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.
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.
While physicists pursue the search for the Grand Unified Theory (GUT) and the expedition to find the Higgs that ought to solidify the Standard Model, philosophers keep inquiring as to what the nature of matter and mind might be and propose various theories. At first sight, the high energy physicist or the philosopher, both human, and the elementary particle seem to have nothing in common, however we contend and argue in this paper that we are looking at different scales of what constitutes universal behaviour and use Herman Dooyeweerd's theory of Modal Aspects to bridge the particle to the mind. To other than a physicist the dual nature of the atom or the so-called elementary particles may be difficult to comprehend and certainly appears unfathomable to intuit. This is due to the fact that the dual nature of matter finds its anchoring within the theoretical and mathematical frameworks provided by quantum mechanics, the latter tends to not be easily accessible to most individual's intuition. What would the consequences be if human nature itself had a dual character? We all know that human nature is both egoistic and altruistic, however it is not often that one considers the fact that egoism is an individual behaviour, while altruism is a collective behaviour. Likewise a particle is an individual manifestation of what we call matter, while wave nature can be considered characteristic of collective behaviour of the same matter.
Recent advances in experimental physics—the queen of reductionist science—aimed at solving the mysteries of the quantum world has led to a deepening of the mystery rather than easing it, dispelling the EPR paradox and pointing out a conceptional error in this now famous gedanken experiment, while lending some authority and validation to quantum mechanics. The strange features of the quantum world are founded on what Bohr dubbed complementarity, or the way a sub-particle entity can behave either as a wave or as a particle; and on Werner Heisenberg's uncertainty principle, which says that a quantum entity such as an electron does not avail itself to a deterministic exact measurement of both position and momentum simultaneously. Such postulates seem to contradict deeply held assumptions by the deterministic and materialistically oriented world of experimental physics where everything, including the atom, can be reduced to a single aspect. There are mounting calls for newer ways of understanding reality that are capable of handling these apparently strange incomprehensible phenomena revealed through the classical observation of the microscopic quantum world. There is also fundamental progress made in bouncing cosmology theories that bridge general relativity to quantum mechanics and provide some insight into the nature of the universe and its transition and pre-history through the big bang.
The thrust of this paper evolves around two pillars. One, is that that the apparent logical fissure emergent in reductionist thought, coming from orthodox science and the application of the scientific method that is manifest in what we know and do not understand in quantum mechanics, can be liaised to our intellectual understanding through the perspective offered by Herman Dooyeweerd's theory of Modal Aspects. The other, is the central and special role humans have in relation to the universe. Through this approach, we will argue that the dual nature of the atom or elementary particles is, rather than being a strange phenomenon, in fact an essential characteristic of what constitutes its nature
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.
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”.
I present a perspective in which the mathematical constant π, traditionally considered a mere geometric ratio of a circle’s circumference to its diameter, emerges as a fundamental invariant in quantum physics. While π has long been recognized for its central role in mathematics and classical physics—appearing in trigonometry, wave phenomena, harmonic oscillators, and statistical distributions—its ubiquity in the quantum domain reveals a deeper structural significance. In this work, I demonstrate that π is indispensable for the normalization of quantum wavefunctions, appearing naturally in Gaussian integrals, and is equally essential in Fourier transforms, ensuring the unitarity of transformations between conjugate variables such as position and momentum. Beyond these mathematical appearances, π is embedded in the very definition of Planck’s reduced constant (ħ = h / 2π), suggesting that it underlies the quantization of action and the discrete structure of phase space. By framing π as a quantum invariant, I argue that it is not merely an artifact of geometry or algebra but a universal constant that governs coherence, symmetry, and continuity in physical systems. Its recurring presence in quantum statistics, probability distributions, and density-of-states calculations indicates that π plays a central role in maintaining internal consistency within the quantum framework. This article inaugurates a series aimed at exploring π as a fundamental building block of quantum reality, bridging concepts from classical physics, quantum mechanics, and statistical theory. By revealing π as a structural constant rather than a mathematical convenience, I offer new perspectives on the underlying architecture of nature, with implications ranging from fundamental theory and quantum computation to cosmology and the interpretation of physical laws.
Quantum mechanics, despite its predictive power, lacks a coherent ontology—the "mechanism" its name implies. Wave-particle duality, entanglement, and the indispensability of complex numbers remain mysteries, suggesting the theory may be incomplete in principle. Drawing on the Physical Information Cosmology (PIC) framework—where the universe emerges via a two-stage phase transition from a conserved Physical Information vacuum—we propose that quantum entities are not particles or waves but three-dimensional projections of higher-dimensional "Physical Information Packets." Each packet inherently possesses three superimposed potentialities: informaticity (correlation), energeticity (wave), and substantiality (matter). This triadic structure, which we term the Information-Wave-Particle Triality, is a direct consequence of the recursive partial transitions (information→energy→matter) at cosmic genesis. We demonstrate that wave-particle duality arises from measurement coupling with either energetic or substantial potentials; the uncertainty principle reflects the mutual exclusivity of these observational modes; and entanglement is the informaticity dimension becoming manifest. The complex number structure of quantum mechanics is shown to be the necessary algebraic representation of a system with two orthogonal ontic dimensions (substance and energy). This framework explains why Bell inequality violations are inevitable from a local perspective within a globally structured tetrahedral universe. It offers a parsimonious, testable ontology that unifies quantum phenomena under the same conserved Physical Information from which all reality emerges. In this picture, PIC plays its own dice—the probabilities of quantum mechanics are not a mark of incompleteness, but the necessary manifestation of the information-energy-matter triality rooted in cosmic genesis.
It has become ever more clear over the past 70 years that reality is best described by a theory that no one fully understands and which cannot be applied to most everyday phenomena. Quantum theory has been subjected to many stringent tests and all of its predictions, however strange, have always been borne out. Originally developed to account for why atoms do not collapse and why they radiate and absorb energy in discrete amounts (quanta), it has now gone far beyond these rather simple beginnings. It is essentially a mathematical theory, so trying to describe it in words is analogous to transforming a picture into a poem. Inaccuracies, distortions and over-simplifications inevitably creep in. Nevertheless, one can convey the essence of the picture, and that is what is attempted here. Some grasp of what the material world is really like, and of the unfamiliar ways in which it can behave, is probably necessary to reaching an understanding of awareness and is certainly needed to comprehend the experimental evidence set out in Chapter 5.