“Entangling” two areas of research so dissimilar seems a veiled mystery. Both expanding dramatically day by day are encapsulating the strangeness of the fractal nature and the paradoxical embodiment of the quantum world. Are we the witnesses of the significant shifts in the so-called “scientific revolution”? Or are we rebelling against the lives of research methods that long ago lost their usefulness to society and an ability to explain and predict? Or is it just an apparent perception of points of turbulence and instability?
In the last century, science has changed. Developments on the frontier of social science methodology are in what the collective has named “new science”- a general designation for the theories generated in separate different disciplines that do not exactly conform to the classical scientific explanation. This new “umbrella term” embraces physics, biology, linguistics, and psychology as well as new theories of chaos, quantum mechanics, and cognitive psychology, which make us rethink and reformulate a phenomenon that surrounds our daily life.
For an understanding of any – and I will extend to “new” –a phenomenon the first condition is the introduction of adequate concepts. Only with the help of correct concepts, we can really know what has been observed. So, as a rule, when we enter a new field new concepts are needed. Take for instance the concepts of classical physics. They are just a refinement of the concepts of daily life and are an essential part of the language which forms the basis of natural science. Then, can it be said that the use of the classical concepts is finally a consequence of the general human way of thinking? According to Heisenberg (1958: 55-81) “natural science does not simply describe and explain nature, it is a part of the interplay between nature and ourselves; it describes nature as exposed to our method of questioning.” Is this maieutic - the inquiry or search for new ideas, concepts or prisms underlying information, the source for a paradigm shift?
Looking through different lenses, “the fractal nature of quantum paths” perhaps was the masked idea in Jadczyk’s book Quantum Fractals, where the author tries to reconcile these two concepts- quantum and fractals- discussing foundational questions which happened to be related to the processes relevant for the creation of quantum fractals.
With Quantum Fractals comes challenges
Quantum
It is common knowledge that quantum mechanics, quantum theory, quantum physics, in their complexity and hard to understand, have proved to be capable of explaining the behaviour of matter in the microscopic world. “At the heart of the matter, there is an immense world, made up of billions and billions of particles, which escapes our senses and our intuition.” Extrapolating the theoretical background to the fascinating field of quantum computing (quantum information) has its consequences: being subject to considerable criticalities -both from a scientific perspective and at the engineering level.
Despite these criticisms, it is important to recognize potential applications though do not represent the full set of business opportunities that leverage recent advances in engineering related to quantum phenomena and which are not yet available at the level of power and reliability needed for solving these types of problems. Still, three near-term commercial opportunities from recent advances in quantum hardware and software can e highlighted: (1) quantum-safe encryption on classical computers, (2) material and drug discovery, and (3) new quantum-inspired algorithms for classical computers (Bova et al, 2021).
Fractal theory and its applications
Being a key feature of a fractal its “self-similarity” it is possible to identify “turbulent” configurations or “outliers" to analyze and manipulate them, and, therefore, use fractal geometry as a tool for analysis and synthesis. With fractals, then, we can explain those events that traditional science considered as irregular aspects of nature tracing them back to the theory of chaos.
From a financial perspective, understanding and interpreting the irregularities and “turbulences” in the markets, using fractal theory through the implementation of adequate algorithms could provide a decisive tool in assessing the risks of “improbable events”, predicting stock market swings (currencies, commodities, as well), daily money transfer between banks, calculating risk when managing portfolios, price derivatives like options, and to better understand how markets function as it can give us insight into human behavior.
According to recent studies, a multifaceted approach combining chaos theory, statistical analyses, refinement methods to model stock shifts in combination with quantum computing will enhance the performance of the developed algorithm, especially in terms of runtime and therefore capability. Effective detection of fractals and almost instantaneous refining of models as offered by quantum computing can result in more accurate and timely predictions about price movement (Bulusu et al., 2020). In other words, given the “chaotic” nature of financial systems, it seems plausible that fractal theory and quantum computing techniques can contribute to more accurate and efficient fiscal forecasts and therefore improved investment and economic decisions.
Final comments
In relation to the conceptualization of quantum fractals inevitably comes the problem concerning interpretation. Some physicists may say “do not worry about interpretation” or declare themselves pantheist when referring to Quantum Theory. Yet interpretation does matter: it shapes the directions of our research and the questions we pose. And I will add, interpretation is the core in any field and follows from philosophical underpinnings. Schrodinger's thought experiment of the cat in the box is just one example. At least, two interpretations are available. Most of us would say the cat is either dead or alive, we must open the box to discover the nature of that reality—i.e., determinist view. Others might claim that the cat is both dead and alive, depending on collective and participatory versions of reality—i.e., constructivists. In this latter case, the investigator develops a worldview to live by that defines the nature of the cat in the box.
Understanding, interpreting, and adopting a new paradigm will determine the relationship between relevant actors and exogenous forces which will reveal a spectrum of behavior from seeming stability to apparent instability, the flow in the process creating new chaos and new order. Still, “the beauty of it lies in the eye of the beholder”. Or as professor Aspuru-Guzik said, there is “a role for imagination, intuition, and adventure. Maybe it’s not about how many qubits we have; maybe it’s about how many hackers we have.”