Heisenberg uncertainty principle and economic analogues of basic physical quantities

In papers [1][2][3] we have suggestsed a new paradigm of complex systems modelling based on the ideas of quantum as well as relativistic mechanics. It has been revealed that the use of quantum-mechanical analogies (such as the uncertainty principle, notion of the operator, and quantum measurement interpretation) can be applied to describing socio-economic processes. In papers [1][2][3] we have suggestsed a new paradigm of complex systems modelling based on the ideas of quantum as well as relativistic mechanics. It has been revealed that the use of quantum-mechanical analogies (such as the uncertainty principle, notion of the operator, and quantum measurement interpretation) can be applied to describing socio-economic processes.

It is worth noting that quantum analogies in economy need to be considered as the subject of new inter-disciplinary direction -quantum econophysics (e.g. [4][5][6][7][8]), which, despite being relatively young, has already become a part of classical econophysics [9][10][11][12].

Ideas [1][2][3] were anticipated and further developed in our works on modelling, predicting, and identification of socio-economic systems [13][14][15][16][17][18][19][20] (complex Markov chains), [19][20][21][22][23] (discrete Fourier Transorm), [24][25][26][27] (multi-agent modelling), [28,29] (dynamic network mathematics), [30,31] (network measurements), [32,33] (uncertainty principle in economics) etc. However significant differences between physical and socio-economical phenomena, diversity and complexity of mathematical toolset (which, on account of historical circumstances, has been developed as the language of sciences), as well as lack of deep understanding of quantum ideology among the scientists, working at the joint of different fields require a special approach and attention while using quantum econophysical analogies.

Aim of work. Our aim is to conduct detailed methodological and phylosophical analysis of fundamental physical notions and constants, such as time, space and spatial coordinates, mass, Planck’s constant, light velocity from the point of view of modern theoretical physics, and search of adequate and useful analogues in socio-economic phenomena and processes.

Time, distance and mass are normally considered to be initial, main or basic physical notions, that are not strictly defined. It is thought that they can be matched with certain numerical values. In this case other physical values, e.g. speed, acceleration, pulse, force, energy, electrical charge, current etc. can be conveyed and defined with the help of the three above-listed ones via appropriate physical laws.

Let us emphasize that none of the modern physical theories, including relativistic and quantum physics, can exist without basic notions. Nevertheless, we would like to draw attention to the following aspects.

As Einstein has shown in his relativity theory, presence of heterogeneous masses leads to the distortion of 4dimensional time-space in which our world exists. As a result Cartesian coordinates of the 4-dimensional Minkowski space (x, y, z, ict), including three ordinary Cartesian coordinates (x, y, z) and the forth formally introduced timecoordinate ict (i = √ -1 -imaginary unit, c -speed of light in vacuum, t -time), become curvilinear [34]. It is also possible to approach the interpretation of Einstein’s theory from other point of view, considering that the observed heterogeneous mass distribution is the consequence of really existing curvilinear coordinates (x, y, z, ict). Then the existence of masses in our world becomes the consequence of geometrical factors (presence of time-space and its curvature) and can be described in geomatrical terms.

If we step away from global macro-phenomena that are described by the general relativity theory, and move to micro-world, where laws of quantum physics operate, we come to the same conclusion about the priority of time-space coordinates in the definition of all other physical values, mass included.

To demonstrate it, let us use the known Heisenberg’s uncertainty ratio which is the fundamental consequence of non-relativistic quantum mechanics axioms and appears to be (e.g. [2]):

where ∆x and ∆v are mean square deviations of x coordinate and velocity v corresponding to the particle with (rest) mass m 0 , -Planck’s constant. Considering values ∆x ∆v to be measurable when their product reaches its minimum, we derive (from (1)):

i.e. mass of the particle is conveyed via uncertainties of its coordinate and velocity -time derivative of the same coordinate. Nowadays, scientists from different fields occupy themselves with the investigation of structure and other fundamental properties of spacetime from p

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