Quantum Economics
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Abstract
A decade after the financial crisis, there is a growing consensus that the neoclassical approach to economics has failed, and that new approaches are needed. This paper argues that economics has been trying to solve the wrong problem. Economics sees itself as the science of scarcity, but instead it should be the science of money. Just as physicists’ ideas about quantum matter were formed by studying the exchange of particles at the subatomic level, so economics should begin by analysing the properties of money-based transactions, which like quantum entities have a fundamentally dualistic nature. By building on ideas from quantum money, quantum finance, and quantum social science, the paper shows that the economy is an archetypal example of a quantum social system, complete with its own versions of measurement uncertainty, entanglement, and so on. This leads to a proposal for a quantum economics, which is to neoclassical economics what quantum physics is to classical physics.
The Serbian scientist M. Petrovich (written in French) published in Paris a book Mecanismes Communs aux phenomenes disparates. Nouwelle Collection Scientifique. (Paris, 1921). (See also review by André Lalande (Revue Philosophique de la France T. 95 (JANVIER A JUIN 1923), pp. 299-302). Petrovich caught in the common scientific, heuristic and monistic value the theory of analogy. In particular, he argued that common mechanisms of heterogeneous phenomena lead to the concept of analogies of whole groups of phenomena. Common features in each such group constitute its “analogical core”, or “core group”. It is true that the core group in the Quantum economy is money. It is also true that “money occupies a special place in the intersection between the world of real objects and ideas of social value, its dualistic properties are experienced by society as a whole” (see Orrell, D. (2016). A quantum theory of money and value. Economic Thought, 5(2), 19-36. But there is a logical aspect of duality. Today everything is built on a logical system belongs either to logic contradictory relations or logic contrary relations. Recall that contradictory opposition is incompatible concept between which no middle-intermediate concepts and which completely exclude each other (e.g. black and white). Contrary concept is also incompatible concepts, but between which there may be some intermediate concept (e.g., between white and black can exist grey). Two types of relations (contradictory and contrary) corresponds to two types of logic, namely sets of the discrete type corresponds to the logic contradictory relations, and sets continuous type logic are contrary relations. In the ordinary perception of the world around us is represented as a set of individual (discrete) objects (things) that are separated in space, pronounced borders. But this psychophysical error. Real world around us is a constantly changing world, it’s a world of continuous processes. What type of logic should be used when considering money? Without a doubt, money is discrete sort of social reality. Generally speaking, to describe the objects in the continuous world by discrete system means deliberately to fall into error. But this error is largely offset by the fact that continuous real-world objects are assigned to discrete values and money. Money is penetrating in such objects (goods and services) can easily to connect continuous with discrete (leave out braсkets the question – is it always possible to adequately make this connection). So, money is the unique means of discrete – continuous type, allowing to work in two spaces – discrete and continuous.
In this lucid and very clearly written article David Orrell provides a short overview about a new branch of economics, called quantum economics, and particularly emphasizes the point that we may have to reassess our understanding of money and look deeper into the money creating process in order to reduce the likelihood of financial bubbles and economic crises to form in the future.
Of course, one can arrive to a similar conclusion without invoking quantum theory. However the quantum theoretical framework may provide a better toolbox for dealing with the features that are characteristic for complex systems such as self-referentiality and interdependence. Quantum physics was established once physicists realized that the observer could never be fully separated from the observed and that the act of measuring the state of a system would feed back and thereby affect the system. Furthermore, observation of one part of a system could have immediate implications for the possible outcomes at distant, not directly connected parts of the system – an interdependence known as (quantum) entanglement.
In this paper David Orrell describes in a convincing manner where to retrieve the equivalent concepts from quantum mechanics in the part of economics that is dealing with the pricing of assets and the money system itself, notably the credit sector and the way money is created “out of nothing” by the central banks. He argues that the traditional economical models rooted in neoclassical approach that has its analogy in classical mechanics is inadequate to describe the complexity of economical systems and therefore may actually do more harm than good by providing a false sense of security and shallow understanding. I couldn’t agree more with him on that point!
As already mentioned, the paper in its current form is very clearly written with little room left for improvement. A minor point would be the following: At several (2?) places in the manuscript the statement is made that “quantities such as position or momentum can never be known exactly”. This is not quite correct. It should read: “complementary variables such as position or momentum can never be known exactly at the same time”. Position or momentum, independently, can be determined up to (in principle) arbitrary precision, however measurement of position and momentum don’t commute and would therefore interfere with each other.
Thanks very much to the reviewer Michael Schnabel for these comments and generous remarks, and for spotting the needed corrections which I will make in a revised version of the manuscript.
This paper notes correctly the failure of neo-classical economics and the need for any theory to include money. The authors then move on to propose quantum methodology as the way forward using the analogy with physics of matter.
In physics, there are a number of experiments which have over the years been repeated many times which clearly demonstrate the validity of quantum methods and the breakdown of classical methods. The double slit experiment is the most well known of these, because it demonstrates the fundamental limitation of the ability of the observer to predict experimental results, Richard Feynman noted that it was a phenomenon which is impossible to explain in any classical way.
But perhaps of more interest here is the case of black body radiation which refers to an object which absorbs all radiation incident upon it and re-radiates energy which is then characteristic of this radiating system only, not dependent upon the type of radiation which is incident upon it. The radiated energy can be considered to be produced by standing wave or resonant modes of the cavity which is radiating. The amount of radiation emitted in a given frequency range should be proportional to the number of modes in that range. Classical statistical physics suggested that all modes had an equal chance of being produced, and that the number of modes went up proportional to the square of the frequency. But the predicted continual increase in radiated energy with frequency does not happen. Quantum statistical mechanics was required to obtain the measured result.
Neo-classical economics is a deterministic theory developed by analogy with Newtonian mechanics. From this theory emerges the concept of the rational agent. This to me seems rather like saying for an ensemble of simple atoms in a balloon they behave somehow like a set of ‘rational’ atoms each moving with the average speed – a picture we know to be incorrect. Velocity distributions have now been measured in some detail and we know ensembles can be characterised by a speed distribution with a width proportional to the temperature of the ensemble. The theory behind this work is no longer deterministic. Rather it rests on statistical mechanics which incorporates the correct ensemble averaging process. However it is still classical in the sense that quantum mechanics is not required.
Working by analogy, it seems to me that the correct next step for economics to take is to begin to explore the use of classical statistical mechanics which can account for money, counting and the required exchange processes. A number of physicists have had some success with these methods and there is clearly more to do.
What is needed to justify the use of quantum methods in economics are empirical results based on real data which are impossible to explain in any classical way. As far as I am aware no such results have been found.
Thanks to the reviewer Peter Richmond, who brings up the important point of empirical evidence. As he notes, quantum physics was inspired by the need to understand empirical results. The idea for example that energy should be transmitted as discrete quanta was first adopted, not for theoretical reasons, but as a practical fix for effects such as blackbody radiation, which involves an ensemble of subatomic events. However the quantum approach is not always needed to model such statistical effects. Drawing an analogy with classical statistical mechanics, he then argues that economics should be driven by the same classical statistical approach, unless there are “empirical results based on real data which are impossible to explain in any classical way.”
While I certainly agree with the need for any theory to explain and be tested by empirical results, I believe the physical analogy used discounts an important historical and technical difference, which is that quantum physics evolved from experiments involving subatomic processes that could not be directly observed, while money is a designed social technology. The role of experiment is therefore somewhat different, and in many cases the empirical evidence for the failure of the classical approach, and the need for a quantum approach, is not to be found hidden in statistical patterns, but is there in plain sight.
Quantum economics combines three major strands which were developed independently: quantum money, quantum social science, and quantum finance. The first of these argues that money has dualistic properties which make it behave in a quantum, rather than a classical, manner. The most basic of these is that money, like energy, is transmitted in terms of discrete quanta rather than as a continuous flow. In physics, this was by necessity inferred indirectly from experiments. In economics, it is a designed feature. The empirical evidence is obvious, both at the level of individual transactions, or in the creation of money by banks. While obvious, it is not easily handled by conventional models which assume continuity.
Another example is entanglement. In physics, this had to be teased out through sophisticated statistical experiments. In economics, if we model a loan agreement using the quantum formalism, with the decision to pay or default as an indeterministic quantum process (as in the appendix), then the entanglement is there in the equation. The entanglement therefore does not need to be observed statistically in order to verify its existence – it is encoded in the terms of the loan – but it certainly has statistical effects, for example in mass defaults. Again this entanglement is not a feature of mainstream models, which downplay or ignore the role of debt, and are blind to the power relationships which underpin it.
The situation in economics is therefore different from the one in physics. Instead of deducing the laws of nature from experiments, we are deciding on the correct mathematical framework for a human social technology or institution. As the paper notes, this doesn’t necessarily imply that economic models have to be explicitly based on a quantum formalism, but they do have to take these properties into account. (For the analogy of particles in a balloon, I would note in passing that it is hard to imagine a balloon where energy is distributed in such a way that eight particles in several billion have as much energy as the bottom half, as in the economy, see p. 14.)
For quantum social science, there are indeed “empirical results based on real data which are impossible to explain in any classical way.” As discussed in the cited papers, this is the whole motivation for the field of quantum cognition, which shows how decisions are shaped by things like interference effects which cannot be modelled using classical approaches (except in a very ad hoc manner). I will revise the paper to add a citation to Yukalov and Sornette (2015) who wrote: “It is the appearance of interference terms that makes the structure of quantum expressions richer than the related classical ones and that allows one to explain those psychological phenomena that, otherwise, are inexplicable in classical decision making.”
Quantum finance too is heavily empirical, however as noted in the paper the focus of the field has been more on reproducing classical results than on challenging them. I argue though that this is only because, as in mainstream economics, the role of money has been downplayed.
The greatest empirical evidence for the failure of the classical approach, and the need for a new approach which addresses the properties of money and human cognition, was the failure of classical models to predict or even understand the causes of the great financial crisis. I agree with the reviewer that it makes sense to design statistical experiments which will distinguish between quantum and classical approaches, and this is an important future step. However, given the failure of classical models; the simple empirical fact that money has quantum properties; and the existing empirical evidence for quantum cognition, I believe that the empirical evidence is already there, even if it doesn’t present in quite the same way as the kind of evidence which motivated quantum physics a century ago, or which is used in modern statistical mechanics. I will amend the article accordingly.
Yukalov, V.I., and Sornette, D. (2015), ‘Preference reversal in quantum decision theory’, Frontiers in Psychology, 6, pp. 1–7.