QUANTUM MECHANICS: THE REAL AND THE POSSIBLE

GIUSEPPE BOSCARINO

Sortino (Siracusa)

Pre-print a cura dell’autore. Originale pubblicato su The Foundations of Quantum Mechanics, Historical Analysis and Open Questions, Lecce (Italy), 13-16 october 1998 editors C. Garola & A. Rossi, University of Lecce, Italy, World Scientific

It is argued that in the history of western culture two traditions of thought, the Italic, or Pythagorean-Democritean, and the Ionic, or Platonic-Aristotelian, have contended the conception of science. The attempt made by many people to base modern science, or quantum mechanics, on the concept of dýnamis - potentia of Aristotelian origin is shown to be fragile and contradictory.

There is a curious, not to say startling, fact in the philosophical-epistemological reflections on the foundations of quantum mechanics made by some of its founders and modern interpreters, such as Popper.

On the one hand, they say that the fathers of modern science were undoubtedly Galilei and Newton, on the other hand, they recognize in Aristotle’s natural philosophy, in his polymorphous concept of dýnamis, “potentia”, potentiality, possibility, etc., the philosophic-epistemological foundation on which modern Q.M. would be based.

Heisenberg, one of its founders, is convinced that [1]:

The concept of possibility, a concept that had a crucial role in Aristotle’s philosophy, is regaining a central position in modern physics. In his opinion, quantum theory mathematical laws can be interpreted as a quantitative formulation of Aristotle’s concept of dýnamis or potentia. This concept of possibility stays halfway between the concept of objective material reality and the concept of spiritual, that is subjective, reality.

Again in Heisenberg’s opinion [2]:

the probability waves of Bohr, Kramers, and Slater can be interpreted as a quantitative formulation of Aristotle’s concept of dýnamis, possibility, later also called with the Latin name of potentia. Possibility, or “tendency” of a fact to happen, possesses a sort of truth in Aristotle’s philosophy. This truth stays halfway between the solid truth of matter and the spiritual truth of idea or image. In modem Q.T., he maintains, this concept of possibility takes on a new appearance: it has a quantitative formulation like a probability and it obeys mathematically expressable natural laws. Here, natural laws expressed in mathematical terms do not any more determine the phenomena in themselves, but their possibility, the probability that something happens.

The concept of complementarity itself, which Bohr devises to save the contradictory aspects that quantum objects would reveal in experiments, and which lays the foundations of his quantum interpretation, is grounded on the concept of possibility or potentiality. If an object reveals itself now as A and then as non-A, for instance now as a wave and then as a particle, this means that it has no determined reality, but it expresses mere potentialities, possibilities. Consequently, it at one time appears as A and at some other time as non-A.

Literature has already underlined the role played by Kirkegaard’s existential philosophy of possibility and the contingentism of the beginning of this century in Bohr’s formulation of his principle of complementarity [3].

This Neo-Aristotelian philosophy of reality as possibility, potentiality, has in the long run influenced a kind of Marxism not only in the field of science but also in the philosophical field [4]. Its promoters thought to revive and bring up to date the old dialectical materialism of Engelsian memory with their ridiculous philosophical-epistemological vocabulary, a real parody of the Hegelian one, linking it up with the so-called new (!?) concepts derived from modem Q.M.. Among the new concepts which according to the Marxist physicist Fock are introduced by Q.M., there is, besides the one of relativity to the means of observation, etc., the concept of potential possibility [5]:

The probability distribution, he writes, reflects the potential possibilities objectively existent in the given conditions.

With reference to this, the epistemologist Tagliagambe comments [6]:

The state of the object, described by the function ψ, is quite objective, in the sense that it represents the characterization, independent from the observer, of the potential possibilities contained in the initial experiment. However, this objective state is not real yet, since the realization of the potentially possible takes place in the registration phase only. In this way, quantum mechanics manages to solve the rigid metaphysical contraposition between possibility and reality that classical physics believed to have solved by making an end of the category of possibility, that is by negating it in general.

Then Tagliagambe continues [7]:

In Fock’s opinion it is possible to consider the interpretation of Q.M. based on the principle of complementarity a theory perfectly suitable to the requirements indicated by dialectical Marxism. The solutions it proposes (for cxample, the removal of the contradictions between the undulatory nature and the corpuscular nature of the electron, between possibility and reality, between causality and probability) represent a series of clear examples of the application of dialectic to the problems of science of nature, and hence they can and must constitute a powerful stimulus for the development of materialistic-dialectical gnoseology.

Even the philosopher of science Popper, who was not a Marxist (on the contrary, he was one of the main critics of Marxism from an epistemological viewpoint) and who through his long life remained, in his own words, a “realist” against the subjectivistic interpretation of the Copenhagen school, ended up, with his propensional interpretation of probability and Q.M., by mixing his realism with the philosophy of possibility and tendencies of the Aristotelian type.

Imitating the style of the Ionic philosophers, the last Popper writes that All is propensity. Expressed in Aristotle’s terminology, this can, in his opinion, mean that [8]:

the being is the actualization of a propensity to become.

Then he writes [9]:

I propose to interpret these “weights” of the possibilities (or possible cases) as measures of the propensity, or tendency, of a possibility to realize itself upon repetition.

Within this propensionistical philosophy, Popper thinks he can solve the QM wave-particle difficuity. As a matter of fact, he believes that QT is, in a very precise sense, a particle theory (he disagrees with Schrödinger on this point) and that it is so in a way that excludes a dualism, or an analogy, or a complementarity, between particles and waves. In short, he is convinced that waves are mathematical representations of propensities, or dispositional properties, of the physical situation (like the experimental device) that can be interpreted as a propensity of the particles to assume certain states. For him, propensities and propensity fields are as real as forces and force lines. Like forces, they are dispositional properties [10].

Lastly, the fact becomes more and more disconcerting as this alleged foundation of science on the category of possibility takes shape within what today is called the third scientific revolution, the so-called new science of chaos, aimed, as they write, at saving mutation, becoming, change and time from the motionless and unchangeable world of classical physics, including Q.M. and relativity.

To further reinforce what I write I shall quote a short passage from Prigogine, one of the main authors of this new (?!) philosophical-epistemological position [11]:

Chaos appears now as a unifying element, not as an obstacle, and “the laws of nature”, conceived as “the laws of chaos”, do not describe any more a close world, subjected to a deterministic intellegibility, but an open world, where the category of probability, that is of possibility, is fundamental.

Thus, the philosophy of potentialities of Aristotelian memory seems to triumph all over the field.

And yet, Galilei and Newton had to fight a strenuous battle against Aristotle’s alleged philosophy-science in order to be able to lay the foundation of modern science, which after all was the continuation of the ancient Italic scientific-philosophical tradition of Phythagorean-Democritean-Archimedean origin in antithesis with the other equally ancient tradition, the Ionic one.

In reality, the category of possibility or potentiality is intrinsic to Q.M. theoretical structure itself.

It is maintained that the measurement of an “observable”, for instance the position of a particle, expressed by a Hermitian operator, the eigenvalues of which give the possible results of the measures, in our case of the positions, causes the wave function ψ to precipitate, which in its turn expresses the overlap of all the possible eigenstates of the particle, that is all its possible positions, in one of these, the probability of which is equal to the absolute squared value |ψ|².

Thus, ψ expresses in QT the overlap of the different potentialities of the observable, still in our case, the possible positions of the particle, while the measurement operation expresses the act through which one of these passes to being, since before that it was not yet, as it was a mere potentiality.

We can, therefore, state in Aristotle’s language, which so much pleases our Neo-Aristotelians [12]:

What has the potency of being can be and cannot be (και ειναι και μη ειναι),

that is to say, “an eigenstate, as it has the potency of being”, can be and not be. A particle can be in a position or it cannot be, but we do not say that it can be and not be at the same time. This would violate the principle of non-contradiction, as it would be against reason the fact that, since a particle can occupy one position or another with different possibilities, it has not, therefore, any position in itself, independently from the act of measumement, as Q.T. maintains.

Aristotle himself forbids this against our Aristotelians. For him, in fact, to be in a place (το ον εν τοπω) [13] is a constitutive mode of being of entities, one of their categories. For him, an entity without being in a place makes no sense.

For Euclides, the absurd, the impossible, the contradictory is the ατοπον, which literally means the placeless.

A body without a position is, therefore, an impossible, a non-real, an absurd, while a body with a position is a possible, a real, a non-absurd; the positions compatible or incompatible with it are its potentialities or impotencies.

In reality, the quotations from our Aristotelians, as well as Aristotle’s pages on possibility or potentiality, are vague, obscure and prolix. It is difficult to make out what they mean, the Neo-Aristotelians’ language is vague, as they do not say what they mean by possibility or potentiality, in what sense these terms are used, whether they have the same meaning or not. Aristotle’s language, besides being vague, is very prolix and obscure.

After all, both refer to the same tradition of thought, subtended to their philosophy, the empiricist one, which is the Ionics’ philosophy as well as Aristotle’s, who thinks he can found the scientific knowledge on observations and sensations, sponging out the role of reason in the building of science, which is the one founded by the Italic tradition of Pythagoras, Parmenides, Democritus, Euclides, Archimedes, later revived by Galilei and Newton.

A short historical-critical reflection on the concept of possible and potential is, therefore, necessary to try to specify and separate the meanings of the two terms in the two traditions of thought, which contended in history for the way of conceiving science, a strife extended afterwards to the Q.M. interpretation and developing at last a criticism to the so-called dialectical materialism mixed with Bohr’s complementarity.

The category of the possible has always been in history a real puzzle or, to put it in the words of a great contemporary philosopher, Bloch, a “cross”.

It will be enough to take a quick look at the different and opposing definitions that any dictionary of philosophy gives of the “possible”. Let’s take the case, for instance, of that one who is considered the founder of modal logic, and by our modern Aristotelians, the founder of the conception of reality as possibility-potentiality.

In Analitica Priora, the “possible” is defined as “what is neither necessarily true nor necessarily false”, while in Metaphysics Aristotle writes that [14]:

Possible (dýnatón) in one sense means what is not necessarily false, in another what is true, in a third what can be true.

In one passage from Metaphysics, he identifies the possible (dýnatón) with the matter (υλη), and in another the “possible” is no longer the property of the proposition, but of the thing [15]:

A thing is possible if it does not meet with any impossibility in attaining the act of which it is said to have the potency.

The difficuity in the medieval language was evidenced by the fact that it was not clear whether the possible meant the thing, de re, or else the proposition, de dictu.

As an example of this difficulty, St. Thomas cited the proposition: Album potest esse nigrum (It is possible that white becomes black).

It is clear that if the possible is predicated of the “white thing”, then the proposition is certainly false. But if the possible is predicated of the proposition “white becomes black”, the proposition is true. In fact, if I have defincd “white = what is not black”, having previously given the property of black, it is evident that the proposition is false, hence impossible. But if I say that “to be white is an apparent property”, so that white can become black thanks to the underlying objects, which aggregate or disaggregate beyond the apparent things, then the proposition is true, hence possible.

But not everything can mutate, there must exist something immutable in the mutation of things. This is the “atom-idea” of the Italic tradition. As such, it is indivisible and eternal. Together with the “void”, it makes possible “the mutation of things”, the “passage from potency to act”, which without them would be contradictory, impossible.

The same can be said of the electron. If in theory it is defined as a particle, then it cannot become a wave, which can only be an apparent property of it. The truth is that any modal proposition on the possible is incomplete. The possible is defined each time within a theory which defines its primitive entities that satisfy some axioms, on the base of which some things are possible, some other things are impossible. Now, QM does not say in its axioms what is spoken of, since they only refer to linear operators in Hiibert’s abstract spaces, to vectors of these spaces and to probability measures (hence numbers). In Q.T., physical quantities, such as “energy and motion quantity”, are substituted by differential operators, by mathematical symbols, which if required can supply a number, which is no longer a ratio between physical quantities but a frequency of observations.

But let’s go back to Aristotle, for whom potency (dýnamis) is something else. Its fundamental meaning is [16]:

“principle that causes a change into another object or the same object as other”.

Now, which meaning of Aristotle’s “possible” do our Aristotelians refer to? And if “potency” (dýnamos) means a principle of change into another object or in itseif, in QM there is no objective principle of change of potentialities, since it is the observer that produces the so-called wave collapse, that is to say the passage from potency to act.

But then again, we read in Aristotle that act precedes potency and that there is no passage from potency to act except in what is already act. Potentialities are the appearance, since what becomes is already act, indeed it was already act. The essence that becomes and reveals itself is what was being (in Aristotle’s language: το τι ην ειναι, which the Latins translated “quod quid erat esse”). In Aristotle’s finalistic universe all is preordained from the beginning, what appears at the end was already at the beginning.

Thus, the reference to Aristotle appears not only confused but also incorrect on the historiographical level, although his prolix and obscure prose allows many interpretations and readings. Our Aristotelians, then, should have said which meaning of “possible” and “potential” they refer to.

The truth is that both Bohr and Heisenberg want to overturn the philosophical paradigm of the ancient Italic science that goes under the names of Pythagoras, Parmenides, Democritus, Euclides and Archimedes by opposing to the clear meanings of their terms of “possible” and “potential” Aristotle’s obscure concept of dýnamis-dynatón, thus evoking fanciful “spiritual realities” that have nothing to do either with physics or with a clear and, on the rational level, debatable philosophy of the possible and the potential.

Apart from the empty talks on the dialectical overcoming of the “possible-real” contradiction and on propensities (in Popper it is impossible to understand whether “propensities” are a number, a physical quantity, or a property of the experimental device), neither Marxists nor anti-Marxists were able to oppose a clear logical-dialectical vision of “possible, real and potential” such as the one expressed in the ancient science of Italic matrix.

According to this, reality is not given by the senses and observations, but by renson starting from ideal entities built with the properties that it abstracts from sensible things and explains thanks to these entities. Observations and measurements control our rational buildings, which constitute the theory, do not found the theory [17].

These ideal entities must be built starting from concrete physical operations (with ruler, compasses, lever, etc.) and thought in a non-contradictory way, since only in this way it can be said of them that they are.

For Parmenides and Euclides the following equalities are valid:

1. Possible = non-contradictory = real = necessary = true.

2. Impossible = contradictory = non-real = absurd = false.

Of the being it cannot be said that it is and that it is not. For Parmenides, the non-contradictory, real entity can be perceived by the rational element only, since phenomena show us contrasting aspects. In a famous fragment he writes [18]:

To think and to be are the same thing.

Following Parmenides’ logic, Democritus says: Atoms and void are possible since they are non-contradictory entities, hence real, hence ideas.

According to some doxographers, Democritus called atoms and void ideas since they are elements of reality.

Democritus follows not only Parmenides’ logic but also Pythagoras’ principle that contraries are the principles of things [19].

Atoms and void are the ones the contrary of the other, A, non-A, and they are principles. Democritus called the one the being, the other the not being.

A, non-A are, therefore, the possible, the real, the necessary, what remains for ever identical to itself, the immutable.

The union of A, non-A is, on the other hand, the whole being, nature, the world of appearances, what changes and becomes through time.

1. AUnon-A is, therefore, the potential, all that nature can reveal, the different unions of atoms and void, without the ones passing into the other, as this is forbidden by Parmenides’ logic, since what is cannot become what is not.

The nothing, the absurd cannot be, it is the intersection of A, non-A.

2. A∩non-A = Nothing = Non-real = Impossible = Non-potential.

The ancient science of Parmenides, Democritus, Euclides, Archimedes and afterwards of Galilei and Newton does not deny the potential, and hence mutation, change, time!

It denies an unreal possible, as contradictory in itself, as Diodorus Cronus asserted, interpreting Parmenides’ thought. A possible that is not real is intrinsically impossible, hence contradictory, non-real, absurd, nothing.

It denies that the potential is the real, of which it can only be said that it is, while of the potential it is said that now it is and then it is not.

To assume the potential as the real is to assume the appearance (what now is and then is not) as the real (what is), but this is not possible in Parmenides’ logic, it is absurd.

To hypostatize in a subject the appearance, AUnon-A, transforming it in A∩non-A (the wave-particle), is for the ancient Italic science an absurd, an impossible.

To conclude, I would like to share some reflections on the materialistic-dialectical interpretation of Bohr’s complementarity and, more generally, of QM formalism.

In the dialectical materialism it is maintained that the law of reality is [20]:

the law of contradiction or the law of the opposites.

Is opposite equal to contradictory?

Opposite is a term defined each time within a precise universe of speech. There is the opposite of a number, of a force, of a vector, etc. Opposite is a property of an individual, while contradictory is a property predicated of a set of propositions, thus of language, not of reality, which according to the ancient Italic thinkers Parmenides and Democritus must be thought in a coherent way. The fact is that in the senseless language of Hegel and Engels contradictory is confused with complementary, the union of entities with the intersection of complementaries, which is the nothing, the non-thinkable and non-speakable of Parmenides and Peano.

The contradiction is to state A∩non-A = True. This is not possibie, since it is false. To assume A∩non-A as the law of reality, as the definition of possible, understood as what now is not and then is, or worse as what is and is not, is to assume the nothing as the law and the principle of the reality.

On the contrary, to assume AUnon-A as law of reality, that is the union of opposites, as the Pythagoreans said and Democritus maintained, is to say a possible thing, in the sense of potential, apparent, but not a possible thing in the sense of real.

If we want to give a sense, from a philosophical point of view, to the language of Bohr, Heisenberg, Aristotle, Hegel, Engels, it is necessary to write that in the potential, apparent reality what counts is the law of opposites, understood as the union of complementaries, which is what the Pythagoreans said and Democritus maintained, while the elements as possible-real-rational are something else.

Our thinkers, therefore, do not say anything new from this point of view, they do nothing but use an obscure and prolix, emotive and obscure, language with the purpose of changing the philosophical-epistemological paradigm of the Italic tradition.

References

1. W. Heisenberg, Physik und Philosophie, Stuttgart, 1960.

2. Ibidem.

3. M. Jammer, The Conceptual Development of Quantum Mechanics, McGraw-Hill, NewYork, 1966, pp. 166-180.

4. L’interpretazione materialistica della meccanica. Fisica e filosofia in URSS, S.Tagliagambe ed. Feltrinelli, 1972. See also the book of the Marxist philosopher E. Bloch, Das Prinzip Hoffnung.

5. Ibidem, p. 299.

6. Ibidem, p. 117.

7. Ibidem, p. 120.

8. K. R. Popper, Quantum Theory and the Schism in Physics, Hutchinson, London, 1982.

9. K. R. Popper, “Quantum mechanics without the ‘observer’ ”, in Quantum Theoty and Reality, M. Bunge, ed (Springer, New York, 1967), p. 32.

10. Ibidem.

11. Ilya Prigogine, Isabelle Stengers, La nouvelle alliance. Metamorphose de la science. Gallimard, Paris, 1979. Preface to the new Italian edition, Einaudi, Torino, 1992, p. XIII.

12. Aristotilis Metaphysica, θ, 8, Oxford University Press 1985.

13. Aristotle’s Physics, Δ, Oxford University Press 1979.

14. Aristotilis Metaphysica, Δ, 12.

15. Ibidem, Z, 7 e θ, 3.

16. Ibidem, Z, 7.

17. For a wider and deeper discussion on “paradigms, theories, experimental models and facts”, see G. Boscarino, S. Notarrigo, Meccanica quantistica: scienza o filosofia?, Laboratorio, Siracusa, 1997. On the two traditions of thought, the Italic and the Ionic, see, for a more precise comparison from a historical and philosophic-epistemological point of view, G. Boscarino, Tradizioni di pensiero. La tradizione italica della scienza e della realtà, La Scuola Italica, Sortino (SR), 1999.

18. Parmenide, La Nuova Italia, Firenze, 1958, Fr. 3, p.l30.

19. Aristotilis Metaphysica, A, 5.

20. F. Engels, Anti-Dühring.

21. M. Jammer, in his historical survey about the precedents of Bohr’s concept of complementarity, forgets to cite the Pythagoreans and their principle of contraries. See M. Jammer, The Philosophy of Quantum Mechanics, A Wiley-Interscience publication, New York, 1974, pp. 104-107.