In this paper we demonstrate that the probabilistic quantum-like (QL) behavior–the Born’s rule, interference of probabilities, violation of Bell’s inequality, representation of variables by in general noncommutative self-adjoint operators, Schrödinger’s dynamics–can be exhibited not only by processes in the micro world, but also in economics. In our approach the QL-behavior is induced not by properties of systems. Here systems (commodities) are macroscopic. They could not be superpositions of two different states. In our approach the QL-behavior of economical statistics is a consequence of the organization of the process of production as well as investments. In particular, Hamiltonian (“financial energy”) is determined by rate of return.
Originally the mathematical formalism of quantum mechanics was developed to serve physical theory of processes in the micro world. However, recently there has been a lot of interest in applications of this mathematical formalism to macroscopic systems and even outside the domain of physics, e.g., in finances, economics, and psychology [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22] and [23], see also [24], [25], [26], [27], [28], [29], [30], [31], [32], [33], [34], [35], [36], [37] and [38]. From the outset we emphasize that one should sharply distinguish between the mathematical formalism of quantum mechanics and quantum mechanics by itself (as a physical theory). Therefore we are discussing not “applications of quantum mechanics” e.g. in finances or economics, but applications of the quantum mathematical apparatus. To distinguish between the really physical quantum models and other models which might be described by the quantum mathematical apparatus, we shall use the terminology “quantum-like” (QL) for the latter case, instead of “quantum”.
We consider the calculus of quantum probabilities as one of the main distinguishing features of the quantum mathematical apparatus. The crucial point of quantum probability theory is the Born’s rule for calculation of probabilities. One of the fundamental consequences of this rule is the interference of probabilities. Another fundamental consequence is the violation of Bell’s inequality.
In this paper we demonstrate that the probabilistic QL-behavior–the Born’s rule, interference of probabilities, violation of Bell’s inequality, representation of variables by in general noncommutative self-adjoint operators–can be exhibited not only by processes in the micro world, but also in economics. In our approach the QL-behavior is induced not by properties of systems. Here systems, commodities, are macroscopic. They could not be superpositions of two different states. For example, a boat or a car can be either large or small, but never in superposition
