1. The Methodology and Significance of Economic Dynamics

2. The Contents of Economic Dynamics

3. Theoretical Preparations

3.3. Theory of the Monetary Nature of Currency

Economic dynamics uses gauge field theory as a modeling method, which is a part of quantum field theory, integrated from quantum mechanics and special relativity. The quantum aspects of economic dynamics will be introduced in the market dynamics section; here we mainly discuss the special relativity model of money. This work was initially presented in Yang (2013) [31] (Modern Principles of Economic Mechanics, Chapters 3 to 5), and has since been further developed by the author. This section describes its methodology, photon-like money nature, light-cone and money cones, and poverty-cones and wealth-cones.

3.3.1. Methodology

A scientific theory must have its boundaries, as it needs to possess falsifiability according to Popper's philosophy of science. A theory without boundaries is termed theology. Therefore, when establishing a new theoretical model, you need to know not only what you intend to say but also what you do not intend to say. The following points are not addressed in this paper.

Firstly, money has dual characteristics: its monetary nature and its money nature, as well as its currency nature. This introduces three research paths in monetary studies. The monetary nature refers to the content typically covered in general economics textbooks, which is highly specialized but less understood. The money nature involves the social cognition and behavioral mechanisms of money, falling under monetary psychology and behavioral finance. This content seems to be somewhat common knowledge; however, its scientific level is quite low due to a lack of conceptualization and modeling. The currency nature studies the systemic overall properties of the relationship between monetary nature and money nature, generally referred to as meta-theory. This paper is limited to discussing the money nature.

Secondly, this paper does not discuss political finance. This topic concerns the national nature of money, known as sovereign money. Sovereign money is issued by national central banks, and sovereign countries depend on a healthy sovereign currency, with its strength rooted in its currency reserves and trustworthiness. Hayek, in the Denationalization of Money [32], advocates for currency free markets and the privatization of currency issuance, which illustrates, in the contrary, that contemporary money is nationalized. This paper does not cover this aspect.

Furthermore, this paper does not delve into the philosophy of money. The leading figure in the philosophy of money is Georg Simmel, whose classic, Philosophy of Money [33], has several Chinese translations. Simmel summarized four types of excellent qualities of money's monetary nature into twelve points. For instance, everyone spends money and everyone receives money. Money is never short of energy; when people want money, they infuse their own energy into it. Money is never short of wisdom; when people budget with money, they infuse their own wisdom into it. Money has a limited capacity for abstraction, continuously evolving invisible abilities, and dream-like imaginative capacities, among others. Finally, money evolves into a unitary system that fits human cognitive channels, where people easily make mistakes in other calculations, but not generally in money calculations. This paper borrows three themes from Simmel: money is not a commodity but the relationship between commodities; money is not functional; money itself represents function; and money is the logic of the market.

Of course, not discussing something does not mean never discussing it. Cognitive science and psychology have many overlaps, but the former emphasizes interdisciplinary conceptualization and modeling, including computational models or mathematical physics models. Where the model leads, the theory follows; where the model is limited, the theory remains unspoken. Modeling is like the currency of theory; the more money, the more speech. If the content phenomenon exceeds the modeling level, it is called insufficient modeling; conversely, it is called excessive modeling. The requirement is for conceptualization to be "just right." This is a principle of contemporary formal philosophy. Some may be puzzled as to why emphasis is placed on conceptualization and modeling in fundamental theoretical research. Conceptualization is progress in cognitive level to avoid simple repetition. Modeling is the evolution of knowledge accumulation to avoid piecemeal progress.

3.3.2. Photon-like Money Nature

Economic dynamics and cognitive dynamics both use the particle physics standard model and the Higgs mechanism as their models. Economic dynamics, with its content trimming meeting the "just right" conceptualization requirement, means its models not only share gauge symmetry groups with the standard model but also sometimes share notation. The language of the standard model is quantum field theory, which integrates quantum mechanics and special relativity. When referring to the money nature as "money particles" depicted by photons, money particles must satisfy two types of photon-like conditions, which are the requirements of quantum mechanics and special relativity, respectively, which are briefly described as follows.

The first condition is quantum mechanics. Money particles have a spin of 1. Spin is an intrinsic property assigned to particles by quantum mechanics, which has no counterpart in Newtonian classical mechanics. Classical mechanics views particles as solid points, whereas quantum mechanics considers particles to have internal space. Just as classical economics does not address the internal mental world of market participants, assuming that under the law of large numbers, different individuals' mental states are averaged out, and it suffices to consider their market behavior as point-like behavior. Economic dynamics, however, commits ontologically and epistemologically to the mental world of individual participants and their internal space. In quantum mechanics, particles have rotational internal space; with rotation comes angular momentum, and spin is the unit measure of this angular momentum.

However, the concept of angular momentum is not intuitive in economics and the mental world. Over a decade ago, I was somewhat confused about this and consulted Mr. Zhengxing Wang from Peking University. Mr. Wang explained that intuitively, you can imagine several directions of rotation in the particle’s internal space. Material particles, such as fermions, generally have two fundamental directions of rotation, such as the spin-up and spin-down of an electron, which are two base states. Other spin directions can be seen as superpositions of these two base states. The number of base states equals the spin quantum number, for example, the electron’s spin is 1/2. Mediators, such as bosons like photons, have only one spin direction, which is the direction of their longitudinal wavefront, hence their spin is 1.

This can be understood as follows: Economic goods, including commodities and services, have two directions or spin base states: yes or no. If a person is hungry and you give him a bowl of rice, he says yes and eat it. After finishing the first bowl, if you give him another bowl, he again says yes and eat it. After finishing the second bowl, if you give him a third bowl, he might say that he is full and cannot eat more. That is, a bowl of rice has two spin directions: being eaten or not being eaten, so its spin is 1/2. Money, however, is different. If you give someone one hundred dollars, he says thank you and accept it. If you give him a thousand dollars, he accepts it again and ask for a check. If you give him ten thousand dollars or more, they still accept it and say a transfer is more convenient. In other words, "money particles" have only one spin direction, which equals one, so its spin is 1.

Note that when applying the concept from physics to social sciences, the voice form used in physics should be converted to passive voice. For example, the spin in physics should be translated to "being spun" in economic dynamics. Saying a bowl of rice or money is spun might seem conceptually awkward, but using people as examples makes it easier to understand. For instance, if someone is job hunting, they have the commodity attributes of the job market. If this person receives a job interview opportunity and is told the results will be announced in two weeks, these two weeks are hard to endure. Today, they might think their interview performance was appropriate, considering their advantages, and feel they will be hired. Tomorrow, they might think about something inappropriate they said during the interview, reflecting on their weaknesses, and feel they might not be hired. This anxiety is the state of being spun.

The second condition is special relativity. Special relativity is based on the invariance of the speed of light, which provides a constant. Each observer is an inertial system with different inertial velocities, but through the Lorentz transformation, all observers see the speed of light as the same, which gives symmetry corresponding to the light speed invariance.

Firstly, the non-functionality of money particles allows them to operate at the fastest speed in the economic world, just as photons operate at the fastest speed in the material world, partly because of the photon's masslessness. According to Einstein's mass-energy equation, particles with mass require enormous (almost impossible) energy to approach the speed of light.

Since childhood, people have learned about the purchasing power of money. Wanting to buy a piece of candy requires asking for coins from an adult. In college, saving money for tuition or buying a used car makes people understand money’s saving function. After starting work, having some spare money, people learn about the investment function of money. These are the potential functional uses of money, which are its functionalities. However, during a conversation, if a familiar friend suddenly asks what you really want, and you reply, "I just want to make more money," the friend fully understands you without needing to specify the exact functions of money.

In the economic world, similar to the masslessness of photons, only money particles can reach this state of self-sufficient non-functionality, and it can be handled with the concept of de-functionalization. No other economic goods can be compared to this, so money operates the fastest. Here, "money speed" is not related to the transaction and market circulation speed of money, which pertains to the currency nature.

Moreover, money particles have finite speed. This is because the money nature is constrained by the currency nature, mainly the national nature of money. The national and sovereign nature of money restricts the issuance amount and exchange rate. Common sense tells us that money is finite. Ordinary rationality tells ordinary people that income is limited. Therefore, people understand that the speed of spending money must be limited. Holding this idea, money speed is thus limited.

Additionally, money speed is conserved. Simmel, in Philosophy of Money [32], stated that money is not functionally objective; money itself is the function, and this function as a meta-economic property is stable. Money is not a commodity; money is the relationship between commodities, and this "relationality" is stable. Money is not the market but the logic of the market; markets can change, but the logic of the market is constant. This is an economic philosophical argument.

As mentioned above, money particles in the economic world are the fastest, finite, conserved, and have a spin of 1, which defines their photon-like nature. The degree of photon-like nature can vary, just as individual differences in the demand for money can vary, which can be achieved through Lorentz transformations to reach symmetry. The key point is that photon-like nature requires consistency in the conceptualization of money nature. Of course, some may say they dislike money and prefer a simple life, which is a respectable religious sentiment, but unfortunately, it is not economics.

In the social sciences, to apply special relativity, one must first find an invariant with photon-like properties. In the cognitive world, it is language; in the political world, it is power; in the sub-economic or sub-cognitive world, it is consciousness, and so on. Thus, photons, money particles, language, power, and consciousness constitute the fivefold photon-like state. If money is the light in economic life, the similar can be said to language, power, and consciousness, people will understand what you mean. This is the power of conceptualization. The next step is to explore how to model this.

3.3.3. Light Cone and Money Cone

Conceptualization and modeling are closely related but differ in style. Developing a new foundational theory requires a substantial understanding of phenomena within the field as well as models outside the field. Conceptualization, also known as conceptual processing, involves revisiting phenomena within the domain after anchoring external models and re-conceptualizing existing theories. Abstract trimming must be appropriate. This is actually the most challenging phase in basic theoretical research. Modeling, also known as model embedding, involves seamless integration based on conceptualization, with technical craftsmanship being crucial. This is the most meticulous phase in fundamental theoretical research. Experience in interdisciplinary research often suggests that the most central aspects across different fields are usually the most communicable. Therefore, whether in conceptualization or modeling, focusing on the core often leads to significantly more efficient results.

Special relativity operates in four-dimensional Minkowski spacetime. We are accustomed to thinking in three-dimensional Euclidean space from elementary school, where a point is defined by three variables and the distance between two points is the square root of the sum of three squared terms. Speed, including the speed of light, is calculated as distance divided by time, and so on. These concepts change in four-dimensional spacetime and need to be redefined. Here are several newly introduced necessary concepts:

The first concept to be reintroduced is "metric," denoted as $g_{\mu \upsilon }$. The metric is the most fundamental algebraic structure in algebraic space. In three-dimensional space, it is positive, $g_{\mu \upsilon }$ = (+, +, +). In the four-dimensional spacetime, the metric is one positive and three negatives,

$g_{\mu \upsilon }=(+,-,-,-)$ or equivalently one negative and three positives, depending on the convention.

Second, a new time dimension is introduced, often multiplied by the speed of light, called the energy dimension. A point in four-dimensional spacetime is called an event.

Third, the concept of velocity is replaced by "composite velocity." In four-dimensional spacetime, the concept of velocity no longer applies, but "composite velocity" is introduced. The corresponding symmetry now states that all objects (including light) have the same composite velocity in four-dimensional spacetime. However, light has the least composite velocity along the time axis and the most in the three spatial dimensions. This aligns with the notion that light is the fastest in three-dimensional space. The idea of this conceptual shift is quite fascinating.

Fourth, and particularly crucial, is the concept of an event's "interval," defined as follows:

$$({∆S)}^2=c^2(∆\mathrm{t}{)}^2-({∆x)}^2-({∆y)}^2-({∆z)}^2$$

The interval $({∆S)}^2$ is defined by a linear combination of four terms. The first term is the speed of light squared multiplied by the time increment squared, with a positive sign, representing the energy term. In the context of economics, the speed of light is replaced by the speed of money, and the energy term represents budget or purchasing power. The other three terms are the squares of the spatial increments, each with a negative sign. In the context of economics, these spatial terms represent consumption.

With these concepts in place, we can introduce the well-known light cone, which is analogous to the money cone model. For a given light source, since light travels fastest, it is reasonable to initially assume it travels in a straight line. From the light source, one can imagine various directions of scattering forming a downward cone. Similarly, scattering in upward directions from the same light source forms an upward cone. The intersection of these upward and downward cones at the source defines the light cone. Replacing the light source with a money source yields the money cone model (Figure 3).

An event can be located on the surface of the light cone, inside it, or outside it. The light cone model provides a significant characterization in economics. Events on the surface of the money cone have an interval of zero, referred to as a "null event" in Chinese. In an economic context, this means that purchasing power and consumption exactly balance each other, often described as being "living paycheck to paycheck." Events inside the money cone have an interval greater than zero and are called "quasi-temporal events," indicating that purchasing power exceeds consumption and there is a surplus, meaning there is no shortage of money. Events outside the money cone are called "quasi-empty" events, with an interval less than zero, signifying that actual consumption exceeds purchasing power, which is referred to as excessive consumption.

In physics, the light cone model introduces worldlines passing from the lower cone through the light source to the upper cone to characterize historical causality. In the context of economics, for example, during the 2007 global financial crisis, the U.S. Congress passed a $700 billion bailout package, which serves as a source of money emission. Not all past economic activities are responsible for this money source's creation; only those events related to causing the subprime mortgage crisis are considered internal time-like events of the lower money cone. Similarly, not all industry companies or individuals benefit from the special appropriations by Congress; most are space-like events. Only those who benefit from the special appropriations are considered time-like events and enter the upper cone.

3.3.4. Proper Cost Value: Poor Cone vs. Rich Cone

In the previous section, it was reasonably assumed that light travels in a straight line, but this is not absolute. When we discussed the generalized relativity model of welfare economics in another paper, we introduced the concept of economic gravity. When considering both Einstein's special relativity and general relativity, under significant gravitational influence, light rays can become polarized, and the light cone itself can deform. For example, during severe global pandemics, the economic gravity as negative curvature has a significant impact, and the monetary nature may lower its noble stance. At such times, while the money cone may maintain its internal topological structure, it may need to bend and twist to adapt to the curvature and winding of the worldlines. These models are illustrated with diagrams in Penrose (2005), The Road to Reality [20]. The model of the poor cone and rich cone can be found in Yang Y. (2013), Modern Principles of Economic Mechanics [31]^.

If readers find the previous descriptions somewhat distant from personal real-life experiences, this section will place personal real-life experiences within the framework of special relativity. A concept in special relativity, seemingly divinely inspired and particularly suited for psychology and economics, especially economic dynamics, is "proper time." A common example involves a pair of twin sisters, each carrying a clock. Suppose one sister travels through space on a spaceship while the other remains on Earth. The time related to the spaceship's speed is called absolute time. The principle states that due to the fast speed of the spaceship, the clock with the sister on it runs slower relative to Earth; conversely, the clock with the sister on Earth runs faster. Thus, when the sister returns to Earth, she is still young, while the other sister has aged. This clock time is called proper time. Proper time is inversely related to speed. Proper time is evidently individual-specific, so when representing proper time with a symbol, it should have a subscript, denoted as ${\tau }_i$, indicating that proper time is a variable that can vary for each individual. Thus, proper time can reflect individual differences. In economics, decisions are always individual actions. Decision-making involves the mind, and the mental world can only be embodied in individual lives. To discuss "group decision-making," one must explain the mechanism by which decisions by each individual lead to what is termed group decision-making. Understanding this principle allows for discussion of behavioral economics.

The market price of a good or service is called the absolute price, meaning it does not vary by individual or clock. However, each consumer has an intrinsic psychological price, called the "proper value," denoted as ${\tau }_i$, which refers to proper time. For example, two classmates go shopping at a mall on the weekend and look for a place to have lunch when they are hungry. They see a high-end restaurant with a buffet priced at 60 dollars per person. One classmate, coming from a financially well-off family, considers 60 dollars for a buffet to be inexpensive. The other classmate, from a poor background, finds 60 dollars for lunch too expensive. Thus, the absolute price of 60 dollars is considered cheap by one consumer and too expensive by another, reflecting that different individual consumers have different intrinsic values for the same absolute price.

The light cone and money cone introduced in the previous section are static cones. By dividing each of the four terms in the linear combination used to define the event interval by proper time or intrinsic value, we obtain the concept of momentum. Accordingly, a momentum cone can be drawn. Since intrinsic value varies from person to person, the momentum cone also varies accordingly. Now, let's transform the static cone described in the previous section into a momentum cone. First, draw a horizontal line passing through the cone's apex (i.e., the top and bottom cone vertices) or slice a horizontal equatorial plane. This creates an angle $\theta$ between the horizontal line (or equatorial plane) and the cone's surface. Momentum varies with intrinsic value, so the shape of the momentum cone varies with momentum. Thus, $\theta$is a variable that differs from person to person and is denoted as ${\theta }_i$; for different individual consumers, the higher the proper value ${\tau }_i$, the larger ${\theta }_i$, which is a proportional relationship.

Next, consider the upper part of the money cone (and similarly for the lower cone). The width of the opening, denoted as $d_i$, is called the consumption impulse. The width of the upper cone's opening $d_i,$, is inversely proportional to ${\theta }_i$, meaning that consumption impulse is inversely proportional to the proper cost value. In other words, the higher an individual's proper cost value, the smaller the corresponding consumption impulse, and vice versa. Simply put, if you think something is more expensive, the impulse to buy it is smaller, which conforms to the common sense.

From a geometric perspective, for an individual consumer, the poorer the person, the higher the proper value ${\tau }_i$, the larger the angle ${\theta }_i$ of the momentum money cone, and the smaller the consumption impulse $d_i$, resulting in a narrower opening of the upper cone. In this case, the momentum money cone becomes thinner and is referred to as the poor cone (see the right cone below). Conversely, the wealthier the person, the lower the proper cost value ${\tau }_i$, the smaller the angle ${\theta }_i$, the wider the opening of the upper cone, and the larger the consumption impulse $d_i$, resulting in a flatter momentum money cone, known as the rich cone (see the left cone below).

Figure 4. Rich cone and poor cone.

Figure 4. Rich cone and poor cone.

Poverty and wealth are always relative; everyone is lacking compared to those above and has more compared to those below. Thus, the individualized intrinsic cone can reflect general individual differences.

4. Summary

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