NETPAPER

An Aristotelian interpretation of quantum mechanics

(this paper was written in 1996)

Summary:

The classical view on physical reality being composed of absolute objects and fields has been challenged by Niels Bohr, who proposed the elementary phenomenon as the basic constituent of reality.

This paper propounds a reformulation of the Copenhagen interpretation in terms of the Aristotelian concept of 'four causes'. This interpretation explicitely incorporates the irrational will-side of nature and leads to the conclusion that it could be impossible for life phenomena and life structures to undergo copying.

This conclusion is important for the study of consciousness, as many arguments used in the debate presuppose that life processes and living structures can be replicated or copied in principle.


1.Introduction.

After the clash with Einstein in 1935 (1,2,3), Niels Bohr started to alter significantly the formulation of his interpretation of quantum mechanics. In his reply to the Einstein-Rosen-Podolsky paper Bohr3 implicitely stated that not isolable objects, but phenomena are the ultimate constituents of physical reality. From 1939 onwards he used the expression '(quantum) phenomenon' explicitely to refer to the whole observational interaction, which is considered to be undivisible in principle(4). Every attempt to analyze the phenomenon will lead to its replacement by another one, equally unanalyzable: "The essential wholeness of a proper quantum phenomenon finds (...) its logical expression in the circumstance that any attempt at its well-defined subdivision would require a change in the experimental arrangement incompatible with the appearance of the phenomenon itself"(5). As Folse(6) rightly stresses, this view of Bohr is rooted not in any dogmatical a priori rejection of the concept of an absolute object (in the tradition of Democritus) but in physical fact (namely in the observation that h>0).

 

Max Jammer(7) places Bohr in the philosophical tradition represented by Aristotle and Thomas Aquinas because he reintroduced into physics the concept of ".. an unanalysable wholeness of form, a notion which from the decline of Aristotelian physics in the times of Galileo and Newton to the rise of field theory with Faraday and Maxwell had no place in physical thought". This paper aims at exploring the consequences of this suggestion of Jammer by reinterpreting the concept of 'elementary quantum phenomenon' in explicitely Aristotelian terms. Aristotle's approach to nature was a very direct and phenomenological one(8); his view of nature was not yet impregnated by the tendency towards mathematical abstraction and reification of the concept of 'absolute object' that characterizes classical physics. For instance, the classical practice of assigning, for every single time point, both an exact position and an exact velocity to a particle, was considered by Aristotle as physically and conceptually erroneous; and quantum mechanics corroborates the Aristotelian point of view on this issue(8). It thus seems natural to reconsider the conceptual framework of quantum mechanics in the light of the Aristotelian conceptual framework. As Wolfgang Pauli once wrote: "Contemporary science has reached the point where the path unraveled by Aristotle (albeit in a rather unclear way) can be followed further on"(9) (author's translation).


2. The four causes and the elementary quantum phenomenon: an overview.

Let us consider the archetypical example of an 'elementary quantum phenomenon' illustrated in figure 1 4. The phenomenon is well known and extremely simple: some time after the temporal opening of the shutter, a registration dot appears on the photographic film. Following Aristotle, four different types of 'causes' (in the sense of 'constituting aspects of phenomenal reality'), each irreplaceable and each ontologically irreducible to the others, are required for any phenomenon to take place.


Figure 1:The experiment of Young, with a single photon (adapted from Bohr 1949; see note 4). a: start configuration: a screen with a shutter, that plays the role of light source (left), an interference screen with a double slit (middle) and a photographic plate (right). b-c: the shutter is opened and closed. d: shutter is closed, nothing happened yet on the photographic plate. Note that, from a sensorial viewpoint, d and a are identical. e: a dot appears at a certain point of the photographic plate. f: when the experiment is repeated a great number of times, the hits collected on the photographic plate outline an interference pattern.


To take a start, let us summarize what is really given as observable or sensorial reality in the phenomenon: the geometry of the apparatus, the fact that the shutter has been opened during a certain time interval and the fact that a dot has appeared at a certain spot on the film shortly after this opening of the shutter. All this is measurable reality.

Not given is the path of any hypothetical light particle or any wave train that could be thought to have moved from the opened shutter towards the blackened spot on the film. Neither given is any actual atomistic fine-structure of the experimental apparatus.

When the experiment illustrated in figure 1 is repeated may times over (under identical conditions), the black dots are seen to appear on different places of the film (figure 1f). Taken together, these dots gradually start to outline an interference pattern. So there are no factual grounds for accepting a deterministic relationship between the opening of the shutter and the position of the corresponding dot- the place where any particular dot is going to appear. Nevertheless, the distribution of the dots over the film is not completely random; some spots are more likely to get dotted, and the overall pattern on the film takes the form of an interference pattern. Given the macroscopic boundary conditions, quantum mechanics allows the establishment of a wave function permitting to deduce, for every surface element of the film, the probability for a hit to occur.

Now these probabilities are certainly part of physical reality, although they have no sensorial reality. Their values allow us to make predictions about the outcome of experiments. Were the probabilities not to have physical reality in some sense, quantum mechanical theory - that allows the calculation of the probabilities - would not be a physical theory at all. Consider the situation of the apparatus before and immediately after the opening of the shutter (figure 1, a and d). Both situations are totally indistinghuisable in the sensorial sense (within the context of the phenomenon under consideration). Nevertheless, the apparatus has been supplemented, after the temporal opening of the shutter, with the potentiality to produce a dot on the film. This potentiality was not present before the opening of the shutter. Thus quantum mechanics leads us to accept the existence of something that has no sensorial reality, but that turns out to be real and objective nevertheless: the potentiality of the system to bring about a certain effect (for instance the production of a dot on the film). This potentiality consists of an array of possible outcomes, each with its own corresponding probability. Quantum mechanics permit us to calculate these possibilities and probabilities.

Now from the purely sensorial point of view there exists an absolute ontological equivalence between these different possibilities: they are all equally non-sensorial. From the point of view of the probabilities themselves, another equivalence relationship exists: the different possibilities are all possible in the same way, and none of them is carrier of the necessity of its own actualization into sensorial reality - otherwise the probabilities would not be probabilities after all. So we have to face two further questions:

1) what selects one of the possible outcomes for actualization?

2) what projects that selected possibility int actual reality?

John Wheeler 10 comments: "In the individual quantum process, prediction comes to the end of the road. Science does not have to be ashamed of its finding. It has only to be honest about it. Why demand of science a cause when cause there is none?" If we keep to the facts of nature, there is indeed no room for any type of 'cause' describable by physical law; otherwise the probabilities given by the wave function would be fake probabilities. Nevertheless, there has to be some factor breaking the ontological equivalence between the different possible outcomes by actualizing one of them. The important point is that this factor is in principle not describable by the quantitative and analytical means of physical theory (although physical theory has to circumscribe the domain wherein these irrational factors are playing their role). Laurikainen(11) has summarized the views of Wolfgang Pauli on this point as follows:

"The scientific world view is very often defined such that it accepts only rational matters (...) Pauli, instead, focused particular attention on the irrationality of individual events, implied by statistical causality. He felt that a component of reality - the irrationality of reality - appeared in it, which must be taken into consideration when causality is conceived as statistical. According to Pauli, this is an essential new characteristic of the picture of the world".

Beyond the classical level of macroscopic data, we came (on conceptual grounds) to distintinguish three further levels of reality: the realm of the potentialities, the realm of the irrational factor that decides which possibility will become real and the realm of the factor projecting that selected possibility into physical reality. The first level is 'physical' in the sense that it remains accessible for quantitative (albeit statistical) description. The second level is 'non-physical' in the sense that it cannot in principle be explored by the method of physics. We can only infer the existence of this level of irrational reality because the very existence of objective possibilities or potentialities calls for the contribution from a factor that remains at the outside of the realm of objective potentialities (because it has to make a 'choice' between these potentialities) and that remains at the same time unassailable by the methods of rational physics (because otherwise the probabilities would not truely be probabilities). Finally, there has to be a third level of reality that effectively projects that selected possibility into actual existence. The outcome of this projection is of course sensorial; but it is non-physical in the sense that it cannot be accounted for by the methods and the formalism of physical theory.

Note that the selecting factor cannot be identified with the projecting factor. The very concept of one possibility being projected into actual existence already presupposes the breakdown of the ontological equivalence between the possibilities.

Now we can look with fresh eyes at the phenomenon illustrated in figure 1. We can discern four realms of reality, irreducible to each other, that together constitute the phenomenon:

A. Firstly, there is the 'form' or 'formal configuration' of the phenomenon, that for our purposes can be defined as the totality of measurable realities that are relevant for the phenomenon under consideration. 'Measurable' we can further circumscribe as: 'susceptible to some interaction with the environment, whilst the phenomenon is taking place, without altering the nature of the phenomenon'. A 'reality relevant for the phenomenon' we can specify as 'an aspect of the phenomenon that one has to know as a boundary condition to be able to apply quantum mechanics to the phenomenon'. For instance, in the phenomenon of figure 1 the whole geometrical constellation of the experimental setup, the opening time of the shutter, are part of the form of the phenomenon. A phenomenon without some formal configuration is unthinkable; we will call the form involved in any specific phenomenon the 'formal cause' (FOC)(12) of that phenomenon (the original Aristotelian concept is broader, and includes also purely qualitative aspects of reality not considered in quantitative physics, but for applications in quantitative physical theory the definition above will suffice). The FOC corresponds to the 'apparatus' in the Copenhagen interpretation of quantum mechanics.

B. With the FOC the boundary conditions allowing the setup of the quantum mechanical calculations are given. For instance, in step d of the archetypical example given in figure 1 the probabilities for the appearance of a black dot on the different points of the film are created and are calculable. This realm of objective possibilities or potentialities is another irreducible aspect of the phenomenon. Heisenberg repeatedly suggested a correspondence between the probability concept of quantum mechanics and the Aristotelian concept of 'materia' or 'potentia' (13). We follow his proposal by identifying the potentiality for change with the Aristotelian 'material cause' (MAC). In quantum phenomena, the MAC can be calculated from the wave function.

C. As already said, another realm of reality beyond the level of mere objective possibilities has to exist, although physics cannot - by the very nature of its methods based on rationality - go beyond the conclusion that such a realm has to exist on logical grounds.

This factor, that somehow selects one among the many possible changes for actualization, we call the 'final cause' (FIC). According to Pauli, the history of modern science has, until the appearance of quantum mechanics, been a history of progress at the expense of the irrational side of reality hiding in this realm of FIC. The FIC is intrinsically creative; its role cannot be explained from the past; it belongs, as long as the phenomenon has not taken place, entirely to the future - there is thus no question of determinism. The very concept of a set of probabilities is irrevocably linked to the concept of a creative and completely unpredictable factor, that selects one of the possible outcomes for actual existence. It is the contribution of this factor that gives the phenomenon its individual stamp.

Pauli saw the irrational factor implied by the probability concept as a manifestation of the will-side of nature; hence his interest in the philosophy of Schopenhauer. This association between the FIC and will has a deep significance. As C.F.von Weiszäcker (14, p.81-84) remarks, Einstein was troubled by the fact that the Now doesn't occur in physics. Classical physics offer a picture of reality that describes possible successions of events along a mathematized time axis; but it doesn't explain why something is happening right now. In classical physics, the Now has no special status with respect to other time points; but it has a special status in physical reality. The concept of the Now is not contained in the laws of physics. Rather, the conscience of the reality of the Now is a prerequisite for these laws making sense at all; science can describe a state of affairs and give probabilities, but that already presupposes the awareness of the Now: "Science describes facts and possibilities; the Now is presupposed implicitely. Scientific laws claim perpetual validness; they don't mention the Now wherein they are formulated"14(author's translation).

D. We are aware of the relevance of the Now and of some physical state of affairs really being the case, not through thinking or logical analysis, but through our voluntary confrontation with the particular concreteness of natural reality. Rational physics or rational thought are unable to refute the ideas that nothing really exists (solipsism) or that the past, present and future states of affairs have the same ontological status (15).

Will is resisted by will. Therefore we can consider as 'natural will' the aspect of natural reality that is able to resist our own human will. It is the particular reality existing in the Now that offers such a resistance; and this tangible reality is brought about not by the mere potentialities deducable from the wave function, not even by the realm of the FIC where certain potentialities are selected for projection into physical existence, but by the factor that does the projection. This factor we will call with Aristotle the effective cause (EFC) of the phenomenon; its contribution completes the phenomenon at hand.

Phenomena are interconnected through the EFC of the preceding phenomenon shaping the FOC of the subsequent phenomenon. Every physical phenomenon is induced by the tangible outcome of a preceding phenomenon, that shapes the FOC of the phenomenon under consideration. As an example, consider the phenomenon illustrated in figure 1. It is initiated by the displaced of the shutter. This displacement as such is part of the FOC, and has to be known in sufficient detail if one wants to calculate the probability of a certain spot of the film getting blackened. But the whole FOC is translatable through time; such a translation does not change the calculations in any way whatsoever. There is nothing in the FOC telling us that it is part of reality at a given moment; physical calculations don't permit to deduce when the phenomenon is going to take place in reality. Nevertheless, the precise time-location of the displacement of the shutter is also part of the phenomenon; it results from the action of the EFC of a preceding phenomenon. For instance, in the elementary phenomenon illustrated in figure 1 the displacement of the shutter could have been induced by some phenomenon involving a device that acts when the desintegration of an unstable nucleus is registrated (as in the contraption menancing Schrödingers cat).

We thus arrive at the scheme given in figure 2. We can think of the phenomenon as starting with the EFC of a foregoing phenomenon projecting the FOC into effective reality; thereby the evolving pattern of objective possibilities for further change (the MAC that is decribed by the time-dependent Schrödinger equation) is started up. The FIC selecting one possible change, and the EFC-induced projection of that selected outcome into actual existence complete the phenomenon (in our example: the real appearance of the dot at some unforseeable place on the film). Thereafter, the outcome can act as the FOC for yet another phenomenon.


Figure 2: the four Aristotelian causes and the elementary quantum phenomenon (phenomenon of type I). The formal cause (FOC; the 'apparatus' in the Copenhagen terminology) and the material cause (MAC; the potentialities described by the state function) constitute together the realm of reality describable by physics (= Aristotelian 'substance'). The final cause (FIC; the factor selecting one of the potentialities for actualization) and the effective cause (EFC; the factor projecting the already selected potentiality into actuality) constitute together the non-rationalizable will-side of the phenomenon. The realm of the formal cause and the effective cause constitute the sensorial aspect of the phenomenon: they build up the tangible, macroscopic aspect of the phenomenon. The realm of the material cause and the final cause constitute the non-sensorial and 'potential' side of the phenomenon. The arrows indicate logical precedence: the material cause (potentialities) is fixed only when the the formal cause is known (as is shown in 'delayed choice experiments'); the final cause cannot but select among potentialitites that are already given; the effective cause projects into reality a potentiality already selected by the final cause.


Physics concern the FOC and the MAC, but do not cover the will-side of nature that determinates (within the limits posed by physical laws) what happens in reality. When start conditions are given, physics can describe the possible outcomes and the corresponding probabilities. But the start conditions cannot be calculated; they are brought about by the EFC of some foregoing phenomenon. Neither can physics predict the real outcome of an individual phenomenon; that outcome is brought about by the FIC, within the boundaries describable by physics. Physics is unable to account for the whole of a phenomenon. As Pauli remarked in a letter to Jung(16 ; Pauli's letter of 27.May 1953): "I said to Bohr that Einstein mistook the incompleteness of physics with respect to real life for an incompleteness of quantum mechanics with respect to physics. Bohr immediately accepted this formulation".


3. The irreducibility of form and the problem of measurement

When taken at face value, quantum mechanics unequivocally claims the so-called 'classical' objects being irreducible to any wave function. It does so by the very structure of its formalism: the formal characteristics of the phenomenon have to be known a priori to allow any calculation of a wave function. The latter then gives the possible further changes (with their respective probabilities) that this form can undergo; it thus describes the MAC of the phenomenon at hand. For instance "..molecular structure makes no appearance in a quantum theory from first principles"(17). Molecular structure has to be added to the ab initio quantum treatment, for instance by adopting the Born-Oppenheimer approximation (whereby the positions of the nuclei are pinned down). A treatment from first principles cannot make any distinction between an isolated molecule of cyclopropane and an isolated molecule of propene; such a differentiation becomes possible only when the molecule is allowed to interact with an external form that enters the calculation of the wave function as some boundary condition. The same considerations of course apply when systems (such as a measuring apparatus) much larger than molecules are considered. For instance, one cannot infer the enantiomorphic specificity (+ or -) of a crystal of tartaric acid from the analysis of any of its constitutent molecules taken in isolation. On the contrary, this molecule - if it is to get some specific form at all- has to interact with its crystallographic environment; it has to be part of some irreducible (call it 'macroscopic') form. Thus the molecule receives its form from the macroscopic body wherein it is incorporated - it cannot be thought of as an isolable 'building block' in the classical sense. On the other hand, the quantum mechanical wave function really puts limits on the array of macroscopic forms and symmetries that can appear at all. Neither macroscopic form nor quantum mechanical potentiality are reducible to each other, and neither can make up tangible reality without the other; their unison alone allows substance to appear. If the quantum treatment is to be related to some specific phenomenon, it is impossible to exorcise this necessity for some form to get introduced ab initio.

The explicit acceptance of macroscopic form as an irreducible aspect of physical reality is the cornerstone of the Copenhagen interpretation of quantum mechanics. The false impression of the Copenhagen interpretation representing an idealistic or positivistic view results from attempts to formulate its theses whitin a classical conceptual framework. It is not realism, but the classical idea of every macroscopic object being a mere cluster of actually existing 'quantal' particles that is rejected.

The controversy around the so-called 'measurement problem' is at the core of the differences. The interaction of a measuring apparatus (when treated as a 'quantum object') with some microscopic 'quantum system' leads to a global wave function that does not guarantee both the instrument and the 'system' being separately in a definite state - a result that seems at variance with observation and that is solved, in the Copenhagen interpretation, by the flat refusal to consider the measuring apparatus as a 'quantum object'. The Copenhagen interpretation clearly reveals its Aristotelian core at this point, because it accepts the macroscopic form (the 'classical object' or 'measuring apparatus') as a basic constituent of reality resisting any further reduction to some underlying atomistic or quantal structure; a viewpoint that is completely in agreement with phenomenological reality, although not with certain brands of materialistic metaphysics. For the latter reason, this aspect of Bohrian thought thus is often considered as puzzling or problematic. For instance, Murdoch (18,p.114) writes: "Bohr (...) cuts the measurement problem off at its roots: it prohibits from the outset the sort of theoretical treatment of the process of measurement that leads to the problem. It is for this reason that nowhere in his writings does Bohr give a formal account of the process of measurement. The Bohrian solution is brilliantly simple; but it gives rise to an acute puzzle of its own, for how is it that the pointer of a macroscopic instrument may display a definite position, say, when the instrument is described in classical physical terms (when we look at it), yet have no definite position when we treat it as a quantum-mechanical object (foregoing inspection of it). A satisfactory solution of this puzzle is required if Bohr's theory is to be succesful". As a matter of fact, this puzzle is solved immediately if only we remain consequently true to the Aristotelian (and Bohrian) point of view. The atomistic features eventually appearing during a 'foregoing inspection' of the measuring apparatus were part of actual existence only whithin the context of the phenomena concerned with that inspection; we cannot transpose them to another phenomenon with another FOC showing up other types of change (this point is further developed in the next section). The puzzle only arises because thinking relapses into the classical mode of thought, with absolute objects and not elementary phenomena being taken as the basic constituents of objective reality.


4.Substance

In the neo-Aristotelian view presented here, the FOC together with the MAC constitute what one can call the 'substance' involved in the phenomenon under consideration. Substance is the aspect of reality describable by rational physics in the broadest sense; it has a sensorial (or formal) side and a non-sensorial (material) side. Neither side is reducible to the other but a close alliance exists: as soon as the FOC is known the start configuration of the MAC is fixed. Within the context of a given phenomenon a clearly circumscribed domain of substance is involved. However, after the phenomenon has taken place (i.e. after some potentiality lurking in that substance has been selected and projected into actuality, whereby that substance has undergone some formal change) the altered substance has to be considered in connection with the whole of substance in the universe to look for the new potentialities that were created. As a rule, the result of the action of the EFC will appear to be part of the FOC of a consecutive phenomenon encompassing another subdivision of substance. The laws of physics permit to see which domain of substance will be involved in the new phenomenon. As an example, consider the experiment in figure 1. We suppose that a device opens the shutter when the desintegration of a nucleus is registrated. This first phenomenon involves the desintegrating nucleus, the registering device and the shutter as formal substance. When the shutter has been displaced, a new circumscription of formal substance involving the apparatus of figure 1 will be part of the new phenomenon, that ends when a registration has taken place on the film. Every domain of substance exists only through the phenomena in which it is involved, but it transcends every individual phenomenon because of this embedment in the whole of substance.

Aristotle developed the concept of substance at least in part to defeat the arguments of Parmenides and Zeno, and recent developments in quantum mechanics have shown his reasoning on this point to be sensible to the highest degree. The arguments invoked by the Eleates against the reality of change and movement are correct in a world of classical objects that are sharply locatable in absolute space-time. In the classical view, the past and the future don't exist in a physical sense; everything that exists is embedded in the Now and occupies a sharply defined position in space. No room is then left for any physical trace of velocity to exist in this Now. By assigning the position of Zeno's arrow to a well-defined spot "..all relics of its velocity have been banished" (19). One cannot circumvent this point by arguing that it is possible to assign, as a purely mathematical construct, a velocity vector to every point mass in space. The gist of Zeno's argument is that no physically measurable aspect of reality can correspond with this mathematical vector within the Now (that is thought to be the sole realm of physical reality).

The problem has even been sharpened by Cantor's discovery of the non-denumerability of the set of real numbers (or, equivalently, of the set of points on a line interval). An object that actually travels along a line interval, with subsequent presence in all the points on that interval, could be considered as a machine denumerating the real numbers (the act of counting being represented by the actual presence in the point corresponding to the number), which is logically precluded.

Therefore, the classical concept of an object successively occupying all the points on a trajectory is logically absurd, in the same sense wherein the concept of a square circle is logically absurd. Just as 'being square' is incompatible with the very concept of circle, the concept of 'actual presence in a spatial point at a given time' is incompatible with the concept of 'having a well-defined velocity at that same time'. Moreover, the classical interpretation of velocity is also at variance with phenomenological reality: it would require an infinite amount of time and energy to observe the supposed presence of an object in an infinite number of points. Theories such as classical physics, or the Bohmian interpretation of quantum mechanics, are thus flawed at the bottom. They introduce into the theory a 'reality' for which there is no evidence (the actual presence of an object or particle in an infinite number of spatial points during a finite lapse of time), and they cover this supposed reality with a concept that is logically inconsistent (the object or particle having an exact position and a well-defined velocity at the same time).


5. Irreproducibility and life phenomena.

Bohr, Heisenberg and Pauli rejected the idea that life phenomena can be reduced to physics and chemistry (20). In this section, we will show that their opinion is a logical correlate of the Copenhagen interpretation.

Physical sciences deal with reproducible phenomena, because the very concept of physical law implies reproducibility. When a phenomenon is not reproducible, physical laws cannot be applied to it. A phenomenon is reproducible when the FOC of the phenomenon can be reproduced to the degree of precision that permits doing predictions. For instance, in the double slit experiment (figure 1), we do not need to know the geometry of the apparatus, or the opening time of the shutter, with infinite precision. We need to know these data to a sufficient degree of precision, that permits application of quantum mechanics to the phenomenon. The laws of physics permit us to decide whether a sufficient degree of precision is reached.

Reproducibility thus implies a certain robustness of the apparatus (FOC in Aristotelian terms). We have to know a number of spatial and temporal parameters of the apparatus, and this implies a certain interaction with the apparatus. The consequences of these interactions are uncontrollable in principle, for the usual quantum reasons. The apparatus is robust when incontrollable changes on the apparatus, that occur of necessity when we are measuring its parameters, remain negligibly small with respect to the degree of precision that is needed to make predictions.

Obviously, there is nothing that guarantees this robustness in all cases. Amplification mechanisms could be part of the apparatus, that would prevent us to remain in control of the parameters that we want to observe. Crucially, we would also be unable to know to what extend the suspected parameters change or remain stable. Under such circumstances, no meaningful separation can be made between the FOC (apparatus) and the MAC (part of substance describable by the wave function), and quantum mechanics cannot be applied to the phenomenon.

As an example, "..we can consider the case of a photon that traverses a chaotic turbulence in a refractively inhomogeneous fluid and thereafter becomes registered on a photographic film (the path length of the photon can be lengthened at will by the use of mirrors). To calculate the wave function that gives the probability pattern for the photographic registration, we have to know the comportment of the turbulence whilst the photon is moving through. The turbulence is chaotic; any tentative to observe its fine structure to a degree of precision permitting to predict its behaviour whilst the photon goes through, will induce (for the usual quantum reasons) an incontrollable change that is amplified to the point of significantly altering the probability distribution to be calculated. The latter is therefore uncalculable in principle. Moreover, the phenomenon is irreproducible in principle, because we are unable in principle to prepare two identical turbulences (again for the usual quantum reasons)" (21). It is quite surprising that the uncontrollable nature of the quantal interaction thus puts a limit to the class of phenomena describable by quantum mechanics.

Reproducible phenomena we will call phenomena of type I. Statistical predictions make sense here, because the phenomenon under consideration can be seen as a member of some well-defined statistical ensemble.

The counterexample of a photon moving through a turbulence is an instance of a type II phenomenon. In phenomena of type II, the apparatus is not robust; no setup is possible, that is sufficiently precise to permit the application of quantum mechanics. For this class of phenomena, we cannot make a sharp distinction between the FOC and the MAC. A phenomenon of type II is unique, in the sense that it can never be equalized with certainty with any other phenomenon.

Phenomena of type III

Phenomena of type I and type II have one important element in common. Although part of the apparatus (in our example: the turbulence) is chaotic in phenomena of type II, another part is not. We still know when we opened the shutter, and when and where the registration on the photographic film took place. Both phenomena of type I and type II are thus individualizable. Consider the building up of an interference pattern in a double slit experiment. This overall process can be analyzed into a set of individual elementary phenomena, each of these contributing one hit to the pattern. The possibility to individualize the elementary quantum phenomenon still holds when the light path traverses a turbulence: the overall process can be separated into a sequence of elementary phenomena.

This possibility to individualize the elementary quantum phenomenon has a very precise origin: even in phenomena of type II, the initation (opening of the shutter) and the termination (appearance of a dot on the film) are located on the robust part of the apparatus, that can be separated from the chaotic part (the turbulence).

But again, this separatibility of the robust part and the chaotic part of the apparatus is not guaranteed in all cases. Consider a typical living organism. This organism contains macroscopic parts, that are certainly robust. Closer examination learns, that these robust parts show ramifications into finer and finer levels, down to the molecular realm, where we still meet a lot of structures (such as DNA) that can be largely understood in classical terms. Intermingled with these structures, down to the level where quantal interaction plays a significant role, and without meeting any well-defined separation between both realms, we find fluid chaos. In a life process, such as growth for instance, the equivalent of some single registration on the photographic plate would be some single change taking place at an hypothetical, well-defined and robust structure, that should exist somewhere at the molecular level. However, no such robust structure can be identified in these cases. In the exemplary phenomenon of type II discussed before, we can observe the appearance of the dot on the photographic plate without taking into account our interaction with the photographic plate, that is needed in order to observe the position of the dot. This is possible because the photographic plate is 'robust': our observing this plate does not alter the plate in any relevant way. In a quantal phenomenon supposed to take place at the molecular level in some organism, this robustness is not garantueed, and most probably it will not be present in a large number of cases. Hence, it is no longer certain that we can observe the occurrence of this change without substantially altering the conditions for further change.

Therefore,it is not guaranteed that the overall process of growth is decomposable, in any real sense, into separate quantal phenomena (as is still the case for the phenomenon of type II).

In such a case, we can observe only a macroscopic process through time. We can observe a finite number of intermediate phases in a plant growing up. But we cannot decompose this overall process into an hypothetical network of individual quantum phenomena supposed to constitute the growth process. The decomposition of the growth process into individual quantal phenomena becomes just as meaningless as the decomposition of the individual quantum process into a series of intermediate stages. If we want to shape our concepts in accord with reality, we have to introduce here the concept of process as an elementary datum.

Elementary quantum phenomena introduce an essentially discontinuous element in nature. They cannot be decomposed into smaller events without altering the phenomenon under consideration. In phenomena of type III (i.e. in processes), the inverse takes place. We cannot reach the level where quantal discontinuity becomes obvious without altering the overall process under consideration. Phenomena of type III are essentially macroscopic, in the sense that the hypothetical level, where quantal discontinuity plays a role, cannot be reached without destroying the phenomenon of type III that we are studying. And in the very special sense, that the supposed quantal discontinuities are no longer given in phenomena of type III, can we say that these phenomena are 'continuous'.


Randomness, qualitativeness and directionality

The concept of randomness implies quantitative probabilities. Consider for instance a series of randomly chosen digits. This randomness implies that every digit has an equal probability of 0.1 of being found at any position in this series.

These quantitative probabilities correspond to an observable aspect of nature, when reproducible phenomena are involved. But phenomena of type II are not reproducible, and the concept of a quantitative probability makes no sense. Hence, the outcome of a unique phenomenon cannot be random in the usual, quantitative sense. Neither does it make sense to say that such a phenomenon is deterministic. Determinism implies that some 'law' connecting cause and effect is involved, but the concept of 'law' already implies reproducibility.

Therefore, we coin the concept of 'qualitativeness' to replace the concept of 'randomness' or 'law' in irreproducible phenomena ('qualitative' is meant here, as the complemental concept to 'quantitative'). The outcome of an irreproducible phenomenon (phenomenon of type II) is an expression of the qualitativeness governing this phenomenon, in the same way as the outcome of a phenomenon of type I is an expression of the quantifiable probability distribution, as expressed by the wave function.

Note that this qualitativeness is limited to the phenomenon under consideration. There is no reason to suppose that a set of isolable phenomena of type II will share an overarching qualitativeness.

The outcome of a phenomenon of type II is still a discrete, abrupt datum, that has no continuity through time (in our example, the dot on the screen appears at one given moment). However, in phenomena of type III, the outcome of the global process cannot be projected into one time point. The conclusion about qualitativeness replacing randomness also obtains for phenomena of type III, because these phenomena are also unique in principle. But whereas the outcomes of phenomena of type II show no extension in time, the outcomes of phenomena of type III do so. The qualitativeness characterizing these phenomena is thus of a new type: there is a qualitative unity through time in the outcome of these phenomena.

As far as a phenomenon of type III constitutes an unanalyzable unity, the qualitativeness of such a phenomenon must also constitute a unity through time. It is in this sense that the qualitativeness that characterizes phenomena of type II, transforms in directionality , that is characteristic of phenomena of type III. Bohr(20) considered directionality in life phenomena as a datum that stands in a complementary relationship to unambiguous describability down to the quantum level.

Directionality does not mean that some 'goal' in the usual (anthropomorphic) sense is strived at. It means that in phenomena of type III, the equivalent of qualitativeness shows unity through time, and cannot be decomposed into a set of unrelated time-point outcomes.

Of course, the analysis presented here does not prove that phenomena of type III operate in living organisms. But is shows that the logical possibility for phenomena of type III exists. Moreover, some pondering on the circumstances wherein phenomena take place, say, in the protoplasma of a nervous cell, suggest that the occurrence of phenomena of type III is very probable. How could we ever observe an individual quantum interaction in this protoplasma, without basically altering the condition wherein that very phenomenon is taking place? How could there be the robust equivalent of a shutter or a phototgraphic plate in this realm? Arguments that rely on the hypothetical possibility of copying living organisms or structures play a key role in the actual consciousness debate(22). If the opinion of Bohr(20), Heisenberg or Pauli would turn out to prevail, all these arguments would become wanting.


References and remarks

1. A.Einstein; B.Podolsky; N.Rosen (1935) "Can quantum-mechanical description of physical reality be considered complete?" Physical Review 47, pp.777-780. Also contained in ref.3.

2.N.Bohr (1935) "Can quantum-mechanical description of physical reality be considered complete?" Physical Review 48, pp.696-702. Also contained in ref.3.

3.J.A.Wheeler; W.H.Zurek (1983) "Quantum theory and measurement" Princeton Series in Physics

4. N.Bohr (1949) "Discussions with Einstein on epistemological problems in atomic physics" pp.200-241 in: P.A.Schilpp (editor) "Albert Einstein: philosopher-scientist" The Library of Living Philosophers. Also contained in ref.3.

5. N.Bohr (1958) "Atomic physics and human knowledge" Wiley, New York.

An interesting summary of the opposing views (Einstein versus Copenhagen school) can also be found in the letters from Pauli to Born, contained in: "Albert Einstein. Hedwig und Max Born. Briefwechsel 1916-1955" Rowohlt 1972. The elder Einstein objects against the Copenhagen interpretation not because he sticks to a deterministic world view, but because he rejects the Bohrian concept of 'elementary phenomenon'. Wolfgang Pauli was a strong defender of the Bohrian concept of elementary phenomenon (see for instance: W.Pauli "Die Idee der Komplementarität" Dialectica 2, pp.312-319 / 1948).

6. H.J.Folse (1985) "The philosophy of Niels Bohr. The framework of complementarity" North-Holland

7.M.Jammer (1974) "The philosophy of quantum mechanics. The interpretations of quantum mechanics in historical perspective" John Wiley & Sons

8. C.F. von Weizsäcker (1974) "Möglichkeit und Bewegung. Eine Notiz zur aristotelischen Physik" pp.428-440 in: "Die Einheit der Natur.Studien" DTV

9. W.Pauli. Letter to Jung dated 27.February 1953. In C.A.Meier (editor) "Wolfgang Pauli und C.G.Jung. Ein Briefwechsel 1934-1958" Springer Verlag (1992)

10. J.A.Wheeler (1983) "Law without law" p.182-213 in ref.3

11. K.V.Laurikainen (1988) "Beyond the Atom. The philosophical thought of Wolfgang Pauli" Springer Verlag

12. From here on, we will indicate the four Aristotelian causes also by the following acronyms: FOC = formal cause; MAC = material cause; FIC = final cause; EFC = effective cause.

13. W.Heisenberg (1959) "Die Plancksche Entdeckung und die philosphischen Probleme der Atomphysik" Universitas 14, pp.135-148. I t has been tried again and again to circumvent this conclusion by the Copenhagen school, that a quantum phenomenon cannot be described exhaustively by a state function, but that the presence of a 'classical object' or 'measuring apparatus' is a prerequisite for this state function having physical meaning at all. At this time, the most popular proposition is probably the 'decoherence solution' by Zurek, that, however, fails to solve the problem (for a short exposition, see: Albert,D.Z., and Feinberg, G. (letter) Physics Today, April 1993, p.81; for a longer exposition, see Bell,J. (1990) Physics World 3, 33-40).

14. C.F. von Weizsäcker "Zeit und Wissen" Carl Hanser Verlag 1992.

15. "We stood talking for some time together of Bishop Berkeley's ingenious sophistry to prove the non-existence of matter, and that everything in the universe is merely ideal (composed of ideas). I observed, that though we are satisfied his doctrine is not true, it is impossible to refute it. I shall never forget the alacrity with which Johnson answered, striking his foot with mighty force against a large stone, till he rebounded from it, 'I refute it thus' ". James Boswell, the biographer of Dr.Samuel Johnson, quoted in H.C.von Baeyer "Taming the atom. The emergence of the visible microworld" Random House 1992. See also: Patey,D.L.(1986) "Johnson's refutation of Berkeley: kicking the stone again" Journal for the History of Ideas, 139-145. Other instances of the same thought can be found in the works of G.K.Chesterton (see: M.Gardner "The why's of a philospohical scrivener" Oxford U.P. 1985, p.30-31).

16. Meier C.A. (editor) (1992) "Wolfgang Pauli und C.G.Jung. Ein Briefwechsel 1934-1958" Berlin: Springer Verlag

This viewpoint of the Copenhagen School has often been misunderstood in a subjective sense. For instance, the quotation of Bohr by Peetersen ("There is no quantum world. There is only an abstract quantum physical description. It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature ". See: A.Petersen (1985)"The philosophy of Niels Bohr" 299-310 in: A.P.French and P.J.Kennedy (editors) "Niels Bohr. A centenary volume" Cambridge (Ma):Harvard University Press.Appeared originally in: Bulletin of the Atomic Scientists(1963) 19, 8-14.) should be understood in the sense indicated by Pauli's letter. Bohr was an utter realist; it was self-evident to him that physical reality exists out there, independent of our observing it. However, this reality cannot be grasped with the concepts of classical physics. Firstly, "there is no quantum world" , in the sense that the wave function describes objective potentialities, not actual objects. Secondly, there is a realm of reality (in Aristotelian terms: the FIC and the EFC) that, although it is completely objective, cannot be described with physical methods. "Physics concerns what we can say about nature", that is, about the FOC and the MAC.

A striking example of such a misunderstanding can be found in the Introduction, by Paul Davies, to the Penguin edition of Heisenbergs "Physics and Philosophy". Davies quotes Heisenbergs summary of the Copenhagen view: "In the experiments about atomic events we have to do with things and facts, with phenomena that are just as real as any phenomena in daily life. But the atoms or the elementary particles themselves are not as real; they form a world of potentialities or possibilities rather than one of things or facts", and comments: "The denial of the objective reality of the external world implied by the Copenhagen interpretation is often couched in more cautious terms, but Heisenberg here provides some of the bluntest affirmations of this position that I have seen". Apparently, this misunderstanding comes into being because the term 'phenomenon' is interpreted in a subjective sense. Bohr, Heisenberg and Pauli used this term in the sense of an objective happening, that however is not analysable into a sequence of classical timepoint-events.

17. Woolley,R.G. (1978) "Must a molecule have a shape?" Journal of the American Chemical Society 100, 1073-1078

18. Murdoch,D.(1989) "Niels Bohr's philosophy of physics" Cambridge: Cambridge University Press

19. Landsberg,P.T. (1988) "Why quantum mechanics?" Foundations of Physics 18, 969-981. For quantum mechanics and Zeno, see for instance: Misra, B., and Sudarshan, E.C.G. (1977) "The Zeno's paradox in quantum theory" Journal of Mathematical Physics 18, 756-763; Singh,I., and Whitaker, M.A.B. (1982) "Role of the observer in quantum mechanics and the Zeno paradox" American Journal of Physics 50, 882-887; Itano,W.M., Heinzen,D.J., Bollinger, J.J., and Wineland, D.J. (1990) "Quantum Zeno effect" Physical Review A, 41, 2295-2300.

20. See for instance: Bohr,N. (1933) "Light and Life" Nature 131, pp.421-423 and 457-459; N.Bohr (1952) "Medical Research and Natural Philosophy" Acta Medica Scandinavica 142, pp.967-972; N.Bohr (1958) "Atomic Physics and Human Knowledge" New York: Wiley; Enz, C.P. (1986) "Bohr, Delbrück, Pauli and Biology" Ann.Acad.Sc.Fenn. Series A,VI Physica, pp.23-32; Heisenberg, W. (1962) "Physics and Philosophy" New York: Harper & Row Publ.

For comments, see also: Folse (note 6); Hoyningen-Huene, P. (1994) "Niels Bohrs argument for the irreducibility of biology to physics" Boston Studies in the Philosophy of Science 153, pp.231-256; Verhulst, J. (1994) "Der Glanz von Kopenhagen" Stuttgart: Verlag Freies Geistesleben.

21. Verhulst J. (1994) "Speech and the retardation of the human mandible: a Bolkian view" Journal of Social and Evolutionary Systems 17, pp.307-337

22. Some examples of philosophical arguments that presuppose the possibility of unambiguous copying of living systems are found in: Chalmers,D.J. (1995a) "The puzzle of conscious experience" Scientific American 273(6), 62-68; Chalmers (1995b) "Facing up the problem of consciousness" Journal of Consciousness Studies 2, 200-219; Dennett,D. (1991) "Consciousness explained" Boston: Little,Brown & Co; Gardner,M. (1985) "The why's of a philosophical scrivener" (see especially p.311), Oxford: Oxford University Press; Unger,P.(1990) "Identity, Consciousness & Value" Oxford: Oxford University Press.

23: As far as I know, the first to possess this concept of the particular nature of living substance was von Goethe. He considered 'liquid substance' (das Flüssige) as "..the proper element of organic formation". However, 'solid substance' ('das Erstarrte') was needed to produce an individualized living being. Therefore, a living being has to take part in both aspects of substance: "The intermediate between liquid and solid substance is soft substance ('das Weiche'), where separate rigid atomistic structrues are completely penetrated by fluidity. Here lies the key for the proper understanding of life pheno mena in soft substance (...) Soft substance is a necessary attribute of every living being".See: von Goethe,J.W. (1989) "Sämtliche Werke nach Epochen seines Schaffens" Band 12,p.337 (editors: Becker,H.J., Müller,H., and Neubauer,J.) München:C.Hansen Verlag. The title of this short treatise by Goethe is:"Grundzüge allgemeiner Naturbetrachtung. Einleitung zu dem noch ungedruckten Werke über die Ur-Teile des Schalen- und Knochengerüstes von D.C.G.Carus" , and it is incorporated in his bundle: "Zur Morphologie II,2".

Bohr(24) expressed the same thought with other words: "...the essential characteristics of living beings must be sought in a peculiar organization in which features that may be analyzed by usual mechanics are interwoven with typically atomistic features to an extend unparalleled in inanimate matter" (Bohr uses 'atomistic' in the sense of 'quantal').

In recent terminology, we could say that Goethe's 'solid substance' is studied in biochemistry and cell biology, whereas his 'liquid substance' is studied in the theory of chaos. Living substance is characterized by this interwoveness, down to the quantal level, of robust structures, such as DNA or proteins, and of chaotic, fluid structures (such as liquid water), that was presented by Goethe. Through the robust structures, the living organism acquires stability and protection against external disturbances; through the interconnection with chaotic structures it acquires - because the processes become phenomena of type III - unity through time, or directionality.

24. Bohr in 'Light and Life' (see note 20). There are some indications that Goethe played a role in the development of Bohr's philosophy ; see for instance Chevalley, C.(1994) "Niels Bohr's words and the Atlantis of Kantianism" Boston Studies in the Philosophy of Science 153,pp.33-55. The beautiful book of Jørgen Kalckar ("Det inkommensurable. Brudstykker af et tonedigt i d-Moll. Goethe-temaer fra vekselsange med Niels Bohr" Copenhagen: Rhodos 1985) reproduces the many discussions of the author with Bohr on Goethe and his work, but it is available in Danish only. Although Bohr showed little interest in specific aspects of Goethe's scientific work, he remarked: "The religious feelings of Goethe, or his poetic attention, were interconnected and in close harmony with his global hinsights in nature, that he had acquired through very extended studies, and that were at least in certain respects, very much ahead of his time (...) even much more than most people today, he understood that nature constitutes a whole. The pious atmosphere or feelings that so remarkably transpire through his works, were rooted in his emerging perception of these unfathomable , mysterious harmonies lying hidden in nature". Bohr's father Christian Bohr was also deeply involved in Goethe's works, and Niels Bohr himself acknowledged his father's importance for his own philosophical outlook. Hence, the concordance between certain views of Goethe and Bohr is probably not accidental.


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