It seems to be a priori impossible to formulate any general theory or model that encompasses all of the properties of complexity. So, one must make do with partial solutions. A possible approach we propose is to take inspiration from quantum theory, since there seems to be a strong analogy between complex systems and quantum systems. Although we do not propose any literal application of quantum mechanical formalism to complexity, we suggest that the language of quantum mechanics is already so well developed - and for a much wider spectrum of problems than most theories - that it can serve as a model for complexity theory. There are many problems common to both complex systems and quantum systems and we suggest that it might be useful to test the applicability of aspects of the “language” of quantum mechanics to a general complex system. What we suggest here is an interdisciplinary talk led between the natural sciences and philosophy, which we believe is the only way in which to deal with complexity “as such”.
It seems to be a priori impossible to formulate any general theory or model that encompasses all of the properties of complexity. So, one must make do with partial solutions. A possible approach we propose is to take inspiration from quantum theory, since there seems to be a strong analogy between complex systems and quantum systems. Although we do not propose any literal application of quantum mechanical formalism to complexity, we suggest that the language of quantum mechanics is already so well developed - and for a much wider spectrum of problems than most theories - that it can serve as a model for complexity theory. There are many problems common to both complex systems and quantum systems and we suggest that it might be useful to test the applicability of aspects of the “language” of quantum mechanics to a general complex system. What we suggest here is an interdisciplinary talk led between the natural sciences and philosophy, which we believe is the only way in which to deal with complexity “as such”.
Why should anyone think that what is so deeply puzzling about the quantum world is really a matter of logic? Why should anyone think that studying the logic of quantum mechanics should be a route to a proper understanding of quantum mechanics? There is a tradition in the philosophy of quantum mechanics, a tradition stronger among philosophical commentators than among physicists, which sees the subject as the business of understanding quantum mechanical language and the way that language relates to the world. It is an idea more strongly held by philosophers – it comes much more naturally to them – because the analytic tradition, in which most Anglo-American philosophers of science are raised, is generally much exercised about words and how they hook on to things. The analytic tradition in the philosophy of quantum mechanics is not unreasonable. Everyone admits that we cannot picture the microphysical world, that a graphic or iconic representation of quantum systems is impossible. Therefore understanding quantum mechanics must be a matter of understanding the logic of the words and the mathematics of quantum mechanics. If this seems implausible, it is because of an ambiguity in our use of the verb ‘to understand’. We understand the physical world, and we understand physics. But physics is not the physical world. It is something of an entirely different sort, a human product, a way of representing the world.
We have recently started to understand that fundamental aspects of complex systems such as emergence, the measurement problem, inherent uncertainty, complex causality in connection with unpredictable determinism, timeirreversibility and nonlocality all highlight the observer's participatory role in determining their workings. In addition, the principle of 'limited universality' in complex systems, which prompts us to search for the appropriate 'level of description in which unification and universality can be expected', looks like a version of Bohr's 'complementarity principle'. It is more or less certain that the different levels of description possible of a complex whole actually partial objectifications are projected on to and even redefine its constituent parts. Thus it is interesting that these fundamental complexity issues don't just bear a formal resemblance to, but reveal a profound connection with, quantum mechanics. Indeed, they point to a common origin on a deeper level of description.
The difficulties of the old quantum theory were largely dispelled by the development of quantum mechanics in the 1920s. First Heisenberg (1925) developed the rather abstract matrix mechanics and soon after Schro¨dinger (1926; see also Eckart, 1926) developed the physically more appealing wave mechanics. Subsequently he showed them to be mathematically equivalent. The physicists were greatly relieved; now they had once again a mathematical formalism that enabled the results of experiments to be calculated. It was possible to move forward. It is certainly a very elegant and indeed beautiful formalism, and does enable the results of many physical measurements to be calculated with great accuracy. It is used daily by atomic and nuclear physicists; there is no other way to make calculations. From the earliest days there has been intense debate about the interpretation of quantum mechanics, and it shows no signs of being settled; if anything it is becoming more intense over the years. As Penrose has remarked, no one understands quantum mechanics. Feynman (1967; see also Sykes, 1994) also admitted that ‘nobody understands quantum mechanics’, and Einstein once remarked: ‘I have thought a hundred times as much about the quantum problems as I have about general relativity theory’ (Pais, 1994, p. 57). It should therefore be evident that the most that can be done here is to try to show where the real difficulties lie, and how the failure to recognize that quantum mechanics is an essentially statistical theory has led to a series of confusing quantum paradoxes. It is just these paradoxes that have often been used to support theological speculations. It is useful to ask what ‘understanding quantum mechanics’ actually means. Certainly it means being able to calculate the results of many measurements. The same applies to Newton’s theory of gravitation, which we understand in the sense that we can use it as a basis of calculation, although we do not really understand the gravitational force itself. Very often, especially in modern physics, the mathematical formalism does not give us the sort of intuitive physical feeling for what is going on that we often obtain from classical mechanics. Perhaps we can never achieve more than this for quantum mechanics. In classical mechanics we can assume that a property that is measured objectively exists prior to the interaction of the measuring apparatus with the observed system. Quantum mechanics, however, ‘is incompatible with the proposition that measurement discovers some unknown but pre-existing property’ (Peres, 1997, p. 14). There is an important distinction between mysteries and absurdities. We may be forced to live with mysteries, but there is no reason why we should put up with absurdities such as the wave-particle duality, tunnelling through potential barriers, acausal events and the collapse of the wave function. These are the quantum paradoxes that will be discussed later on. They arise within the Copenhagen interpretation of quantum mechanics and are solved by other interpretations. These alternative interpretations enable us to make conjectures about what is going on, even though we cannot understand it in detail. This is acceptable and a stimulus to further research. It is certainly difficult enough to understand quantum mechanics, but there is no need to try to visualize logical absurdities in the effort to do so. Quantum mechanics is a mathematical formalism that makes it possible to calculate the results of some experiments. Anything more than this, such as questions about the interpretation of what is measured and whether it tells us what is actually going on in the system being studied, belongs to philosophy. Thus we are concerned here with what is essentially a philosophical debate; if it were just a matter of physics the debate would have been settled long ago. One of the difficulties is that it invokes the results of experiments and uses the language of quantum mechanics. Inevitably this language uses philosophical terms and then it is easy to give the impression that the philosophical propositions are in some way entailed by the physical results. These in turn can influence theological thinking. In order to be quite clear which arguments are justified and which are not, it is essential to separate the three levels of discourse: physical, philosophical and theological. Our task is to relate these together, and this immediately raises the traditional problems of the philosophy of science, including the relation of experiment to theory, and of theory to explanation. We begin by discussing experiments, distinguishing between those that are real and those that are imaginary.
At each level of hierarchy, especially in the relevant energies for the phenomena under study, various concepts and entities of physics emerge. While reducible to other levels that are smaller in size or higher in energy, many of those degrees of freedom are frozen and do not come into play, so that it is the emergent entities that are relevant. With examples such as temperature and phases of matter, this approach to complexity is seen as fundamental, with lessons also for emergent concepts in other sciences. In blurring over the coherences of quantum wave functions, classical mechanics,with its familiar concepts of position, momentum etc., is itself emergent from quantum physics. Much of the mystery of quantum physics lies in this distinction between the underlying reality, which is out of reach directly, but accessible only through these emergent concepts, however natural they may appear.
We have developed an app for iOS-based smart-phones/tablets that allows a 3-D, complex phase-based colorful visualization of hydrogen atom wave functions. Several important features of the quantum behavior of atomic orbitals can easily be made evident, thus making this app a useful companion in introductory modern physics classes. There are many reasons why quantum mechanical systems and phenomena are difficult both to teach and deeply understand. They are described by equations that are generally hard to visualize, and they often oppose the so-called “common sense” based on the human perception of the world, which is built on mental images such as locality and causality. Moreover students cannot have direct experience of those systems and solutions, and generally do not even have the possibility to refer to pictures, videos, or experiments to fill this gap. Teachers often encounter quite serious troubles in finding out a sensible way to speak about the wonders of quantum physics at the high school level, where complex formalisms are not accessible at all. One should however consider that this is quite a common issue in physics and, more generally, in science education. There are plenty of natural phenomena whose models (not only at microscopic and atomic levels) are of difficult, if not impossible, visualization. Just think of certain kinds of waves, fields of forces, velocities, energy, angular momentum, and so on. One should also notice that physical reality is not the same as the images we make of it. Pictures (formal, abstract ones, as well as artists' views) are a convenient bridge between these two aspects.
Since the beginning of the XXI st century, there has been a process of intense convergence and interpenetration of two seemingly opposing sciences – quantum mechanics and psychology. In accordance with it, the question arises about a common methodological foundation for these sciences. The article shows that the “first philosophy” of Aristotle can serve as a general philosophical methodology for these sciences. In the context of the metaphysical triad necessarypossible-real, the “intersection points” of A. I. Mirakyan’s transcendental psychology and A. Yu. Sevalnikov’s interpretation of quantum mechanics. The article examines the features of the formation of a new direction in modern psychology, which studies the problem of mental phenomena generation. At the same time, a comparison is made with the transcendentalism of Descartes, in which its limitations and incompleteness are revealed. It is shown that both in transcendental psychology and in quantum mechanics (W. Heisenberg) epistemological problems arise associated with the impossibility of using the language of their classical predecessors. In both sciences, it becomes necessary to apply a new language, a new way of thinking and a new logic of understanding the phenomena under study. All this allows us to conclude that both in transcendental psychology and in quantum mechanics, researchers are dealing with a new ontology of reality that differs from the reality studied in classical physics and in the phenomenology of classical psychology. The article substantiates that the main methodological reason limiting the possibilities of carrying out theoretical studies of deeper layers of reality is the use of the product (physical) approach. The product approach is based on the language used to describe the observed reality. It became necessary to divide reality into observable and unobservable. In the language of metaphysics of modalities, this is translated as «being in possibility» and «being in reality.» One of the “intersection points” of quantum mechanics and transcendental psychology is the category ofpossibility, in which the essence of reality is expressed, which both disciplines compared in this article seek to describe and explain