Over many years, there have been multiple touchpoints between the natural and social sciences. This resulted in the application of ideas, concepts, and formalisms from physics, mathematics, and even biology to economics and finance. The considerations elaborated on in the journal Quantum Reports are discussed here.
Image Credit: Marina Sun/Shutterstock.com
The contributions of Nicolae Georgescu-Roegen can be best remembered here, since he is known for the law of entropy and its connection to the economic process.
A newly emerged research movement aims to apply quantum formalism to socioeconomic sciences. It led to the development of quantum-like models for analyzing and explaining decision-making activities and cognitive processes, which have a key role both in psychology and in many economic and finance models.
Studies of such developments are seen as representing the application of quantum mathematics—a synthesis of linear algebra, the theory of probability, operator algebras, and infinite-dimensional linear vector spaces—in the socioeconomic sciences.
Quantum-like models can be considered to offer a quantum mathematically analogous (QMA), rather than a quantum physically analogous (QPA), analysis and explanation of the processes that take place in the socioeconomic realm.
This article gives a detailed understanding of the QPA approach and how it may prove to be more comprehensive than the QMA approach.
The quantum theoretical framework provides a wide range of wave function interpretations, allowing for multiple perspectives on the physical ultimate reality. Physicists such as Rutherford, Sommerfeld, and Bohr pioneered experimental and theoretical efforts in the quantum domain, and these investigations were extended by the pioneering contributions of several legends, contributing to the development of modern quantum theory in the 1920s.
These viewpoints differ from one another, among other things, in relation to whether quantum theory provides a complete explanation of reality (or does not), as well as the function of the observer (or lack thereof) in the quantum framework. As a result, the QPA approach will entail taking into consideration quantum theory’s physical foundations, which do not appear to have been taken into account in the pure QMA approach.
Before explaining why the QPA approach is more comprehensive than the QMA approach, it is important to remember that quantum theory is first and foremost a physical theory of nature.
Further Reading: Covid Testing Based on Quantum Mechanics
Even after nearly a century, the ultimate general goal of most quantum experimental setups remains the same: these setups are built to draw probabilistic inferences only in terms of spectroscopic or interferometric intensity distributions, despite being much more modified and sophisticated than previous versions.
The quantum theoretical discoveries have been in lockstep with the quantum experimental findings, as is the case with any physics theory. The seeds and roots of the formulation of quantum theory can be found in the preceding classical physics frameworks and paradigms, as it is one of the stages of evolution in the many-centuries-old science of physics.
The latter is also referred to as the problem of the appearance of a classical realm in quantum theory and is typically investigated by employing the well-known decoherence program.
Results and Discussion
With this context in mind, it can now be claimed that the QPA approach will result in a more comprehensive analysis of socioeconomic activities than the pure QMA approach.
In a normal socioeconomic decision-making situation, the decision-maker is presented with a set of options. The corresponding decision-making process can be thought of as evolving:
- From the desire of the decision-maker to participate in the socioeconomic decision-making context
- Through the decision-maker’s initial preferences
- To the actualization of a specific choice of the decision-maker, pertaining to the impact of the relevant socioeconomic condition on her/him
Furthermore, in the QPA context, the two decision-makers are denoted to be identically prepared identical systems if both are participating in the same socioeconomic decision-making context, despite possible differences in their respective cognitive biases and idiosyncrasies. The diversity in behavioral decision-making would then be represented by an ensemble of such decision-makers.
The QPA approach will be predicted to offer appropriate models, so that such diversity manifests itself in terms of variation in the quantified initial preferences and actualized choices of decision-makers.
The preceding discussion shows that a QPA analysis would make us more accountable in terms of precision and consistency by allowing a much wider perspective for the investigation of socioeconomic activities than a pure QMA interpretation. In this regard, we believe that the QPA approach will be more comprehensive than the QMA approach.
Developments that use the mathematics of quantum theory in the socioeconomic sciences are regarded to depict a quantum mathematically analogous way of describing and analyzing socioeconomic activities. This study offered a plausibility argument for the exhaustiveness of the QPA approach by using a generic decision-making process and specifying what could be expected from the QPA approach.
Regardless of whether one chooses a conventional or non-conventional perception of quantum theory, it would be fascinating to see how a QPA approach could express the analogous socioeconomic structure of non-locality, how a QPA socioeconomic Bell-type inequality could be derived, and whether it is breached in suitably designed QPA socioeconomic studies.
The QPA method can also be used to investigate what is meant by the corresponding socioeconomic version of the measurement problem. A proper QPA strategy is likely to result in a socioeconomic version of the quantum-to-classical transition dilemma.
Athalye, V & Haven, E (2021) Socio-Economic Sciences: Beyond Quantum Math-like Formalisms. Quantum Reports, 3(4), pp. 656–663. Available Online: https://www.mdpi.com/2624-960X/3/4/41/htm
References and Further Reading
- Bachelier, L (1900) Théorie de la spéculation. In: Annales Scientifiques de l’Ecole Normale Supérieure; Société Mathématique de France: Paris, France. 17, pp. 21–86.
- von Neumann, J & Morgenstern, O (2007) Theory of Games and Economic Behavior. Princeton University Press: Princeton, NJ, USA.
- Georgescu-Roegen, N (1966) Analytical Economics: Issues and Problems. Harvard University Press: Cambridge, MA, USA.
- Choquet, G (1955) Theory of capacities. Annales de l’Institut Fourier, 5, pp. 131–295. doi.org/10.5802/aif.53.
- Chateauneuf, A & Jaffray, J Y (1989) Some characterizations of lower probabilities and other monotone capacities through the use of Mobius inversion. Mathematical Social Sciences, 17, pp. 263–283. doi.org/10.1016/0165-4896(89)90056-5.
- Chateauneuf, A (1994) Modelling attitudes towards uncertainty and risk through the use of Choquet integral. Annals of Operations Research, 52, pp. 3–20. doi.org/10.1007/BF02032158.
- Debreu, G (1959) Theory of Value. Yale University Press: New Haven, CT, USA.
- Chichilnisky, G (2008) Markets, Information and Uncertainty: Essays in Economic Theory in Honour of Kenneth J. Arrow. Cambridge University Press: Cambridge, UK.
- Mantegna, R & Stanley, E (1999) Introduction to Econophysics: Correlations and Complexity in Finance. Cambridge University Press: Cambridge, UK.
- Baaquie, B (2013) Statistical microeconomics. Journal of Physics A, 392, pp. 4400–4416. doi.org/10.1016/j.physa.2013.05.008.
- Khrennikov, A (2010) Ubiquitous Quantum Structure: From Psychology to Finance. Springer: Berlin, Germany.
- Busemeyer, J & Bruza, P (2012) Quantum Models of Cognition and Decision. Cambridge University Press: Cambridge, UK.
- Chichilnisky, G (2015) A Topological Characterization of the Space of Events and Frameworks of Rn; Working Paper. Stanford University: Stanford, CA, USA.
- Baaquie, B (2018) Quantum Field Theory for Economics and Finance. Cambridge University Press: Cambridge, UK.
- Anscombe, F & Aumann, R (1963) A definition of subjective probability. Annals of Mathematical Statistics, 34, pp. 199–205. doi.org/10.1214/aoms/1177704255.
- Savage, L (1954) The Foundations of Statistics; J. Wiley: New York, NY, USA.
- Kahneman, D & Tversky, A (1979) Prospect theory: An analysis of decision under risk. Econometrica, 2, pp. 263–292. doi.org/10.2307/1914185.
- Klibanoff, P., et al. (2005) A smooth model of decision-making under ambiguity. Econometrica, 73, pp. 1849–1892. doi.org/10.1111/j.1468-0262.2005.00640.x.
- La Mura, P (2009) Projective Expected Utility. Journal of Mathematical Psychology, 53, pp. 408–414. doi.org/10.1016/j.jmp.2009.02.001.
- Busemeyer, J. R., et al. (2006) Quantum dynamics of human decision-making. Journal of Mathematical Psychology, 50, p. 220. doi.org/10.1016/j.jmp.2006.01.003.
- Hawkins, R J & Frieden, B R (2017) Quantization in financial economics: An information theoretic approach. In: The Palgrave Handbook of Quantum Models in Social Science; Haven, E & Khrennikov, A (Eds). Springer: Berlin, Germany.
- Reginatto, M (1998) Derivation of the equations of non relativistic quantum mechanics using the principle of minimum Fisher information. Physical Review A, 58, pp. 1775–1778. doi.org/10.1103/PhysRevA.58.1775.
- Bohm, D & Hiley, B (1993) The Undivided Universe: An Ontological Interpretation of Quantum Theory. Routledge: New York, NY, USA.
- Li, Y & Zhang, J E (2014) Option pricing with Well-Titchmarsh theory. Quantitative Finance, 4, pp. 457–464. doi.org/10.1080/14697680400008643.
- Modinos, A (2014) From Aristotle To Schrödinger: The Curiosity of Physics. Springer: Cham, Switzerland.
- Beck, M (2012) Quantum Mechanics: Theory and Experiment. Oxford University Press: New York, NY, USA.
- Athalye, V., et al. (2011) Investigation of the Leggett-Garg Inequality for Precessing Nuclear Spins. Physical Review Letters, 107, p. 130402. doi.org/10.1103/PhysRevLett.107.130402.
- Holland, P. (1993) The Quantum Theory of Motion. Cambridge University Press: Cambridge, UK.
- Dürr, D & Lazarovici, D ( 2020) Understanding Quantum Mechanics: The World According to Modern Quantum Foundations. Springer: Cham, Switzerland.
- Vaidman, L (2019) Quantum Nonlocality. Entropy, 21, p. 447. doi.org/10.3390/e21050447.
- Schlosshauer, M (2007) Decoherence and the Quantum to Classical Transition. Springer: Berlin, Germany.
- Athalye, V & Kumar, A ( 2006) Decoherence of superposition of molecular chiral states due to Rayleigh scattering. Journal of Physics B: Atomic, Molecular and Optical Physics, 39, p. 2633. doi.org/10.1088/0953-4075/39/12/002.
- Feynman, R., et al. (2010) The Feynman Lectures on Physics: Volume III. Basic Books: New York, NY, USA.