Holistic character of physical concepts

ON THE HOLISTIC CHARACTER OF PHYSICAL CONCEPTS

"Toute science est avant tout l'etude d'une phénoménologie"

RENÉ THOM

In physics, we are systematically trying to eliminate subjective influences due to the limitations of our senses, by formalizing and automatizing the experimental procedures. Ingenious instruments take the place of the naked eye. Galilei made his important discoveries when he used a telescope to get a closer look at the heavenly bodies. This is certainly true. It is also true that mathematical abstraction plays a crucial role in physics. But we must not forget that at the same time physics is ultimately based on experimental evidence, that is, it relies on the possibility of verifying hypotheses about nature by help of insights, obtained through experiments performed in that world which presents itself to us in sense perception. In arranging and carrying out his experiments, the physicist deals with ordinary, macroscopic, material bodies. To be able to do this, he must rely on the world picture of common sense. The 'contextual knowledge' is usually so self-evident to the scientist, that he might not even be aware of its crucial importance.

This should not be taken to mean, however, that one has to bring knowledge of the way our senses function, or, still worse, the "mind" of the observer, into physics -- as has sometimes been suggested in order to "explain" certain seeming paradoxes that are due to the propositional and probabilistic character of modern science. I see no convincing reason why we should have to abandon 'the principle of the self-containedness of nature', so beautifully stated by A N Whitehead in "The Concept of Nature":

In sense-perception nature is disclosed as a complex of entities whose mutual relations are expressible in thought without reference to mind, that is, without reference to either sense-awareness or to thought .... Natural science is exclusively concerned with homogenous thoughts about nature. ²

Since physics is about nature - i.e., since the mathematical formulae in physics are not about mathematics, but about something which is grasped through mathematical concepts - we have to be a bit careful not to overlook, what I would call, "the phenomenology of physics". The science of physics is deeply rooted in a capacity of seeing the physics in natural phenomena and processes. The description of the structure of physical phenomena, the separation of what is essential from what is accidental, is a basic concern of the physicist that cannot be "explained", except by reference to its self-evidence and fruitfulness.

Let me return to the phenomenon of coloured shadows, as discussed above. =>

It was certainly wise of Galilei to use a telescope in order to improve his knowledge of the planets. This is also what we do instinctively, when we want to examine something, trying to find out what it is - we take a closer look, in order to see more details. Starting with the magnifying glass, by more and more advanced instruments, we penetrate deeper and deeper into matter. Is this method always appropriate? If we study a coloured shadow by approaching it, it finally disappears. (The same is true for the so called "blocked pictures", where you recognize for instance the features of Abraham Lincoln if you hold the picture at a distance, but not if you look closely at it.)

After all, what makes us think that we get a more basic knowledge of an object by going into the details of it? Why do we think that the smallest parts are more "simple" than the object as a whole? Maybe, for any natural phenomenon, there is always a certain range of scale within which it presents itself most obviously and unambiguously. In biology, for instance, the question about the difference between life and dead is certainly fundamental. But most researchers in this field would feel inclined to say that when you look closer at it, the boundary between life and dead becomes more and more diffuse, which makes you doubt whether there is really any fundamental difference. As I see it, this conclusion is not fair. The first task of any scientific inquiry is to find out how to make the phenomenon under study more distinct, more pure, more stable.

This seems to be an important methodological issue within the sciences. Logically, there are several possibilities: One is that by going to lower levels you arrive at elements that are more invariant, more unitary and seemingly indivisible than on the level you started from. The opposite possibility is that when you go to lower levels you encounter unstable and fluctuating structures, eventually ending up in mere chaos. A third possibility would be that the morphology, when you go into details of it, gives way, not to chaos, but to a new morphology.

This would be a pertinent observation, for instance, to sociology. Sociological phenomena are most precisely defined in terms of relations and interactions between individuals. But if you search for a still more detailed theory by "looking into" the individuals, not respecting their indivisibility, then the uniqueness of each individual becomes more and more obvious, each one having its own inner cosmos.

Another example is given by phonetics. On the level of the utterance of whole sentences, there is a high degree of structural stability, but if you hypostatize phonetic micro-units of some kind - with the intention of explaining the stability of the whole by the invariance properties of these "atoms" - you may run into pseudo-problems. (We will return to this in the next volume of this report series.) In his book "From being to becoming" Ilya Prigogine writes:

Since the beginning of Western science, we have believed in the "simplicity" of the microscopic - molecules, atoms, elementary particles. This conception... can hardly be maintained today. The elementary particles that we know are complex objects that can be produced and can decay. If there is simplicity somewhere in physics and chemistry, it is not in the microscopic models. It lies more in idealized macroscopic representations.³

Thus, when penetrating into matter, suppose we do not actually get "closer" to it, but instead look into a new cosmos, which opens up to us, and where the objects are as far away as are the stars and nebulae on the sky......

But atoms are not "parts" of a piece of matter, and the DNA-molecules are not "parts" of a living organism, in any simple sense. Science deals with "underlying processes", "the mechanisms behind" and the like.

Once again I bring an example from colour science. When I look at colour samples and observe for instance an orange patch, I can report what I see, estimating the proportion of yellowness to redness in that particular hue. At the same time, a brain researcher might be able to study what is going on in my brain simultaneously to my seeing the colour. And a physicist can specify the spectral energy distribution of the radiation, reflected from the colour sample. All these are "underlying facts". By how can I ever make sure, that these three classes of data - the behavioural, the neuro-physiological and the physico-chemical - do really refer to one and the same act of perception?

Gerhard Roth discusses this point in an article on reductionism in biology. He concludes:

One of the central problems of reductionism in biology, therefore, is to show the identity of phenomena belonging to different descriptive and conceptual domains.⁴

Traditionally, there is a tendency to maintain that since the colour of a shadow cannot be analysed per se it has no physical reality, it is something our imagination projects onto the shadow region. Physical reality is ascribed to such entities that do not just disappear, but meet with resistance the scientists attempt to "get in touch with them". In a way, this is the enigma of material presence. Still it is an open question whether we rely too much on spatial coincidence and immediate local contact, as well as on the possibility of a continuous transition between levels, in taking for granted this "identity of the object under inquiry".

This raises the question about the meaning of "constituent parts". There are at least two radically different meanings, pertinent to the present discussion. Let us return to colour, once again. The Newtonian, prismatic spectrum is a band of seven colours: red, orange, yellow, green, blue, indigo and violet. This is a description of how it looks at some distance. On the other hand, in his theory of light Newton proposed that white sunlight 'consists' of the 'sorts of light' that present themselves in the But this composition is not something you see, while looking at a spot of white light.

Likewise, a certain orange colour may be described as "a yellow-red hue, with 30 % yellowness, 70 % redness". This does not mean that the colour in question is physically made up by a mixture of yellow and red pigments in this proportion. It is just a description of the 'orange' in its relation to 'red' and 'yellow'. On the other hand by superimposing for instance a red and a green beam of light you may obtain yellow light. Considering how this yellow was brought forth it is reasonable to say that it "consists" of red and green. But these colours are not "parts" of the yellow. Phenomenologically the yellow is simple and pure.

A last example. The phenomenon of a coloured shadow consists of at least two parts: the shadow region and its surround - the surrounding area, that is, in relation to which it is shadow. The shadow figure cannot be taken out of its context and studied in isolation. The coloured shadow, as well as the yellowness and redness of an orange hue and the seven colours of a spectrum, are all parts, but non-interacting parts, of the respective wholes. It is a question about necessary coexistence. Let us in this case speak of the 'formal parts' of a whole. If you treat formal parts as if they were interacting 'physical parts', you will soon find yourself struggling with pseudo-problems.

When I say about a coloured shadow that it cannot exist independently, what kind of statement is this? Is it a logical statement? Or is it an empirical statement, that is, is it something that just happens to be this way, but could as well have been otherwise? In his famous "Remarks on Colour" Ludwig Wittgenstein asks some questions, similar to the above:⁵

I am told that a substance burns with a grey flame. I don't know the colours of the flames of all substances; so why shouldn't that be possible? (I-40,41)

Why is it that something can be transparent green but not transparent white? (1-19)

Why can't we imagine transparent-white glass, even if there isn't any in actuality? (I-31)

If someone didn't find it to be this way, it wouldn't be that he had experienced the contrary, but rather that we wouldn't understand him.(II-10)

The question is: is constructing a 'transparent white body' like constructing a 'regular biangle'? (III-138)

I don't know whether pure red is lighter or darker than blue; to be able to say, I would have to see them. And yet, if I had seen them, I would know the answer once and for all, like the result of an arithmetical calculation. Where do we draw the line here between logic and experience? (III-4)

To be sure, I can speak about "a piece of transparent white glass", if I do not care about what I am saying. But I could never demonstrate such an object, or even imagine it. There is no continuous process, leading from an opaque white to full transparency, without the whiteness getting lost on the way. This concerns the way colour is, in its presentational immediacy.

So far I have spoken about colour, and one could doubt whether this topics falls within physics. But even more genuinely physical propositions can be discussed in similar terms. For instance, the statement that a perpetuum mobile cannot be constructed -- is this based on the empirical evidence, that nobody has so far ever seen a device of that kind? No. It is a matter of principle that it cannot exist, in fact, cannot even be consistently conceived. So if some inventive genius would one day come to the physicists and say: "Well, old fogeies, here you are!" I am quite sure he would get the reply: "Yes, but this is not what we call a perpetuum mobile". Compare Wittgenstein's remark II-10 above!

The same is true for the statement that no material object, or any signal whatsoever, can travel faster than light. Or, for that matter, that there cannot be any anti-gravitational force. To a physicist, if he has a well-founded feeling for what physics is about, some naive proposals sound as absurd as the above cited queries of Wittgenstein within colour science.

Since I think notions dealing with the a priori structure of physical phenomena are essentially holistic, it would be worth-while to take a look at some well-established physical concepts, from this particular point of view.

Consider Newton's laws of mechanics. The first law states: A material body on which no forces act from outside remains in its state of rest or homogeneous motion. (Homogeneous motion means movement with constant speed and direction). What lies behind this "principle of inertia", as it has also been called? The point of departure is our efforts to understand the various phenomena of motion. If we think of movement as 'the being of an object at successive positions at successive moments of time', then we have to answer the question: What makes the object change its position? What is the cause of the movement? Now, according to the principle of inertia, this as a meaningless question. There is no cause, nothing makes the object change its position, homogeneous movement is just a possible state of being of matter. Thus, the question is treated, not as a matter of causality, but as a matter of form. (Homogeneous motion does only formally, but no "really", consist of a series of point-events.) History shows us that this was a fruitful way of treating the problem of motion of bodies in general.

Together with the linear rules for addition and decomposition of velocities, the first law has holistic consequences. For instance, the trajectories of all fragments of an exploding projectile are correlated with each other in such a way that, taken together, they determine the trajectory the projectile would have followed, had it not exploded. If a particle of known velocity and mass disintegrates into two particles that fly apart, by measurements on one of these particles one can predict the outcome of measurements on the other one. This correlation between distant measurements does not imply that there has been some exchange of information, by some kind of coupling or signal travelling between the particles. Rather, it depends on the fact that the two particles are formal parts of one and the same given whole, defined by the state of the original particle. (This shows that 'being a formal part' is not meant as an arbitrary convention, but concerns the a priori structure of physical phenomena - "the way things are".)

What about waves, and the interference of waves? I observe a water-wave and follow it riding over the sea, eventually crushing into the cliffs. Alternatively, if I look steadily at a certain spot, I can see the surface of the water quietly rising and falling. Actually, what sort of object is a wave? Is it something I imagine? Does it "really" exist? Can a wave be said to be a physical object?

Anyhow - it is a basic and extremely fruitful concept in physics. In physics, waves are closely related to the concept of 'interference'. Consider the way interference of light is discussed in most elementary text-books. You are shown a sketch about as follows:

Two rays, or wave-trains, of light, emanating from the two slits a and b, meet at point A and superimpose destructively so as to give darkness at this point. At another point B two other rays may add constructively, giving a maximum of intensity. Which case you get depends on the difference in length of the path covered by the respective rays when they meet.

Now, if you say that two lights add to give darkness, this seems paradoxical, since energy plus energy must give energy. So, if light is really there, at A, it must be possible to detect it somehow. On the other hand, if light is not there, what is it that interferes? If we say that a ray a interferes with another ray b, then a and b must be there, to be able to interact. But, according to physics, there is just as much as nothing at A, if the destructive interference is complete. This shows that you cannot properly speak of interference, in terms of two entities interfering with each other. Interference is something which takes place within a region of space. Interference is a holistic concept. If you have darkness at some place, then you must by necessity, simultaneously, have enhanced intensity at some other place. What happens at A is a formal part of a whole, including also points such as B. When you speak of "rays of light" as independently existing, as in the argument above, you get into seeming paradoxes.

The "wave" is the concept we use to formalize this holistic aspect of light. A wave is a specific co-ordination of local events over space. It involves by necessity a number of (at least two, usually infinitely many) spatial points. It must have its "here" as well as its "there". Moreover, it must have certain symmetry properties, to take care of the general condition of total energy conservation. (This symmetry leads to periodicity.) Thus, interference is not a kind of 'interaction', nor is it a superposition of effects. If, mathematically, you say that the light intensity at A is given by a sum of amplitudes that add up to zero, these amplitudes do not exist individually, but just formally, as parts of a given whole.

Let me, finally, make a few observations concerning quantum mechanics. Abner Shimony is certainly right in pointing out that quantum mechanics furnishes interesting examples of holistic concepts .⁶ The so called Einstein-Podolsky-Rosen paradox, the by now famous Bell's theorem, and the ingenious experiments by Clauser, Aspect and others; that falsify Bell's inequality -- all this means a real challenge to the traditional way of conceiving the nature of things. Despite their seeming simplicity, these experiments -- even as thought experiments - involve so many relevant, as well as irrelevant, aspects, however, that it is extremely difficult to get a clear concept about their essential structure. Let me put down some such aspects.

A fundamental principle of quantum mechanics is the principle of coherent superposition of states. Most puzzles of quantum mechanics can be traced back to this principle. It derives its origin from the classical idea of 'interference' which is inherently "holistic", as I have argued above. At the atomic level interference cannot be thought of as any kind or interaction between physical objects - this was emphatically pointed out by Dirac in his, by now classical, introduction to quantum mechanics:

Each photon interferes only with itself. Interference between two different photons never occurs.⁸

This is what makes two-slit experiments at the quantum level (extremely low intensity) so puzzling. When we describe physical systems as made up of component systems, a logically consistent application of the superposition principle leads to the result that (and now I am citing Jauch):

"the state of the compound system cannot be completely determined by measurements on the component systems alone. There are thus physically distinguishable properties which express themselves as correlations between observations on the component systems".⁹

As concerns Shimony's use of "entanglement" to describe the consequences of the principle of coherent superposition, I agree that it expresses a kind of holism: The state of the whole cannot be settled by measurements on the separate parts. It is also true, as he maintains, that entanglement has nothing to do with interaction, in the sense of causal interaction. The two distant observations do not "influence" each other. As long as no measurements are performed on the separate "parts", these are only formal parts of the whole that is represented by the state function.

It has sometimes been maintained that it is a consequence of quantum mechanics, that distant measurements are sometimes correlated. I do not see how that argument goes. The quantum mechanical considerations behind Bell's theorem do not involve any assumptions concerning spatial distances whatsoever. It tells us just nothing about this particular issue. The fact, that the distance between the two detectors does not influence the observed correlations (even when appreciably larger than the coherence length of the radiation), is an experimental finding and should be acknowledged as that. As a matter of fact, all considerations concerning physical space as having the quality of extension (that is, as containing solid objects, volumes, line elements, planes, closed curved surfaces etc.) belong to the tacit assumptions that are taken for granted when physical formulae are interpreted. The enigma of "non-locality", whatever it means, cannot be solved within quantum mechanics. In the last analysis it demands a renewed inquiry into the concepts of space, time and causality.

To try to explain the state of affairs by reference to "action-at-a-distance", is highly questionable. First, because the concept of 'action' is not applicable to formal parts of a whole, as pointed out above -- provided I am right in suggesting that the two "particles" in the above-mentioned experiments, before being registered, are only formal parts of the studied phenomenon. Secondly, because I doubt whether the concept of 'distance' could be consistently defined independently of the concept of 'action'. Perhaps this is exactly what defines distance between objects, that there can be no immediate action from the one onto the other! In such case, action-at-a-distance would be a self-contradictory notion.

REFERENCES AND FOOTNOTES

1) Quoted from Rene Thom: Paraboles et Catastrophes - Entretiens sur les Mathematiques, la Science et la Philosophie; Flammarion, Paris 1983, p. 5

2) Quoted from "The Concept of Nature" (1920). I am aware of the fact that Whitehead in his later writings may seem to have abandoned this idea. This is pointed out e.g. by Sten Philipson in his doctoral thesis: "A Metaphysics for Theology -- A Study of some Problems in the Later Philosophy of Alfred North Whitehead and its Application to Issues in Contemporary Theology" (Acta Universitatis Upsaliensis, Studia Doctrinae Christ.Ups.22, 1982), p 37. That man, as a living creature, is included in nature -- as an unseparable part of it -- and that man's perception is just "Natures conversation with herself", as Goethe puts it in his Farbenlehre, is no to be denied. Thus, the doctrine that science is exclusively concerned with homogenous thoughts about nature (i.e. that nature can be thought of as a closed system whose mutual relations do not require the expression of the fact that they are thought about) is far from self-evident , and would be emphatically denied by quite a number of philosophers of science. But the point is that it means an epistemologically important delimitation of the scope of science. Thus, one can say that the scientific enterprise consists in the exploration of the possibilities of homogenous thinking about nature. To be sure, metaphysics must include other aspects as well. The doctrine of the self-containedness of nature makes physics an underlying part of metaphysics, but prevents it from being adopted as metaphysics.

3) Ilya Prigogine: "From Being to Becoming", Freeman & Co, San Francisco 1980

4) Gerhard Roth: "Biological Systems. Theory and the Problem of Reductionism", in: Roth & Schwegler (ed.) "Self-Organizing Systems - An Interdisciplinary Approach", Campus Verlag, Frankfurt/Main 1981, p 110

5) Ludwig Wittgenstein: Remarks on Colour, (ed. G.E.M.Anscombe) Oxford 1977

6) Abner Shimony, in his paper to this workshop, Parts & Wholes, vol 1, (1983) Compare also Claes Aberg's contribution in the present volume.

7) See for instance: Alain Aspect et al., Phys Rev Letters, 47 (1981) 460-463 Aspect and collaborators measure statistical correlations between various states of polarization of the two photons, emitted in cascade at the decay of a welldefined excited state of Ca atoms.

8) P.A.M.Dirac: Introduction to Quantum Mechanics, Oxford 1930 (quotation Ch.I,2) Josef M. Jauch: Foundations of Quantum Mechanics, Allison-Wesley,1968, p.180 see also Michael Drieschner: Einfuhrung in die Naturphilosophie, Wissenschaftl. Buchgesellschaft, Darmstadt 1981, pag. 102-103 and 121.

9) Josef M. Jauch: Foundations of Quantum Mechanics, Allison-Wesley,1968, p.180 see also Michael Drieschner: Einfuhrung in die Naturphilosophie, Wissenschaftl. Buchgesellschaft, Darmstadt 1981, pag. 102-103 and 121.