Recognising Top-Down Causation by George F. R. Ellis

Dear Eckard

you are quite wrong to be hurt by my comment that the time would be much better spent reading the Feynman lectures. I often read them for elucidation.

You'll find the relativistic derivation of the transformation laws for electric and magnetic fields on pages 26-1 to 26-10 in Volume II, and that of the Lorentz equations of motion on pages 26-11 to 26-13. They clearly show (Table 26-3) both why motion of an electron generates a magnetic field, and motion past a magnetic field generates an electric field (and hence a current). Basic stuff for electrical engineers.

George Ellis

The theme of this essay and this thread is the existence of both bottom-up and top-down causation in science in general, and in physics in particular.

Some interesting issues have arisen from the postings on this thread that have addressed this theme. To avoid confusion I'll deal with them in separate postings. Here is the first.

Issue 1: Contextual Logic

Frederico Pfrimer's posting on September 14th at 17:18 GMT lead me to read his interesting essay, which contains the following statement:

".. the main wrong assumption of physics is not a physical assumption, but a millenary logical assumption: the principle of excluded middle .... This principle says that a proposition is either true or false, in other words, either the proposition or its negation is true"

I responded on September 24th at 19:23 GMT "I think that you might be saying that the truth or falsity of a proposition may depend on its context. That is very close to the concept of contextual effects that I discuss in my essay." I believe this is a key idea: that the way the logic at the lower level operates may depend on the higher level context within which it is imbedded. This is one way of cashing out Frederico's proposal.

At each level of the hierarchy, there is a set of logical and causal relations that operate. In first order logic , a predicate P(a) is a statement that may be true or false depending on the values of its variables a. The issue then is whether those variables can be determined purely at that level of the hierarchy, or whether they depend on variables defined at lower or higher levels. In the first case, the logic at the level considered is affected by bottom up causation, and hence is not determined purely by the variables at that level. In the latter case, it is affected by top-down causation, with the same outcome. Thus whether a specific proposition is true or not depends on parameters defined at other levels --- which means the principle of the excluded middle for logic at that level is in effect modified: truth or falsity is contingent on context.

The process is particularly clear in the case of conditional branching or looping in computer programs. The program continues on one path if a condition T(a) is true, and on another one if it is false. If T(a) is based on variables that are evaluated in other subroutines, it depends on criteria evaluated in the program as a whole rather than in the subroutine where the condition is evaluated. This logical difference then goes on to cause different flows of electrons at the physical gate level (cf.the discussion of computers in my essay). The underlying physics of course allows this, indeed it enables it to happen. Essentially the same conditional branching happens in many cases in molecular biology (see Gilbert and Epel: Ecological Developmental Biology for details).

Accordingly I believe Pfrimer's and my essays are in sympathy with each other in a profound way (even though this was not what he had in mind!)

George

In view of the interaction above, here is a note on how special relativity interacts with bottom up and top down causation in the case of electromagnetism:

The electromagnetic field is described by an anti-symmetric tensor F, made up of electric and magnetic field components. The micro level laws are (i) Maxwell's equations for the electromagnetic field, including the Gauss law, with particles such as electron and protons as sources; (ii) the Lorentz force law for the effect of electric and magnetic fields on charged particles such as protons and electrons.

The transformation laws for electric and magnetic fields under change of velocity v in the x-direction follow from the nature of Lorentz transformations, see Feynman Lectures in Physics Volume II, pages 26-5 to 26-10. They are

[math]E'_x = E_x,\,\, B'_x = B_x,\,\,\\

E'_y = \frac{E_y - v B_z}{\sqrt{1-v^2}},\,\, B'_y = \frac{B_y vE_z}{\sqrt{1-v^2}},\,\, \\

E'_z = \frac{E_z v B_y}{\sqrt{1-v^2}},\,\, B'_z = \frac{B_z - vE_y}{\sqrt{1-v^2}}.\,\,

[/math]

With the Gauss law, these show why an electron in motion generates a magnetic field. They also show why an electron moving in a magnetic field will experience a transverse electric field that will then affect its motion.

The bottom level dynamics is the way the micro level electric and magnetic fields interact with each other according to Maxwell's equations, with the charged particles as sources, and these fields in turn exert forces on those particles via the Lorentz force law, that cause them to move if they are free to do so.

Bottom up effects are the way that billions of electrons in motion at the micro level generate measurable electric currents at the macro level, such as in a generator, and the way that forces on billions of charged particles at the micro level can add up to generate macroscopic forces, such as in an electric motor.

Top down effects are for example the way that electric coils (macro entities, not describable in terms of micro level variables) constrain the motion of electrons in specific directions. This is why the micro fields they generate add up to macro level fields (see for example Feynman Lectures in Physics Volume II pages 13-5 to 13-6); without the constraints exerted by the wires, no such macro fields would be generated. Similarly the constraints generated by the design of the electric motor ensure that the individual forces on electrons and protons are channelled so as to add up to measurable macro level forces. This constraning effect is top down action from the level of machine components to the level of protons and electrons.

How does special relativity fit in? Magnets in the generator create magnetic fields. It is the motion of the generator coils in these fields that creates the local relative velocity v that (via the above equations) then causes an electric field to act on the electrons and make them move to form a current. In an electric motor, it is the motion of electrons in coils that generates local magnetic fields that are utilised to generate rotation. The above equations are at the heart of what happens in both cases. And they result because of the application of the full set of Lorentz Transformation laws --- the heart of special relativity --- to the electromagnetic field.

It is for this reason that the daily operation of electric motors and generators, via their design (thanks to the good offices of electrical engineers - a top-down effect from the human mind into the physical world), is a demonstration of and confirmation of both special relativity theory, and the efficacy of the combination of bottom up and top down effects.

George

And I so carefully previewed those equations! Oh well, here they are:

[math]E'_x = E_x,\,\, B'_x = B_x,\,\,\\

E'_y = \frac{E_y - v B_z}{\sqrt{1-v^2}},\,\, B'_y = \frac{B_y vE_z}{\sqrt{1-v^2}},\,\, \\

E'_z = \frac{E_z v B_y}{\sqrt{1-v^2}},\,\, B'_z = \frac{B_z - vE_y}{\sqrt{1-v^2}}.[/math]

I give up. You'll have to read them in Feynman.

I give details below in my posting of Sep. 28, 2012 @ 07:41

The equations are

[math]E'_x = E_x,\,\, B'_x = B_x,\,\,\\

E'_y = \frac{E_y - v B_z}{\sqrt{1-v^2}},\,\, B'_y = \frac{B_y vE_z}{\sqrt{1-v^2}},\,\, \\

E'_z = \frac{E_z v B_y}{\sqrt{1-v^2}},\,\, B'_z = \frac{B_z - vE_y}{\sqrt{1-v^2}}.

[/math]

[they probably won't display properly as there is a fault in the system; they preview correctly]

George

One further comment: hidden macro assumptions

If one looks for example at the Feynman derivation of the magnetic field due to electrons flowing in a wire coil, the wire is represented as a structureless macro entity, even though it is made up of atoms and electrons. We just take this macro structure (the physical wire) for granted in all such derivations. This is analogous to the Copenhagen interpretation of quantum mechanics, which is the de facto way things are thought of by experimentalists: detectors and mirrors for example are indicated in their diagrams as structureless macro entities, because their nature and mode of operation is taken for granted. It's not what the experiment is about.

Thus the causal effectiveness of macro entities is taken for granted in both cases (the way the wire channels the flow of electrons, the way the mirror transmits and reflects light and the detector records incoming photons). Yes of course they are made up of atoms and electrons at the micro level, but that is irrelevant to their role in the experiment, which role is due to the macro organisation embedded in these structures. These structural constraints act down to organise micro events (as is very clear in the case of the wire: its physical structure prevents electrons moving sideways out of the wire).

This top-down aspect of what is going on is hidden because we take it for granted. It's just part of what we assume to be the case, so we don't notice it.

George

Hi Joel

Indeed. The calculations leading to understanding of this spectrum are basically the present day version of the resolution of Olber's paradox (why the is the night sky not as bright as the surface of the Sun): one of the oldest calculations of global to local effects. My paper here makes that link. The divergence underlying Olber's paradox is also essentially the divergence that prevented Newton from ever creating a cosmological model based on his gravitational theory. Ted Harrison's books Cosmology: The Science of the Universe is a great source on all this.

Gworge

Dear Crisit

your presentation is very nicely done. I agree completely with your emphasis on the importance of global conditions, which of course is fully in agreement with my essay. I also agree about quantum theory maybe having influences into the past.

As to wave function collapse: you state "But we can assume that the interaction with the measurement device (and the environment, as the decoherence program requires) only disturbed the unitary evolution, and the collapse is only apparently discontinuous" This is pretty close to my concept of the apparatus acting down on the particles to cause an effective collapse. "The measurement of O1 in fact refines both the initial conditions of the system \psi, and those of the apparatus \eta". I think I agree: this is a case of what I call adaptive selection (which occurs in state vector preparation).

Where we disagree is that you want to preserve unitarity: I think its clear you can't. The top down action from the apparatus causes non-unitary behavior at the particle level. I think that's clear in the case of state vector preparation.

Best wishes

George

Frank

"what do you think is the legitimate and true goal of modern physics and modern science?"

It is to understand the mechanisms whereby physical things work (the natural sciences) and how livings beings exist and function (the life sciences), together with understanding the historical process whereby they came into being (the historical sciences.)

Science cannot deal with issues of aesthetics, ethics, or meaning. This is because it deals either with issues that can be tested by replicable experiment that any community of scientists should be able to reproduce,or with observations of things that exist historically where any scientist can examine these historical remains and test the theories about them that others have proposed. The core of science is testability by observation or experiment of proposed theories.

Things like television sets are the product of technology, which utilises science to create useful artefacts. They are the outcome of abstract thought, and exist because of top-down action from the human mind to the physical world. No scientific theory can either predict or explain the existence of television sets, because they are not predicted by Maxwell's equations, Newton's laws of motion, or any other set of fundamental equations that describe how physics works.

George

Yes interesting.

To me the very important thing is how when you chunk things in this way you change their properties. Thus neutrons decay in 11 1/2 minutes when free, but are stable for billions of years when incorporated in a nucleus. Electrons interact by Thomson scattering when free but not when bound in an atom. A hydrogen atom is not longer a hydrogen atom when combined into water.

If you believe that identity is described by patterns of behaviour or interaction of an entity, then context changes identity. That's why the billiard-ball model of bottom up interaction does not work in most cases.

The Large Scale Structure book won't help much in all this. It's about gravity and does not deal with octonions. Actually rather than octonions I's go for geometric algebra

George

Hi Tom

"Context or multi-scale variety? I think the former assumes independence of identity and context, while the latter assumes continuous functions over multiple scales. In other words, I think the model is not bounded by context implying arbitrarily chosen conditions; rather, self organized and implying self-limitation."

Well it's hard to avoid the usual way of talking, where one says hydrogen is bonded with oxygen to give water, even though they are neither hydrogen nor oxygen once bonded. Your description is more accurate but also more difficult to follow intuitively. One hangs onto the idea that it is the components that make the object exist, even when, as your comments imply, they lose their identity when this occurs. It's a historical statement really, about where the combined entity came from.

Yes I meant Doran and Lasenby, developing out of Hestenes' work.

George

Hi Conrad

You say in your essay "The problem is that measurements are inherently contextual. They can't be analyzed into simple, self-contained elements without losing sight of what makes them work." Absolutely right!

Just a comment on vision: you say "so it requires a huge amount of complex low processing to support the seemingly stable sensible view of the world you see as you glance around." Yes, but also it actually it requires a huge amount of *high level* information to interpret what we see, because the light striking our retina, even though it conveys a vast amount of information, does not convey enough information to unambiguously tell us what is there. Eric Kandel explains this in detail in his book The Age of Enlightenment: he emphasizes that it is only because of top-down processing form the cortex that we are able to form visual images.

Yes I agree with you about time and information (you may have seen my new paper on time). And then you say "So it's conceivable that what we're looking at is an evolutionary process operating through a kind of natural selection, analogous to biological evolution. Instead of many organisms replicating themselves, reproducing their species, here we have many local systems contributing to the reproduction of their common environment, as a body of shared, self-defining information." Yes I agree - you will see in my quantum essay how I also emphasize this process of adaptive selection works in physics processes such as state vector preparation. It also lies at the heart of the difference between Hamiltonian and Lagrangian dynamics, as I comment elsewhere in this thread. I thinks it a key feature of how physics works, as well as of how biology works.

Congratulations on a great essay.

George