nonzero mass particle, does it obtain its mass from some kind of 'arising' from a ¿vacuum? structure?
But this, of course, I know, would be more amenable to a mathematical description than to a intuitive one.
Which do you think, SelfAdjoint, are "those things that really matter"?
Some underlying 'field', 'math', 'structure'...?

Well the interaction of the particle with the Higgs causes it to respond more sluggishly to a force, giving it less of an acceleration, and since by Newton, mass = force/ acceleration...

The current thinking of physicists is that the basic underlying facts of nature are SYMMETRIES, and the conditions under which those symmetries are broken. In 1918 Emmy Noether published her famous theorem about physical systems described by a Lagrangean expression, as quantum field theories are. She showed that if the Lagrangean expression is invariant under a group of symmetries, then there is a conserved quantity and a current for it in the physical system. Conservation of momentum, energy, and angular momentum are due to the invariance of the Lagrangian for Newtonian physics under spatial translations, clock resettings, and angular orientation. More involved symmetries give us conservation of electric charge and of various subatomic quantities like isospin.

There is partly successful work to derive all of physics from a family of symmetries, perhaps with some general idea of causality appended, sometimes not. But the color and specificity of the world arises from BROKEN symmetries. And the Higgs mechanism is an example; the massless nature of the quarks that I spoke of is due to the symmetry groups that rule the Standard Model. But the Higgs field comes in and breaks that symmetry, giving mass to the particles.

 

[antfm]

Thanks for your help, SelfAdjoint. You really know what you are talking about and is great that you share your knowledge here.

One more question, if you don't mind.
Do symmetries require a spatiotemporal background to be conceptually developed, or is the breaking of these fundamental symmetries itself which gives raise to spacetime?

I guess, from the heard attempts of physicists to develop a background independent theory, that the first option must be the case.
But, if so, isn't there some kind of vicious circle at the heart of modern physics if Relativity produces spacetime geometry as a manifestation of a particular field (gravitational field), and Field Theory presuposses a spacetime geometry to be displayed?

Rosenberg's theory is not commited, I think, to any particular physical description in its conceptual aspect; spacetime would evolve from an underlying 'causal mesh' that he tries to bring into consideration, being open to which physical theory in particular is able to explain it.

Do you have, SelfAdjoint, any tentative ideas for a spacetime structure emerging from some underlying principle, in ,more or less, the way that fields or particles emerge from a fundamental symmetry breaking?