# Complementarity, Knowledge, and Reality

MECHANICISM

Realism

We can introduce the elements of Mechanism in the context of Newtonian dynamics.  A Newtonian system is an assembly of particles submitted to external and internal forces.  The state of each particle is specified by means of its position and its velocity.  That state can be conceived as the state in itself of the particles, independent not only of what the observer knows or decides to measure, but also of the same existence of that observer.

It could be argued that to measure those variables it is necessary to interact with the particles by means of an apparatus of measure which always produces dispersion in the values obtained.  One can responds that in principle it is possible to improve the technology and to do such dispersion as small as one wants.  In addition, any correlation between the dispersions of the position and the velocity does not exist and it is possible then to make both dispersions as small as we want. It is reasonable thus to conceive the existence of a state without dispersion and such state would be the state in itself of the system.

We can call realism the conception of the existence of a state in itself of the particles that compose a Newtonian system.

A consequence of realism is that if a property of a system is determined, that property will be valid in any observational context.  There are not mutually exclusive properties.  There are not mutually exclusive concepts from the logical point of view.  One can sustain the existence of a conceptual monism

Determinism

The dynamics of the evolution of the state of a system of particles is described by deterministic equations, which means that from the state of the system in a given time, the state in a future or past time is totally determined.  One must emphasize that the existence of deterministic equations does not suffice for determinism.  It is necessary also that the existence of an objective state of the system. That is to say that realism is necessary to have determinism

Reversibility

Another aspect of Mechanicism comes from the reversible character of the equations.  Every system governed by them presents a totally reversible evolution.

Reductionism

The following aspect of Mechanicism is a little more metaphysical.  It is clear that any system in the universe, be an inanimate macroscopic body, be a being alive and even a human being, is composed of parts.  According to the Newtonian dynamics those parts are the particles that we speak further up.  It looks as reasonable then to suppose that all the properties of those systems of particles can be explained from the particles that compose it and their interactions.  In other words all the properties of those systems would be reduced to the properties of the particles.  If we call emerging those properties of the whole that could not be explained from the properties of the particles and their interactions, reductionism would say that not such properties exist.

It must be noticed that determinism and reductionism imply that the whole world is governed by the most ferrous determinism.

Non-anthropic character

From reductionism and the inherent reversibility of the evolution of the parts that compose each system of the world, we conclude that the time as perceived by us the human beings, would not be more than an illusion.  Reductionism and determinism imply that free will would be also an illusion.  The two just mentioned consequences constitute what we can call the non-anthropic character of Mechanicism.

BREAKING MECHANICISM

Now we can examine the conflict that arises between Mechanicism and the quantum phenomena and formalism.  Let us begin with the quantum phenomena.

Quantization of the action

One of the bases of Mechanicism is the assumption that all the physical phenomena can be explained by the algorithm of classical dynamics.  Now well, all the equations of classical dynamics can be obtained from the variation of a physical quantity called the action. When such variation is made equal to zero the equations are obtained that govern the evolution of the system. To obtain the variation it is necessary that the action be a continuous quantity.  The most prominent aspect of the quantum phenomena is that they show that the action has a discrete character, which is known as the quantization of the action, and which made impossible an explanation of them by means of the algorithm of classical dynamics.

It is true that the reductionism could still be maintained saying that the properties of all the system of the world would be reduced to the laws of quantum physics and not to those of classical physics. We have seen however that the elements of Mechanism are narrowly tied with the equations of classical dynamics. We can expect then that many of those elements are not anymore valid.  And in fact this is the case as we will see now.

Contextual character of the variables

The quantum phenomena reveal a contextual character of the variables that describe a particle: if one tries to diminish the dispersion in the measurement of the position of a particle, the dispersion of the velocity begins to grow and vice versa.  In the limit in which the dispersion of one of the variables tends to zero, the dispersion of the other tends to infinite.  Everything happens as if the variables would depend on the experimental context in which they are observed, making extremely problematic to maintain a reality in itself for such variables.  The fact that position and velocity are the variables that, according to classical dynamics, define the dynamic state of a particle, extend the problem to the same dynamical state of the particle, that with difficulty can now be considered as a state in itself, independent of the observational context.

Mutually exclusive concepts

In the quantum phenomena it happens also that in order to describe the behaviour of a same object it is necessary to employ concepts that, like that of wave and particle, are mutually exclusive from the logical point of view.  This adds to the difficulties to attribute a reality in itself to the state of a particle.

The experiment of the double slit is one of the experiences in which the necessity arises of using mutually exclusive concepts from the logical point of view for the description of the behaviour of a same object. If a beam of electrons is made to pass through a screen with two narrow slits on it, and nothing is done to determine through which slit each electron passes, it is necessary to employ the concept of wave for describe the behaviour of each electron.  If in some way a change is made in the experimental device that permits to determine through which slit each particle passes, the behaviour of each electron is nevertheless that of a particle.

An explanation can be tried however supposing that the modification in the experimental context in some way “disturbs” the particle and changes its behaviour.  In fact, if by means of a shutter one of the slit is covered, the electrons passing through the other slit behave as particles.  If the slit is uncovered, the electrons that pass through both of the slits behave as waves.  One can try an explanation saying that the opening of the slit “disturbs” the electrons that pass through the other and produces a change in its behaviour. The perturbation would travel from one slit to the other.  Now well, as in principle the two slits can be as separated one of the another as we wanted, it would happen that the perturbation would have finally be transmitted instantly, that means with an infinite velocity.  One of the fundamental principles of physics that affirms the existence of a maximum velocity for the transmission of the interactions would be then violated.

The delayed choice experiment

In the delayed choice experiment everything happens as if the decision that the observer makes now would have an influence in what the electron has done in the past.

An ideal arrangement to carry out a delayed choose experiment is the one shown in figure 1

There is a beam of photons. We place in its way a semitransparent mirror E that divides the beam in two halves.  One of them will be reflected and will form a beam in the up direction and the other will be transmitted forming a beam that will continue in the same direction that the initial beam.  The reflected beam as well as the transmitted beam will encounter a mirror that reflects them ninety degrees. The beam cross each other and each one of them enter to a detector that we mark as D and d.  If we suppose that the initial beam is of so low intensity that in practice the photons enter one to one to the apparatus, we found that only one of the detectors is fired each time.

We can make the following reasoning: each photon that arrives to first mirror, the semitransparent one, reflects itself or it is transmitted.  In the first case, it follows the path that carries it to detector D; in the second case, it follows the path that carries it to detector d.  The experience is equivalent to observe the path that the electrons follow. The photon shows a corpuscular behaviour.

Let us consider now a variation of the experiment (figure 2)

What we have done is to insert a second semitransparent mirror in the point of crossing of the two beams. This mirror recombines the two beams.  In fact: a part of the beam that goes toward detector D continues now the path that goes to detector d and a part of the beam that goes toward detector d continues now by the path that goes to detector D. Effects of interference between the two beams are now produced that depend on the differences of paths between the second semitransparent mirror and each one of the detectors. It is possible to arrange things in such a manner that the intensity of the resulting beam that goes toward detector D, after passing the second semitransparent mirror, be equal to zero, that is to say that we have a destructive interference for that beam.  It is concluded then that the intensity of the resulting beam that goes toward the other detector is 100% the intensity of the incident beam.  Likewise things can be arranged in such a manner that the intensity of the beam that goes toward detector d, after passing the second semitransparent mirror, be equal to zero.  None of these facts can be understood unless a wavelike behaviour is attributed to the photons.  And as the experiment can be done with an initial beam of so low intensity that in practice each photon enters one by one to the apparatus, we should conclude that each photon behaves like a wave.  With the presence of the second mirror, the experience is equivalent to that of the two slits when both remain open.

In conclusion: it is the presence of the second semitransparent mirror what decides about the behaviour the photon is going to exhibit, if corpuscular or wavelike.  Without the second mirror, the behaviour is manifestly corpuscular, which means that the photon follows only one of the two possible paths.  With the second mirror is present, what is manifested is the wavelike behaviour, which implies that a part of the photon follows one of the paths and another part follows the other. We confront again the fact that, depending on the experimental context, the photon is going to manifests one or another of two mutually exclusive properties.

In this experiment, nevertheless, something even more surprising is manifested. In fact we can calculate how much time takes a photon to arrive to the region where the second mirror can eventually be placed, and we can differ to the very last moment the decision to place or not that mirror.  This fact of waiting till the moment when the photon is already in the surrounding area of the place where the second mirror can be located, gives its name of “delayed choose” to the experience.  Everything indicates that the fact of placing or not a mirror in a given moment defines if the photon shows one or another of its two possible behaviours.

If the corpuscular behaviour is the one that is manifested, it must be considered then that the photon has followed one or another of the two possible paths; if on the other hand what is shown is the wavelike behaviour, the consideration must be that a part of the photon has followed one path and another part has gone by the other. It seems evident that when the photon arrives to the place where the second semitransparent mirror can be located it has already travelled through its path, either by one route or either by both routes. Therefore, the placing or not of that mirror would not be able to change the way as the photon has done its travelling.  Nevertheless, depending on the placing or not of the mirror we found that the photon goes by the two routes or goes by one alone.

The surprising conclusion is that everything indicates that what is done in a given moment seems to influence the behaviour of the photon in the past, violating thus one of the most fundamental intuitions about the causal relations that maintains that the cause cannot be subsequent in the time to its effect.

Let us examine now new aspects related to the quantum phenomena that are quite difficult to insert in the framework defined by Mechanicism. These features are revealed by the formalism.

Wave functions

In classical mechanics, the state of a system is determined by the positions and the velocities of the components of the system.  In the quantum description the state of the system is represented by a wave function; this means that everything we know about a particle in a given moment will be represented by its wave function.  Now well, we know that the waves obey the principle of superposition.  What will signify this principle in relation to the state of a quantum system?

The superposition of two waves gives as a result another wave.  If the state of a quantum system is represented by a wave function, the superimposition of two quantum states will result, then, in another quantum state.

Let us consider for example the two slits experiment. We suppose that one of the slits that we call 1 is covered.  We have then a quantum state that corresponds to the case of electrons that pass by slit 1. To such state corresponds a wave function. If the other slit, that will call 2, is covered, we will have the case of electrons that pass by slit 2. A wave function  is assigned to such state. If the two slits are now opened the quantum state will correspond to a combination or superposition of the states  and

Now well, we can consider that superposition of states as a wave that spreads from the slits.  The quantum theory says that the probability of finding the electron in a given point of the screen that is located in front of the two slits is determined by the value of the wave function and the rules of quantum mechanics tell us how to find that probability, which will be the squared value of the wave function. In this situation we have interferences, therefore in some points of the screen the values of the waves and  are equal and opposite that is to say we find destructive interference. In such a case the value of the superposition is zero and the same happens with the probability to find there the electron. In other points it can happen that we have constructive interference, which means that the value of the superposition is different from zero and, therefore, the probability to find there the particle is different from zero.

We suppose now that, by some procedure, we observe the passing of each electron through the slits.  If it is observed that the electron passes through slit 1, it means logically that the probability to observe it near slit 2 will become equal to zero in that instant.  That is to say  becomes equal to zero.  When arriving to the screen, the probability to find the electron in a given point of it will be obtained therefore only from because, as we see,  is zero. In a similar way, if is observed that the electron passes through slit 2, that means that  become equal to zero and the calculation of the probabilities for the electron arriving to a given point on the screen will be obtained from only.  In this situation will not have interference, therefore only one of the two waves is involved each time and never a superimposition of them.

Our formalism, with his rules of use: with his algorithm, describes then in a perfect way what happens with the experiment of the two slits, just as we describe it in a previous section.

The collapse of the wave function or the problem of the measurement

The observation of the path of the electrons through each slit, changes then the wave function from a superposition of Y1 and Y2 to a value equal to Y1 or to Y2 and the change occurs instantly

This process, in which a part of the wave function disappears when a measurement is made, receives the name of collapse of the wave function.  The properties of the collapse are extremely strange from the point of view of Mechanicism.  First of all, the process is not deterministic.  In fact: before the observation of the passage of the electrons through one of the slits, there is a probability, which we will call , of finding the electron crossing slit 1 and a probability, which we will call, of finding it passing through slit 2.  That is to say: there is a probability equal to  that, when we determine through which slit the electron passes, the term Y2 becomes zero, in other words there is a probability  that the wave function collapses to Y1. Similarly there is a probability equal to  that the wave collapses to Y2. The following questions arise almost immediately in the context of Mechanicism:  What defines that the electron turns to be described only by one of the two terms of the superposition?  Is it the interaction with the apparatus of measurement?

Any measurement process can be reduced to three stages:

a) Preparation of the system: the apparatuses are placed, the initial condition is determined. A state is assigned to the system.

b) Evolution of the process: the system is left to evolve without interfering with it.

In the case of the double slit experiment one has:

Preparation of the system: the device emitting the electrons, the diaphragm and the screen are located; the parameters are set and the system is “turn on”.  A wave function is assigned to the electrons.

Evolution of the process: the electrons are left to follow their paths.

The measurement is made:  it is determined through which slit the electron passes.

Now, there is nothing special that permit us to make a fundamental distinction between the interactions involved in the preparation and those that take place in the measurement. Both of them are nothing more than physical interactions. There is no reason then to consider a measurement as something special and different to any other physical interaction.

Now then, in its time-honoured book on quantum mechanics, John von Neumann analyzes the process of measurement in quantum mechanics affirms that it is possible to obtain all practical results if two possible processes for the temporal evolution of the wave function are accepted.

The first process preserves the superposition of the states: if there is initially a superposition, the evolution will produce subsequently also a superposition. The evolution is completely deterministic, without any probabilistic element.  The equation describing the evolution is like a classical wave equation.  The system follows that evolution during the second stage of the process of measurement, when we do not interfere with it, when do not perform any measurement on it but leave it to evolve under the influence of the physical interactions that are present. We can call to this process the process d

In the third stage, when the measurement is performed, the system follows a second process that is not deterministic. For that reason we can called it process i.  During that process, in which the system interacts with the apparatus of measurement, the wave function collapse to one of the possible states that can result from the measurement. All the other possibilities disappear. This comes about in a not deterministic manner: we cannot determine beforehand which state will result after the measurement; all we can do is to calculate the probabilities.

Now then, as we remarked above, a measurement is no more than an interaction.  The only thing that distinguishes it from other interactions is that we are utilizing it to obtain certain information.  That means that what converts an interaction in a measurement is the use that we give to it.  But the interaction in itself is physical and we do not see what it has to do with the use that we want to give to it.  How can the electron know that some physical interaction is a measurement and consequently it must follows process i?  It seems reasonable to suppose that the electron should always follow process d.  Nevertheless, if we know that the interaction is a measurement – and we ourselves design our measure and decide that an interaction is a measurement -, we have to employ process i.

Let us suppose a laboratory where we place a cat alive, a radioactive atom, a Geiger counter that detects the radiation emitted by the atom when it disintegrates and an automatic mechanism connected to the counter.  When the radiation arrives to the counter, the mechanism breaks a container of crystal filled with a deadly gas.  We close hermetically the laboratory and turn on the counter. Let us suppose also that at the moment when we close the laboratory the probability that the atom disintegrate is 50%.  Obviously the probability that the atom does not disintegrate is also 50%.  If the atom disintegrates, it emits a radiation that is detected by the Geiger counter.  The automatic mechanism breaks then the container with the deadly gas which is diffused in the laboratory and causes the death of the cat. In other words: if the atom disintegrates, the cat dies.  If the atom does not disintegrate, there is not radiation, the container is not broken, the gas is not diffused and the cat continues alive.  As the probability that the atom disintegrate is 50%, there is then a probability 50% to find the cat dead when we open the laboratory.  The probability to find the cat alive is also 50%, because that is the probability that the atom does not disintegrate.  If we carry out many of these experiments with many laboratories and many cats, half of the times we would find alive cats and half of the times dead cats.

We can consider the whole process as a measurement.  The preparation of the system consists in the placement of the cat, the atom, the counter and the mechanism with the container filled with the deadly gas and the act of closing hermetically the laboratory and turning on the counter.  The evolution of the process is what happens in the laboratory after we close it and we turn on the counter.  The measurement will consist in the opening the laboratory to see if the cat is alive or dead.  The state of the cat will play the role of the needle of a detector whose position indicates us the result of a measurement.  In our case, if the cat is alive, we will know that the atom disintegrated.  If it is dead, we will conclude that the atom has not disintegrated.

How will quantum mechanics describe the former situation?  Let us consider the atom.  We know that there is a probability of 50% that the atom disintegrates and of 50% that it does not disintegrates. According to quantum mechanics we will have then to describe the atom by a superposition of two wave functions, one describing the atom without being disintegrated and the other that describes it disintegrated.  As everything that is inside the laboratory are physical systems composed by atoms and electrons which are described by quantum mechanics, everything inside the laboratory can also be described by a wave function.  There will be a function that describes the non disintegrated atom and all the remainder of the laboratory in the situation in which the atom has not disintegrated. Similarly there will be a wave function that describes the disintegrated atom and the remainder of the laboratory in the situation corresponding to the disintegration of the atom.  At the very moment when we close the laboratory and turn on the counter, everything that is in the laboratory will be described then by a superposition of those two wave functions.

But the fact is that while the laboratory is closed we do not interfere by means of any measurement with what is inside.  Because of this we have to consider that everything that is in the laboratory follows process d.  Process d preserves the superposition, for that reason we have to conclude that after we close the laboratory and until we open it again, everything that is inside is going to be in a state of superposition, which is the superposition of a quantum state that describes the cat alive and another state that describes the dead cat.

We said that the measurement will consist in the opening of the laboratory to see if the cat is alive or dead.  If it is alive, we will know that the atom disintegrated.  If it is dead, we will conclude that the atom has not disintegrated. Due to the fact that a measurement is performed, in the very moment when the laboratory is opened the superposition collapses. We have affair to process i.  One of the states of the superposition disappears.  If the cat is alive, the state that described the dead cat disappears.  If it is dead, what disappears is the state that described the living cat.

If what matter to us is simply the practical results to describe experiments, we have nothing to worry about. But, what if we ask ourselves about what happens in the laboratory before we look inside?  This question is a very natural one for a person who is used to think in terms of an objective reality that has a state independent of the observation.  The answer that coheres with the quantum description that we have done is that, after closing the laboratory and turning on the counter, and whereas nobody reopened it, the cat will be in an indefinite state, in which it will be simultaneously “alive” and “dead”, or as “floating” between “being alive” and ” being dead”.

The previous description seems at first sight totally absurd.  We know well that if we open the laboratory we will find the cat or completely alive or completely dead, and by sure not “suspended” between those two possibilities.  It is clear that we do not have any way to know the state of the laboratory unless we open it to observe it. We have then to conclude that the cat remains during the time that the laboratory is closed in an indefinite state, and that the mere opening of the laboratory, which can be considered as a process of measurement, obliges the system “to decide” between the realization of one or the other of the two possibilities?

Not-locality of the collapse

All previous things defy the better established intuitions we have about the bodies that are accessible to our direct perception: the macroscopic bodies. We have supposed that in a given moment we open the laboratory and observe what occurs inside. At this very moment the collapse takes place.  We imagine now that we locate in a corner of the laboratory a video camera, which we can switch on. The camera will film what happens inside and will send a signal outside showing what comes about in the laboratory. Let us suppose that instead of opening the laboratory we switch on the camera in a given moment but rather than regarding the emitted signal we send it to another person with a television set located thousands of kilometres away from the laboratory. At the very moment when that person observes what occurs in the laboratory, the measurement and therefore the collapse will comes about. That means that what produces the collapse can be so far away as we want of the laboratory where the collapse takes place and therefore this occurs instantaneously. The process of the collapse violates then the law of maximum velocity of the physical interactions. In technical term, this type of instantaneous connections constitutes what is called the non-locality

BOHR´S INTERPRETATION

Science and objective as synonymous of non ambiguous

Bohr (Bohr, 1934, 1957, 1963) considers that the goal of Science is the increase and ordering of the experiences which are communicable without ambiguity. In other words, Science occupies itself with the expressions exempted of ambiguity which for Bohr are the objective expressions. Let us analyze in what sense it is reasonable to equate objective to non ambiguous.

Ambiguous are all affirmations with two or more meanings which make them uncertain or mistaken. The subject receives the communication and gives it more than one meaning, or each subject gives it a different meaning. To the contrary a non ambiguous affirmation has only one meaning for each subject. The meaning is independent from the subject.

Objective is what is related to an object that really exists outside of the subject. This object has real existence, it has reality. If it is considered that its reality is in itself, independent from the subjects, then what is relative to it is independent from each subject. If it is considered that its reality is only phenomenal, not making reference to a reality in itself, but rather only to what appears to the subjects, even then what refers to it must be independent from each subject, must be inter-subjective because to the contrary, it will depend on each individual subject and its reality will be subjective. What is objective is then independent of each subject.

A first conclusion is that objective and non ambiguous are both independent of the subject.

Now then: everything that is objective is non ambiguous but not everything non ambiguous is objective. A mathematic model that is not in accordance with the experience can be non ambiguous without being objective. Classical Mechanics is not ambiguous. But it is only objective if the velocities are very smaller than that of light and if the typical physical actions are much larger than the quantum of action.

It can be affirmed that the non ambiguous is not necessarily objective but it is a good candidate to be objective. The non ambiguous that result as valid because of experience, will be considered as objective. If it does not result as valid, it will be considered as non objective.

Now then: the judge that defines whether something is ambiguous is the experience. Nevertheless, all experience requires a conceptual framework. In particular all scientific experience requires a non ambiguous conceptual framework. This, for example, is what allows for precise and objective experiences in Classical Mechanics.

The non ambiguous relies on non ambiguity to decide if it is objective. The search for objectivity is equated then with the search for on ambiguity.

The unicity of language

What then is the language that allows context definitions of non ambiguity or rather objectivity? Bohr sustains that the only language that we have had, that we have, and that we will ever have, is the language that is common to the human race, the power or faculty of language that is different from any specific language. Amongst its basic elements are space, time and cause. This language commonly ambiguous allows however context construction of non ambiguity. Bohr seems to coincide with Kant in the fundamental importance granted to the previous concepts. Nevertheless he does not ask after its nature or its origin. Rather he accepts its existence pragmatically as fundamental elements of the only language that we humans have, which we can always refine in order to communicate certain experiences without ambiguity, experiences which we could, according to Bohr, call objectives, because when detached from ambiguity, they don’t have any element which makes reference to a particular observer. The previously stated is the fundamental linguistic thesis of Bohr, which, in previous writings, I’ve named the unicity of the common language. (Roldán, 1991)

According to Bohr, in physics, the only language to define contexts of non ambiguity or objective contexts is that of classical physics. His argument is essentially as follows: When confronting any physical theory with the experience, not mattering how abstract the theory could be, the tools and results of measurement have to be described through classical physics. This means the theory which supports the experience, according to Bohr, is in physics the classical theory. Even if the challenge which presents quantum phenomena did not exist, it could be argued that the necessary logic that it is so is not seen, because the possibility exists to build another theory that supports the experiences, including those predicted by classical physics. The counter argument will be that it is not necessary to build another theory to support the experience if the existing one describes the instruments and results of measurement correctly. Because it is a fact that a problem is presented with quantum phenomena, we have to analyze the matter in this context.

The situation with classical physics is the following: It constitutes a theory exempted of ambiguity. To decide about its objectivity it is subjected to experience. This experience is supported in the framework of the same classic theory, that is to say that the apparatuses and the results are expressed in the framework of that theory. The context in which the results are organized is obviously that of classical mechanics.

What happens with the quantum phenomena? They are obtained through apparatus whose support is classical physics. The results: points on screens, positions of needles, and so on, are expressed in the framework of classical physics. But these phenomena cannot be fit within the context of classical physics. When Bohr sustains that the language of physicists is that of classical physics he not only affirms that the instruments and the results of measurement are expressed through classical physics. As a matter of fact if it was not like this, quantum phenomena would not have been discovered. In a certain sense it is a trivial affirmation. The strong point of his thesis is that what is implicated is that all physical phenomena must fit, in some way, in the framework of classical physics, because it is the only language that allows a context of objectivity in physics.

It can be argued that there is no logical reason why it is like this, and that the fact that quantum phenomena cannot fit within the classic context indicates that a language different to the classical must be found that allows them to fit. Does the same quantum theory not constitute this context?

The problem is that we do not perceive a quantum superposition. The phenomena do not appear to us in these superpositions. The theory affirms that a system is in a state of superposition in a given moment. But when taking the measurement only one state appears. As the theory makes correct predictions, we can accept the existence of superpositions. But as the phenomena are never superposed the evidence of superpositions is indirect. The theory talks about superpositions but what appears, the phenomena, appears in the framework of classical theory, where there are no superpositions, where things have a trajectory, where mutually exclusive concepts cannot be applied to the same object.

Why then do we not let ourselves be guided by the quantum theory and construct a new theory for the apparatuses and the phenomenal results that allows us to include them in the context of this theory? Such a theory would have to accept phenomenal things that we already know as ruled by classical physics and propose new phenomenal entities. These new entities and the known ones will give the new context. The electrons could be accepted as particles with a trajectory and we could say that the quantum state vector represents other phenomenal entities. It is a logical possibility. The only thing is that the new entities must not be local which means that the labor is very arduous. As a matter of fact it is the program of David Bohm and his school.

If Bohr insists in not moving out of the framework of classical physics, somehow he has to find a way to use it that allows for the organization of quantum phenomena without leaving the classical framework. And it must respond to all the quantum paradoxes. If he does this, it can be said that his proposal, not needing to introduce new phenomenal entities, is more economical.

The fact is that the logical necessity it is not very clear that the physical phenomenal entities have to inevitably be described in the framework of classic physics. But if Bohr is successful in his program, we can accept it as a successful intuition. It is guessed that some price has to be paid and if we do not want to pay it, we will have to find an alternative. It is also guessed that with the alternative of Bohm a price equally has to be paid.

And why not say that reality is the abstract theory? The fact is that this theory is in the world of mathematic reality, ideal. And for a theory of this type to be scientific it has to confront the phenomena that are in the world of our perception. Using platonic terminology, the abstract theory is in the intelligible world and our perception is in the sensible world. And the conceptual framework of the sensible world is definitely not that of the abstract theory. Maybe this is where the strength of Bohr’s thesis lies. It is the sensible world that allows for the decision if an abstract theory, which “lives” in the intelligible world, is a scientific one; and this sensible world is ensconced in classical theory.

Would it not be easier to look for classical models to which quantum theory could be reduced? The problem is that it is not possible to reduce quantum physics, which requires discreet action, to classic physics, fundamentally based in the continuity of the action. The model proposed by Bohm is in fact not classical, it cannot be.

To understand the rest of Bohr’s program we accept his thesis of the unicity of the language of classical physics for the explanation of the physical phenomena and we will examine the logical consequences of this acceptance.

The fundamental quantum paradox. Irrationality of the quantum

The thesis of the unity of the common language, united to the fact that the quantum phenomena cannot be explained by through this language creates a paradox. In effect, if the only language that we have to achieve the communication of certain experiences without ambiguity- which would be the only ones with an objective character and therefore the only ones that could be qualified as scientific- does not allow us to understand and explain quantum phenomena, how can these phenomena then be considered as scientific? The paradox acquires greater seriousness if we remember it is exactly the quantum phenomena that allow us to understand the stability of mater, stability which is a necessary condition for the development of our common language. It is not strange then that, for Bohr, the preceding is the fundamental quantum paradox.

With the language of classical physics, the existence of the quantum of action cannot be explained. If this language is the only one which allows explanations, then the existence of the quantum of action is not explicable. It is what Bohr denominates as the irrationality of the quantum.

Now, it is the existence of the quantum of action  which allows the stability of mater. And without this stability the classical language, which is what allows for explanations, is not sustained. If this was not so, how could we have formulated our concepts? Even more, how could we exist in this physical plane? It is then the existence of which makes possible the very existence of the only language which allows us to have explanations. We cannot, therefore, pretend to explain that which allows us to explain. So the existence of is what allows for explanations. Because not only can we not explain that which allows for explanations, but there is also no need to explain it, so the existence of is not explained and does not require an explanation. Bohr then proposes to accept the existence of as a fundamental fact which “is not explained and does not need explanation”.

Indivisibility

Bohr considers it the principal consequence of the existence of the quantization of action. It one wants to divide a quantum phenomenon other incompatible phenomenon does appear. One example is the experiment of the two slits, or in general any intent to divide a phenomenon in its different possibilities or “paths”. In which sense is a consequence of the quantization of action? The theory that takes the action as quantized, predicts that when intending to divide a phenomenon another incompatible phenomenon is found. And this is verified by the experience. In this sense indivisibility is a consequence of the quantization of action.

Indivisibility gives Bohr the key to a new use of classical language, to a new method of description which does not imply going outside of classical language.

Complementarity

So, how to speak about quantum phenomena? Do have to renounce forever to any type of explanation? Or will there be a new way to use language in order to construct a new type of explanation? Will a new logical relation between concepts exists, which will allow us to explain even those things that seem far from any type of explanation through the normal use of language? A positive answer is what Bohr gives with his proposal of complementarity.

Within the thought of Bohr, a quantum phenomenon is an indivisible whole which includes the instrument of observation. This implies the object under observation cannot be perceived as something totally independent from the instrument of observation. As a consequence of this, it is not now possible to attribute independent properties to the object. A property which, like position, can be assigned to an electron in a given phenomenon, cannot continue being assigned in a phenomenon which allows the property of velocity to be assigned. And this dependency on the experimental context, which is presented for the assignation of properties, is which allows the contradictory properties of wave and particle to be attributed to an electron, because it cannot be attributed in the same phenomena. And neither can it be attributed independently from the experimental context, wherefore it does not make sense to ask if the electron is a wave or a particle. The question that makes sense is: given this experimental context, can the concept of wave be used?, or that of particle?

Bohr affirms that although concepts like wave and particle are mutually exclusive since, as we registered before, something cannot act like a wave and particle at the same time, nevertheless both concepts are necessary to exhaust all possible information about an electron. Bohr proposes then to consider them as complementary: as mutually exclusive, in the sense that we cannot combine them in the same reasoning in respect to an electron, but both being necessary to show everything that is possible about an electron.

Bohr proposes a similar relation for the concepts of position and velocity: they are mutually exclusive but necessary to show everything we could know about an electron. Because they are mutually exclusive they cannot combine in reasoning about an electron; this means that a trajectory cannot be attributed because this implies at the same time knowledge of position and velocity in every instant of time.

The properties are contextual and mutually exclusive. We do not go outside of classical language, we only change the logical order of the concepts.

Non ontological interpretation

Indivisibility impedes the attribution of properties in themselves to a quantum system, therefore the quantum formalism cannot be interpreted in terms of reality in itself.

Indeterminism

II is necessary to recall now the relation that exists between determinism and the mechanistic fragmentation, or divisibility or strict separation between the subject observer and the observed object. Bohr considers that fragmentation as a basic element in the mechanistic conception of nature.

We have said that determinism sustains that the present state of the world totally determines its future. Nevertheless, in order to know the state of a system, it is necessary to interact with him and, consequently, it is necessary to perturb it.  In classical physics one admits that it is always possible in principle to compensate the perturbation or, in other words, that one can always know or define this perturbation.  Classical physics permits us therefore to consider that the subject is essentially separated from the object.

We should notice first of all that if one finds that determinism is not valid, that fact does not imply necessarily the impossibility to do a separation between the observer and the observed. In fact, one could conceive the existence of an intrinsic indeterminism, which would mean that one could consider the laws of the nature as essentially statistics, so that even if it would possible to define and to compensate the perturbation of the object produced by the observation, all the same one could only predict the intrinsic probabilities of the given events.

On the other hand, if the strict separation between the subject observer and the observed object is not valid, it is then impossible to define the perturbation of the object and, consequently, determinism becomes a thesis difficult to maintain.

In fact, once he was convinced of the impossibility to maintain in the quantum domain a strict separation between the object and the instrument with which it is observed, one of the more important conclusions of Bohr is precisely that the determinism is not acceptable in the quantum phenomena.  For him, quantum mechanics possesses consequently an inherent statistical character.

BOHR´S ANSWER TO THE PROBLEM OF MEASUREMENT

The role of the instrument

We have said that for Bohr a quantum phenomenon is an indivisible wholeness that includes the apparatus of observation. In that totality, nevertheless, a fundamental distinction should be done between the instrument and the remainder of the phenomenon.  In fact: if we want to have an experience, the unicity of the classical language requires that the description of the experimental arrangement and of the data be done in classical terms, in order to make possible a communication without ambiguity of the experiment.  A part of the totality constituted by the phenomenon should be described then through the ordinary use of the classical language.  In other words: the instrument is that aspect of the quantum phenomenon that is described by classical physics.

An important aspect of a quantum phenomenon is that in order to go from an experience A to an experience B complementary to A, what is considered as the instrument will change.  We can illustrate this point with an example.

Let us consider an experience that permits us to observe the interference of electrons.  We have then a source f of electrons that impact on a diaphragm D with a slit. In front of that diaphragm there is a second diaphragm d with two slits.  In front of this and a certain distance there is a photographic plate P.

Which is the instrument?  The instrument is constituted by the source, the two diaphragms and the plate.

The previous experience does not permit us to know by which of the slits in the second diaphragm each electron passes through. To find a way to know it we can reason as follows:  each electron is going to produce a movement in the first diaphragm when it passes through the slit.  The knowledge of the movement produced in that diaphragm would permit us then to decide through which slits of the second diaphragm each electron will passes. In fact: if after passing by diaphragm D, the electron passes through the upper slit in diaphragm d, we can expect that the movement that it produces in the diaphragm D will be different to the movement if would produce if he passes later by the lower slit of diaphragm d.  We are not able, nevertheless, to know the movement produced by the electron in diaphragm D because this last one is stiffly fixed.  To determine such movement we design another experience in which the first diaphragm is not fixed but is hanging on a spring r in front of which there is an apparatus A that detects the movement.

It happens nevertheless that, though we can decide now which path the electron follows and we can consider them as particles, the interference disappears.  This is shown clearly by means of the mathematical analysis, which forces us to conclude that in order to be able to know with the necessary precision the movement of the diaphragm, it is necessary to treat it now by means of the quantum algorithm.  We arrive then to the following conclusion: in this experience, which is complementary to the previous one, the first diaphragm no longer is part of the instrument.

It is possible to present other examples of this type in which a body is part of the instrument in an experience but can not be considered as part of the instrument in the complementary experience.  Because of this fact it is possible to affirm that the frontier between the instrument and the rest of the phenomenon changes. The frontier is then a mobile frontier. But it is not really a frontier in the ordinary sense, because for that it would be necessary that one could separate the instrument from the remainder of the phenomenon, which is not possible due to the inherent indivisibility of every quantum phenomenon.  There is not any logical restriction for the distinction of different aspects in an indivisible whole.  What does indivisible the whole is not the impossibility to distinguish different aspects, but the impossibility to separate those aspects, because if we do that the whole would not be what it is.

#### The closure of the quantum phenomenon

For Bohr, a quantum phenomenon is not completed until an irreversible mark is not produced in the instrument of observation. In the two slits experiment, the phenomenon only is completed or, as Bohr says in his particular terminology, closed or closured, when the irreversible mark in the photographic plate is produced. Before the phenomenon is closed or completed, it is not legitimate neither to ask any question about the object, neither to decide what concepts to utilize with regard to its behaviour, and neither to do valid inferences about it.

Because of this, in the framework of Bohr´s interpretation, the questions that were posed in the experiment retarded choice, about what had happened with the photon before it arrives to the point where we can located or not the second semitransparent mirror were not legitimate, because nothing can be said about the photon until the phenomenon is not close by its detection by means of an irreversible effect in the apparatus.

Another important aspect of the notion of the closure of the phenomenon is that to complete the phenomenon the presence of a conscience is not required; only the irreversible effect in the apparatus is required.  For Bohr, a phenomenon is a phenomenon when it is “closed” by an irreversible effect in the instrument. In a quantum phenomenon, as conceives by Bohr, the observer is necessary to define the complementary aspect that is going to be manifested, and that observer does not have the right to affirm of what aspect he treats in the meantime he have not done the arrangements of the case; but once the experimental device is definite, the presence of the observer no longer is necessary for having the phenomenon.

Bohr and the problem of the measurement

One of the assumptions of the problem of the measurement or the paradox of the cat is that the intuitive behaviour of the macroscopic bodies, which is the one described by classical physics, is accepted as natural and obvious.  Concerning that assumption one must recall the following: according to the bohrian interpretation, it is the experimental context which decides if a macroscopic body can be described by means of the classical language or, on the contrary, it must be described by means of the quantum algorithm.  We saw already further back the case of a macroscopic diaphragm that in an experimental context was treated as a classical object, and in another experimental context complementary to the first one, was described as a quantum object.  The key point for Bohr is that if a macroscopic body is involved in an experimental context in which it plays the role of instrument, it has to be described classically.  If the experimental context is such that the physical actions with respect to it are of the order of the quantum of action, the body must be described by means of the quantum algorithm.  In the case of the paradox of the cat, this last one is utilized like an instrument; therefore it must be described in the classical language, in which a superposition of a state “dead cat” and a state “alive cat” does not have any sense at all.

In conclusion: the problem of the measurement is dissolved for Bohr because he refuses to accept one of the assumptions necessary for formulating that problem.

INDIVISIBILITY AND COMPLEMENTARITY

Indivisibility as a fact

It will be a fact if the linguistic theses of Bohr are accepted.  If they are not accepted one can rejects indivisibility as a fact, maintaining that we have instead not locality. Indivisibility implies impossibility of ontological description.  Non locality does not imply such conclusion. Bohm maintains, for example, that is possible to give an ontological description of the quantum phenomena by means of the creation of new concepts. Following him, the particle has position and velocity but a quantum potential exists also which is the cause of all the not local phenomena.  In the ontological vision of Bohm what we have is not locality and not indivisibility.

Indivisibility and its presuppositions

The presuppositions of indivisibility are two:

a) An experimental fact: the quantization of the action.

b) A linguistic thesis: the unicity of the common language.

In fact: if one accepts that is not possible to develop another language (which is the essence of the thesis of the unicity of the common language) and one observes that the language of classical physics is just a refinement of the common language that was developed precisely to describe the apparatuses and the experiences physics, one must conclude that for the description of the apparatuses and the experiences in physics it is not possible to go beyond the classical language.

Now then, the quantization of the action implies that it is not possible to account for that fact with the language of classical physics can realize, therefore that fact is an irreducible, or inexplicable fact, or better it is a fact not only not explicable but that do not require an explanation. Indivisibility is a consequence of the quantization of the action, therefore is not explicable and do not require an explanation. It is also an irreducible fact.

On the other hand, if one accepts the quantization of the action and the indivisibility as fundamental, irreducible facts, one has to conclude that there exists an inherent contextuality of the properties of a system, which implies the impossibility of an ontological description.  As a consequence the language could never be developed to describe reality in itself. We can not go beyond the language that we have. If indivisibility is accepted as an irreducible fact we must conclude then that our language is essentially fixed. In that sense it is unique.

Under the presupposition of the unicity of language, the indivisibility is a fact. Under the presupposition of the indivisibility as an irreducible fact, language is unique.

If one of the presuppositions is denied the other one is also denied.  That is to say, if the unicity of language is denied the indivisibility as an irreducible fact is denied and vice versa. We see then the logical consistency of the two presuppositions.

GENERAL CONCEPTION OF COMPLEMENTARITY

Extension of complementarity outside physics.

In quantum mechanics, complementary concepts exist that are mutually exclusive from the logical point of view, like the concepts of wave and particle, and concepts that are not logically exclusive, like those of position and precise moments. This means that the character of mutual exclusion, which is crucial for the identification of two concepts as complementary, is not determined by logic. This character is determined by the mutual exclusion of the experimental contexts that defines its use.

Now then, when it is affirmed that two concepts are complementary, and that therefore are mutually exclusive, what is meant is that both concepts cannot be used in the same reasoning. This implies that analysis, questions, inferences that involve the one excludes with analysis, questions, inferences that involve the other. Therefore, in respect to an electron, there cannot be talked about a trajectory, which implies the mental combination of the concepts of precise position and precise moment. Therefore also the duality wave-particle is resolved, because the experimental concepts which define the use of the concepts of wave and particle are mutually exclusive, which prohibits us from using both concepts in the same experimental context. We are not then confronted with a situation which obliges us to use the two concepts in the same context, which would be paradoxical because of the logical mutual exclusion of the two concepts.

The question about how to extend complementarity outside of the ambit of physics in which the experimental contexts are clearly defined is valid and arises naturally. And it becomes more important if fields where scientific observations are not made are considered. In relation to this type of question, it is important to remember the indissoluble relation that exists between experience and theory, a relation that implies that all experience is impregnated by theory, and that it is as precise and fallible as the theoretical framework that sustains it. Lastly, an experience is a network of concepts, and for that reason if two experiences are mutually exclusive this means that the networks of concepts linked to them are mutually exclusive.

The previous conclusion allows us to hope that complementarity can be extended to fields different from physics. If two networks of concepts are mutually exclusive, then so are all the reasoning based on these networks of concepts. But because they are complementary, both networks of concepts are required to exhaust all that can be known about the same object. Therefore we cannot hope to exhaust all the descriptions of the object with a single network of concepts. And neither can we hope for a description in terms of properties in themselves of the object, because all its properties appear to us as contextual, relative to a network of concepts that is not the only one possible about its behavior.

A PRECISE DEFINITION OF COMPLEMENTARITY

Bohr never gives a precise definition of the idea of complementarity. Einstein wrote on this subject that despite all the efforts which he had made he had not arrived to a precise formulation of the principle of complementarity of Bohr. The assertion of Einstein illustrates the difficulty to find a definition that Bohr himself by no means presented explicitly in his writings. I however believe that it is possible to define with precision the complementarity if one takes into account the linguistic theses of Bohr and his considerations on the fundamental impossibility to analyze the existence of the quantum of action  and the indivisibility which it confers  the quantum phenomena.

I present the following proposals like a precise definition of the mode complementary to description.

The meaning of the concepts

If the quantum phenomena are an indivisible wholeness which includes the instrument of observation, a possibility arises that concepts that result as valid in a given experimental context are not valid in a different experimental context. Within a conception in which the observed objects can be conceived completely separate from the observer, the observed properties can be attributed to the objects in a totally independent manner from the method of observation. They will be completely independent properties from the experimental context and there will not be any reason for not continue attributing them to the objects in totally different experimental contexts. If the quantities we measured are not, however, independent from the experimental context, nothing can assure us that we can attribute these to the objects in all experimental circumstances.

To decide then if one can use or not a given concept for describe the information obtained in a given quantum experience, it is necessary to keep in mind all the experimental arrangement.  If a concept turns out to be adequate for a given type of experience or given experimental arrangement, we are not therefore necessarily authorized to use it without restriction in any another type of experience or experimental arrangement.  It is possible that we can use it, it is possible that not.  Though it is true that the concepts are defined inside a theoretical structure and in that sense it can be affirmed that in a way they are defined by the theory, the indivisibility restricts now its use, and it is the experimental context, or better the type of experimental context, what defines if we can use or not a concept to describe the experience.

It is the experience what defines the use of the concept.  Now well, the meaning that we are giving to the word use is here extremely restrictive: if the type of experience does not permit the use of a concept it signifies that we cannot utilize it in our reasoning.  Thus, in the experience that permits us to use the concept of wave we cannot utilize in our reasoning the concept of particle.  The employ of that concept in our reasoning would lead us to a conflict, to a paradox.  That is to say, the employ of in that experience turns it into a meaningless concept. In other words relative to that experimental context the concept is meaningless.  Because of this we can affirm then that the meaning of a concept is defined only by means of a precise type of experimental context.

One must notice that what is being proposes is not a mere operational definition of the concepts.  What it is affirmed is that we are not authorized to utilize without restriction a concept whose use is sanctioned by a concrete type of experience, to account for any another type of arbitrary experience.

Mutually exclusive experiences and concepts.

The indivisibility opens then the possibility of mutually exclusive experiences and concepts: two concepts will be mutually excluding if the possibility does not exist to define their meaning by means of only one type of experience. In other words, in the case where the experimental contexts mutually exclude, the corresponding concepts will also be mutually exclusive. Two mutually excluding concepts cannot then be combined in the mind to have a conceptual single image.

The normal way of description

It is the manner as the common language is utilized in the ordinary life or in the classical physics.

The instrument and the interior of the quantum phenomenon

We have said that a quantum phenomenon is an indivisible wholeness which includes the instrument of observation.  In that totality, nevertheless, a fundamental distinction between the instrument and the remainder of the phenomenon should be done. In fact: if we want to have finally an experience, the unicity of the classical language requires that the description of the experimental arrangement and of the data be done in classical terms in order to make possible a communication without ambiguity of the experiment.  A part of the totality constituted by the phenomenon should then be described in the normal mode of description.  That part is the instrument. I propose to denominate the interior of the phenomenon, the remainder of the phenomenon which cannot be described in the normal mode of description. The interior is manifested in the instrument through an irreversible effect.  For example, the mark that leaves an electron in a photographic plate.

The quantum object.

On the other hand, when you go from an experimental context which allows to define, for example, the concept of position of an electron, to another mutually exclusive context which allows for defining of the concept velocity, both that which is interior and that which is instrument generally change. Nevertheless, something of the interior stays constant and this something, which in the case we are looking at is the very electron, is what I propose to call the quantum object. In other words there are couples of phenomena such that an aspect of their interior remains constant. I will call this aspect the quantum object and we will say that the two phenomena have the same quantum object.

To illustrate more the idea let us recall the example presented in the section were the role of the instrument was presented. In the experience that permits us to observe the interference of electrons, the instrument is constituted by the source, the two diaphragms and the plate and the interior is the beam of electrons. In the experience that allows us to know by which of the slits in the second diaphragm each electron passes through, the first diaphragm is not fixed but is hanging on a spring r in front of which there is an apparatus A that detects the movement. The instrument is constituted now by the source, the second diaphragm, the plate, the spring and the apparatus A. In that experience the first diaphragm no longer is part of the instrument. The interior is the beam of electrons and the first diaphragm. The quantum object in the two experiences is the beam of electrons.

Complementary experiences or phenomena.

Two experiences or phenomena will be complementary if they are mutually excluding and they have the same quantum object

Complementary concepts

We call complementary concepts those defined by mean of complementary phenomena. They are mutually excluding but necessary to exhaust all the information that can be defined about a same quantum object.

The complementary mode of description or complementarity

It is the manner of utilization of the language by means of complementary concepts.

We should recall that what decides, in the complementary mode of description, if is possible or not to combine two concepts in a single conceptual image, are the experiences by which the meaning of the concepts in question is defined and the existence or not of the possibility to combine in one alone the corresponding devices of measurement.

The frontier between the instrument and the interior of the quantum phenomenon.

If one goes from an experience A to an experience B complementary to A, what was considered the interior and was considered the instrument will change.  It can be affirmed that the frontier between the instrument and the interior change, that the frontier is a mobile one.

APPLICATIONS OF COMPLEMENTARITY

There are several proposals of possible uses of complementarity in different areas of knowledge. To discuss all of them will make this paper unduly long. I will present then here only those that I thing are more relevant for the general argument.

Complementarity in the relationship between the whole and the parts. Emergent properties.

There are several possible uses of complementarity that are frame-worked in the context of the relationship between the whole and the parts. The idea is that the whole and the parts are in a relationship of complementarity. If the context is not previously specified, any question about if all the properties of a whole are reduced to the properties of its parts is meaningless.

There is a context, in which the understanding of the whole is achieved by identifying its parts and the interactions between them. All the properties of the whole that make sense in this context are explained starting from the properties of their parts. None of those properties are emergent. In this context the analysis of the whole is enough to understand its properties. The whole is here conceptually subordinated to the parts. There is another context, mutually excluding with the previous one, in which the whole shows purely global, emergent properties which cannot be understood by means of the analysis in their parts. The emphasis here is on the whole that can be considered as indivisible. Since the study of the whole in that context is not carried out by means of the analysis in its parts, it is necessary to name it differently. It can be said that it is a synthetic and not an analytical study, although the synthetic word gives the idea of a synthesis that would be made starting from the parts identified by means of the analysis. Maybe it will be better to use the word global or holistic, for the study of the whole in this context. One would have then a complementarity between the analytical approach and the global or holistic approach.

In the context of the analytical approach all the questions are solved in terms of the interactions of the parts. There it makes plain sense to affirm that the whole is no more than the aggregate of its parts, because no property is emergent. In the context of the global or holistic approach there are properties that can not be understood from the parts and their interactions. Both contexts are necessary to understand all the properties of the whole, some of which are explained in a reductionist way and others should be considered as emergent.

In summary we have a complementarity between the whole and the parts. Or rather: between the language of the whole and the language of the parts. We have also a complementarity between the analytical, reductionist approach and the global, holistic approach.

Complementarity between sociology and psychology

Psychology would be the language of the parts: the individuals. It would form the context in which it can be considered that the fundamental parts of society, the individuals, have a great complexity of interactions, from which something arises which is the social phenomena. In that context society is considered the fruit of the human beings. There the individual and the psychological phenomena are the fundamental aspects. There would be then social elements that are reduced to the interactions between the individuals.

Sociology would be the language of the whole: the society. It would constitute the context in which it can be considered that every human being is born in a social environment that is external, imposed to him; a fact over which he does not have any option. In that context it can be affirmed that the human being is fruit of the society. There the social, the sociological phenomena, are fundamental. Social emergent elements would then exist.

Both contexts, that in which the individual is fundamental and that in which the social is fundamental would be mutually exclusive, but both necessary to exhaust all that can be known of that highly complex system that is society.

It would not make any sense then to ask what is fundamental, if society or the individual, unless the context in which the question is asked is specified.

Other proposals are: complementarity between Dynamics and Thermodynamics, complementarity in biology, complementarity in psychology, and complementarity between the teleological approach and the approach in terms of efficient cause.

Complementarity in Moral

In moral issues teleology is expressed in terms of free will. If in biology one can argue that teleology, in the sense of a design, can be rejected for the sake of a program that invokes embryology and evolution, in matters of moral responsibility seems impossible to banish the teleological ideas. If it is considered that, supposing that even the biological phenomena are reduced to the description only in terms of efficient causes, the human being is exhausted as body with that type of description, with that network of concepts, as a mind the human being requires another conceptual network, another context which is eminently teleological. Questions that don’t make sense in one context will do so in another. But it is necessary to consider both networks of concepts to respond to all the questions that arise in the human phenomenon.

Let us analyze a little more the proposal of complementarity in Moral to define better what is being said and what is not being affirmed. It is sustained that there are two complementary contexts: a teleological context where questions about purposes, ends, and in general of moral responsibility make sense, questions about the human being as a mind, as a spirit, and another non teleological context in terms of efficient causes in which questions about the human being as a body make sense. We can consider the first context as that in which questions relating to the spiritual aspect of the human being are asked, while the second context is that in which the questions make reference to the purely material or animal aspect of the human being. Only in the network of concepts of the spiritual aspect do moral questions make sense.

Complementarity between the humanistic approach and the scientific approach

This use of complementarity is intimately related with the one that we have just considered. The culture or the humanistic approach, with their emphasis on that which is properly human, that includes the mind, morals, the ends and purposes, is deeply at odds with the culture or purely scientific approach where the elimination of the slightest sign of teleology is invoked. Complementarity between the context where only scientific questions make sense and the context where the humanistic questions about the human being are framed, would resolve the conflict and would form a bridge between the denominated abyss between the two, that perhaps cease to be so.

Complementarity mind body

Deeply related with the two previous uses of complementarity would be the complementarity between the language of the body and the language of the mind. That is to say between the network of concepts where questions about the mind make sense and the network where questions about the body are framed. This is how would be overcome the polemic about the primacy of one or the other aspect of the human being which has given origin to all forms of materialism faced with all forms of idealism.

Behind each use of complementarity there seems to be a type of totality or indivisibility. This is a point that is necessary to investigate in each use of complementarity. In quantum physics one confronts the indivisibility of the quantum phenomenon that constitutes a totality that includes the instrument of observation. In thermodynamics there also seems to be an indivisibility that would be behind the complementarity between dynamics and thermodynamics. In biology would be a matter of the totality of the organism. In psychology there would be the indivisibility of the ego that observes and the conscience that is observed. In the human being the indivisibility of mind and body. In general one would have the human experience as a totality that includes the same human being as subject of the experience.

SOME CONCLUSIONS

Complementarity sustains that the phenomenal world is shown as composed by mutually exclusive but necessary experiences to exhaust all the possible information about an object. The networks of corresponding concepts are therefore mutually exclusive but necessary to exhaust the knowledge of the object. The properties of the object are not in themselves but rather contextual; relative to a network of concepts that is not the only possible one.

Complementarity opposes conceptual or philosophical monism,because it sustains that a unique conceptual network doesn’t exist to contain all phenomena. The world shows up as multicontextual, in a variety of necessary but mutually exclusive contexts. Now, although complementarity sustains that each experience is relative to a context, it should be remembered that once the context has been found, the use of the language is once and for all fixed.

The descriptions that are framed in mutually exclusive contexts are in turn mutually exclusive descriptions of phenomenal reality. Each one is however correct, true, relative to their context. But that context is defined in an interaction between the subject that knows and a reality that not for being empirical ceases to be external to the subject’s mind. The context, and therefore the truth of each description, is not something that is defined by a mere socio-linguistic agreement. Far from invoking a cultural or social relativism, complementarity rather recognizes the fact that the experience is much richer than the language that cannot include it with a single contextual network. Complementarity implies that the idea of a unique description of reality that can be formulated in the human language seems doomed to failure.

The deterministic descriptions and those that include final causes are not now antagonistic but rather complementary. It is what one has in the case of the description of the total human experience.

It is no longer possible to conceptually erase the observer. The phenomenal reality is presented as structured in mutually exclusive experiences and it is the observer that defines the type of experience. But once elected the experience the concepts remain fixed. Although the phenomenal reality is external to the subject it is not independent from him. The old metaphor of the world as a book can illustrate the idea of a reality external to the subject but however inconceivable without the subject’s existence. This reality is even conceivable with an existence previous in time to the existence of the subject. Let us imagine in fact that somebody writes a book for their future descendants. The book exists before its future readers but it cannot be conceived independently of their existence because it is structured so that they can read it. The future reader is therefore implicit in the book. The book has an external and previous in time existence to the existence of its reader but that existence is not independent of the reader’s existence.

The whole and the parts have a relationship of complementarity. There are contexts in which it can be considered that the properties of the whole are completely understood starting from the properties of the parts. In that context one can plainly affirm that the whole is made up of parts and doesn’t have emergent properties. In turn there are contexts in which properties exist of the whole that are emergent, that are not reduced to the mere interactions between the parts. Both types of contexts are mutually exclusive but they are necessary to exhaust all the information about the whole.

Complementarity as an antidote against dogmatism

Questions about freedom and the moral responsibility that involve decisions, purposes and goals, don’t make sense in a context, in a network of concepts in which teleological descriptions don’t fit. If it is considered that it should be possible to respond to all the questions about the human being in that network of concepts, the obvious conclusion is that such questions don’t make sense, they are apparent, because the human being would not have any real freedom or any real moral responsibility. Science can again be invoked saying that psychology or sociology should finally explain that trend of the human being towards that which is moral, or that zeal to answer questions of a moral type. It is clear that if the only accepted context is that where any reference to final causes is rejected, the explanation of such sciences should be given within that context. That implies that what would be a matter of explanation, without appealing to final causes, would be the reason of that human need for believing in appearances, or the reason why it is perhaps necessary for the social cohesion or even for the possibility of the existence of a society that the individuals are convinced and have faith in something that in fact is not more than a chimera. Leaving aside how very little convincing such a type explanation can be for a human being facing morally important decisions, it is to be expected that in such a conceptually monistic position, any answer that is given inside a context where final causes are accepted will be rejected and even received with hostility. If that hostility increases with a high emotional dose, it is not strange to find as a result a poisonous and prosecuting dogmatism.

On the other hand, if it is considered that the only valid context to respond to all the questions about the human being is a context where teleology plays an important role, it is clear that questions that demand a network of concepts where the explanations in terms of final causes are not accepted, would be considered senseless questions. It won’t be strange then that the rejection to the network of concepts that don’t include teleology is translated in an acerb, poisonous and intransigent dogmatism.

All pretensions to reduce the human experience to a single network of concepts only lead then to dogmatic positions that leave a great number of valid concerns with regard to the human being without answer. Complementarity sustains that the human experience is too rich and complex to pretend to exhaust it with a single network of concepts, that the existence of mutually exclusive contexts should be admitted which should however be accepted to be able to give an explanation to all the vastness of the human experience.

Complementarity is not identified with relativism

Now then, the recognition of the existence of networks of mutually excluding contexts and of the truth relative to those contexts of the answers to the human queries does not mean that a type of cultural, social or linguistic relativism is being invoked.

In quantum mechanics, what define the contexts are the experiments and the network of concepts associated with them. In the case of the complementarity that would exist between psychology and sociology, the existence of two mutually exclusive contexts is sustained, one in which what is fundamental is the individuals, and what is derived or logically subordinated are the social aspects, and another in which what is fundamental is the social aspects, and what is logically subordinated are the individuals. It is supposed that the elements that compose each context are neither arbitrary, nor defined a priori, but rather they should be revealed by the scientific investigation. Among these elements will be the processes that happen in each context or are framed in each context, and the conceptual network associated with them. It is hoped that the investigation will permit to define those social aspects that are the mere fruit of the interactions between the individuals, and those aspects of the individual that are the fruit of that which is social. These last aspects will be considered as emergent because of not being reduced to the mere interactions between the parts of the social which are basically the individuals. In the proposed complementarity in no way there is a type of socio linguistic agreement implied that defines the contexts.

It is supposed in addition that the existence of the complementary contexts is independent from the form of the culture. The content of the contexts will depend on the culture but not the complementary structure of what is socio-psychological.

Complementarity accepts an empiric reality that is external to the subject, which does not arbitrarily define the contexts in which his questions make sense. The subject exists and the empirical reality exists, and the fact that the empirical reality is not independent of the existence of the subject does not mean that it is an invention of this last one, like the fact that the human being is not independent from the existence of the society in which he or she lives doesn’t mean that he or she doesn’t exist. Rather complementarity recognizes that the subject and the empirical reality constitute an indivisible wholeness in which both aspects, the subject and the empirical reality, have an existence. A different matter is if besides that empiric reality finally a reality in itself exists that can give an explanation to the natural questions that arise from the deep relationship between the empirical reality and the subject for whom that reality appears. We will speak briefly of this topic in the section that follows.

Complementarity and Reality in itself.

Complementarity does not necessarily commit us with non-realism. To accept it as an epistemological principle does not imply the acceptance of a non ontological position. d’Espagnat, for example, has a realistic position but accepts quantum mechanics as a complete theory and speaks about a complementarity between mind and matter. Complementarity allows for grounds of dialogue between objectivists and non objectivists. One of its great virtues is that it is useful both for agnostics about what is Real, as it seems it was Bohr, as for convinced realists such as d’Espagnat.

In conclusion: the acceptance of the epistemology of Bohr and of the empiric character of physical reality, doesn’t commit us then necessarily with a total rejection of the notion of independent reality.

CLOSING REFLEXIONS

It is important at the closing of this paper to state in an explicit manner what is the invoked reason to hope that complementarity will be play a leading role in epistemology in general. In others words what is the reason to expect that the phenomenal world is shown as composed by mutually exclusive but necessary experiences to exhaust all the possible information about an object. The proposed raison d’être of complementarity is metaphysical. It starts with God and His creation as a manifestation of His attributes.

The creation is indivisible, but of an infinite complexity. If it is the creation of an infinite God then it is also of an infinite complexity. Unity, fundamental attribute of God, is manifested in an infinite diversity and complexity to the finite mind of man. This complexity has as a consequence the impotence of human language to explain the entirety of the dimensions of the Real with a single system of knowledge. As we saw, in Science one find experimental contexts with mutually exclusive aspects that nevertheless share the same object of knowledge. This makes it necessary, in order to exhaust everything that can be known about the object, the use, in a new form of description: the complementary form, of the associated concepts with each context. We said that in quantum mechanics is where complementarity is manifested in the most precise manner due to the highly abstract and formal character of theory. It is in this theory where the relation between indivisibility and complementarity can be appreciated in its most precise manner. It is in the ambit of this theory where one can try to develop a more precise idea of complementarity, with the aim of be more sure or have a better guide about how to apply this complementarity in different contexts. In quantum mechanics, as we show, the indivisible is the quantum phenomenon which includes the whole observational arrangement and therefore the observer. Complementarity indicates that in the dominions where there is an indivisibility which includes the observer, the language must be employed in a complementary mode of description.

If we think about Reality in its entirety, in its spiritual and material dimensions, it is natural to anticipate then that the observer, who is part of this immense totality, cannot expect to encompass it all with one system of knowledge. If Science shows us that not even with respect to the experiences about the unanimated material world, can the observer be considered separate from the object, if not even this kingdom which we can say is the most simple in the creation, can the observer hope to encompass with a single system of knowledge, much less can the subject pretend to be able to encompass all the infinite complexity of the creation, in its spiritual and material dimensions, with a single system of knowledge.

REFERENCES

Bohr, N., 1934. Atomic Theory and the Description of Nature. Cambridge University Press,Cambridge.

Bohr, N., 1957. Physique atomique et connaisance humaine. Gauthiers Villards, Paris.

Bohr, N. 1963.Essays 1958-1962 on Atomic Physics and Human Knowledge. Interscience Publishers, New York.

Roldán, J.; Language, Mécanique Quantique et Réalité; Université de Paris, Panthéon-Sorbonne, 1991.

d´Espagnat, B., Une incertain réalité, Gauthier Villars, 1985.