When Quantum Formalism Adds Little to an Economic Model

# Quantum Mechanics and Economics... What


# Quantum Mechanics and Economics... What












I was reading this paper: Financial Turbulence, Business Cycles and Intrinsic Time in an Artificial Economy.

The author has the model presented here: Quantum Evolutionary Financial Economics

But I am confused. There's all this build up of using quantum mechanics and quantum probability in the model, but the only thing he adds in the code is a normally distributed stochastic variable he calls the "business cycle quantum game term." What is quantum about this? Why bother with all the quantum formalism if the end result is effectively just Gaussian white noise? I'm not formally trained in QM, so am I missing something? Example of relevant portion of code (from second link):

> Business Cycle Quantum Game Term: to business-fitness-dynamics ask patches [ set z random-normal 0 1.000 ]; Gaussian wave packet reduction around the standardized fitness operator ask patches [ set $M_b = (1 - m) (b \cdot x_{t-1} - (b + 1) \cdot x_{t-1} ^ 3) + m\cdot r_{t-1}$ ] ; cubic map update (equation (18) with $M_b := f{_b,m}$) ask patches [ set $x_t (1 - \epsilon - \gamma) \cdot M_b + \epsilon \cdot \text{mean} [ M_{b}]\,\text{of patches}$ + $\gamma \cdot z$ ]; $F$ update and result of the quantum wave packet reduction in terms of the fitness field operator eigenvalue end

I also don't get this (from the second link):

> There are three main advantages of the quantum approach to Evolutionary Financial Economics: The explanatory effectiveness is expanded by the fact that one does not need any prior probability assumption, instead, one models the system's inter-relations and dynamics and from that result dynamical probabilities. Probabilities can have evolutionary and game theoretical interpretations. The adaptation process of a Complex Adaptive System (CAS) can be fully integrated with the probability formation and quantum game equilibrium assumptions.

Can classical methods not do any of these things?

## Answer by oliversm (score 5)

https://quant.stackexchange.com/a/27505

I have had a read through the paper that you quoted and have the following comments which you might find helpful:

(I am formally trained in QM, so hopefully there shouldn't be any errors in the physics portions of the answer, but if there are any questions then please comment).

A few comments about Quantum Mechanics (QM):

Quantum mechanics is a physical theory of measurement originally developed to describe phenomena at atomic scales or smaller. The reason this was needed was because things appeared to behave strangely, and this is reflected in the theory being built on the concept of probability amplitudes, which (to paraphrase Feynman) "are unlike anything observed before". The significance of this is that how probabilities are computed in QM are unique to QM (as far as we know). Why I stress this is because it means that only when we are trying to describe physical processes should we interpret what is computed as a probability.

The QM framework:

If you ever get the chance to learn some QM, you will see that it is primarily formulated in linear algebra (cf. The Schrodinger Equation). This means that mathematically all we worry about are eigenvectors and eigenvalues, and how these change when we either apply a matrix (an operator), or change basis.

Returning to the paper:

The paper gives a brief (and in my opinion flimsy) justification of a model of companies, where these are arranged in a regular fashion (a lattice). There is an interaction between the companies which determines the changes in the supply and demand, which we describe by the state of the system (note the similarity to the role of a QM wavefunction). The paper then effectively proposes an overall function (an operator) which is dependent on this state. This can be thought of as the Hamiltonian of the system, and the aim of the game is to find the eigenvalues to this Hamiltonian (which in physics we would identify as the energy levels). This whole framework is fairly common in quantum mechanics, and especially so in quantum field theory (QFT), and seems to resemble a typical approach to modeling condensed matter (cf. The Heisenberg Model for ferromagnetism).

What is quantum about the system:

Nothing.

Why bother with all the quantum formalism if the end result is effectively just Gaussian white noise?

I can only guess at this point, but it seems reasonable to assume that the author clearly has some knowledge of QM, and hence has identified that the framework he is using in his model involves very similar structures to those physicists use everyday. Hence if he poses the maths problem in a language that physicists might understand they are motivated to read the paper, cite the paper, extend upon the paper, etc. (Remember that a huge number of physicists turn to the financial industry).

I think many of the references to quantum game theory (and similar obscure fields) are superfluous.

Can classical methods not do any of these things?

The phrase classical methods is perhaps not well defined.

Physics and financial maths in general:

Although I think the quoted paper is a poor example, there is a huge field of applying approaches used in physics to areas in financial mathematics, including some of the areas mentioned involving QM and QFT. The main tool we can take from physics is Statistical Physics, and a good example of how this can be applied to finance is given by:

- "Theory of financial risk and derivatives pricing: From statistical physics to risk management", Bouchard and Potters

which gives great examples of using Hamiltonians, Lagrangians, etc. applied to finance.

I hope this helps.