Toy Theory: normative dynamics of Yin Yang and five elements


Recently, a friend asked me if it is possible to use modern physical methods to study Yin Yang and five elements, the content of Chinese traditional culture?

At first, I naturally thought that this was nonsense, but on the contrary, if I did not consider the actual situation and thought completely from the perspective of opening a brain hole, it would not be completely impossible to study it with modern physics.

If, we assume,Yin Yang and five elements are physical reality that can be described by normative theory, what should it look like?

Well, let’s start entering the brain hole time.

First of all, the five elements are related to each other. We abstract the specific contents of the five elements and express them only with symbols, which is the following relationship:

  • Symbiosis: a begets B, B begets C, C begets D, D begets e, e begets a
  • Phase grams: a G C, C G E, e g b, B G D, d g a

Such a relationship can be described by a pentagonal array. Xiangsheng is an external Pentagon and Xiangke is an internal pentagram.

The key is, how can we use normative theory to describe this relationship? In particular, how to use groups to describe this relationship?

Without considering Yin and Yang, we introduce an attribute free “Qi”, which does not have any attribute of the five elements, but can be transformed into any of the five elements, which is represented by Q. In this way, a total of six elements of five elements plus gas are called “element field”, which is a real scalar field.

Next, we construct the five element Shengke relationship as the following mapping:

Thus, we can construct a five element Shengke field, which is a gauge field:

All other elements are 0. We record these ten sets of generators asAt present, the gauge field in space can only be a linear combination of the above ten generators.

Since we have added the gas element without attribute, the Shengke field now has such a characteristic:

This feature is very important, as we will see later.

Then, regardless of yin and Yang, we try to construct the dynamic model of gauge field.

We useIt has six independent components, and the value of each component is a real number. And by ShengkeVector field composed ofIs a vector field in which each component is a gram generating action:

Next, according to the idea of traditional gauge field theory, we can construct the following action density:

This is the form of standard gauge field theory, and we can add the familiar Lorentz gauge fixed condition。 After removing the self interaction terms of all free motion items and Shengke field, there are the following interaction terms between the five element field and Shengke field():

Obviously, the relationship between the five elements is realized through these two items.

Let’s look at the motion equation of five elements Shengke in the classical case, which can be easily derived from the action density as follows:

It is very troublesome to solve this equation directly, such as the Shengke field strength tensorIt contains the quadratic term of Shengke field, so the whole equation of motion of Shengke field is a partial differential equation of second-order matrix, which is difficult to be solved directly.

But, on other hand, we notice properties of the Shengke field mentioned earlierObviously, this characteristic will also be transferred to its field strength tensor:Therefore, by summing all elements in the equation of motion of the Shengke field strong tensor, we can obtain:

This meaning is obvious: the change of element I depends on the amount of all elements that can generate it and the corresponding Shengke field, which is very consistent with our five element intuition.

Substituting this result back to the equation of motion, we can get:

That is, the static mass of the five element field must be 0, and although the Shengke field can act on the five element field to cause the change of element Shengke, the five element field is not the source of Shengke field, but the source of Shengke field itself. Therefore, if the Shengke field does not exist in space in advance, even if there are more five element fields, it is impossible to create the five element Shengke change out of thin air. Of course, from another point of view, the change of the distribution of the five elements field in time and space must be accompanied by the Shengke field, and it not only leads to the Shengke field, but determines the specific value and direction of the Shengke field at the changing position, so it can also be regarded as a source.

In addition, without considering the self action of Shengke field, its equation of motion is the most common and typical wave equation, but the equation of motion of five element field is a first-order partial differential equation. Obviously, their behavior is very different.

Not only that, because the field strength tensor of Shengke field contains the primary term and secondary term of Shengke field, the interaction between Shengke fields can become very complex and interesting, showing a lot of complex interaction. For example, if there are two Shengke fields a generating B and B generating C at the same time, the equation of motion will become:

It can be seen that at this time, in addition to the expected two wave equations (the first and second), there are two more coupled equations, so that the two fields are not so independent. Of course, this set of equations has a very simple form:In this way, the above equation will degenerate into (the gauge fixed condition is also recorded here):

Obviously, if the gram field of a generating B is not light like, then the coefficientIt must be constant and the equation of motion becomes:

Obviously, the plane wave, spherical wave and even column potential whose wave direction is orthogonal to its own direction can meet the conditions.

If a generates gram field like light of B, the coefficient may not be constant, so the equation is:

Then we can take that the Shengke field from a to B is still a light like field whose wave direction is orthogonal to its own direction, andIt is also a wave field, so it is satisfiedAt the same time, the two must meet the following coupling equation:

NamelyThe wave direction of is orthogonal to the wave direction of Shengke field and Shengke field. In other words, we can think that although the action directions of the two Shengke fields are the same at each point, there is a difference in intensity, and the change propagation direction of the difference is orthogonal to the direction and propagation direction of the field itself.

It can be expected that if ten kinds of Shengke fields exist in the initial state, the final interaction will be very complex, and the simple orthogonal relationship will no longer meet the conditions. We will face a large lump of Shengke fields completely “entangled”, in which the dynamic relationship and algebraic relationship will be very complex.

For example, if there are several gram generating fields: a generates B, B G D, d g a, a G C, C G E, e generates a, then at this timeMust be constant to zero, soAndThe complex algebraic relationship must be satisfied between them, so that these four terms must offset each other, otherwise it will cause problems that should not existThe appearance of element a, that is, element a itself can be created out of nothing or disappear out of thin air. From this point of view, maybe it is the basic principle of the array

Next, let’s consider Yin and Yang.

From our simple emotion, yin and Yang should be the object of binary opposition that counteracts each other. But in traditional Chinese medicine, we found that a person may have Yin deficiency and yang deficiency at the same time. In fact, we can find that yin and Yang should not offset each other, but should coexist with each other, but there is a certain transformation between the two.

From this point of view, the simplest choice is to compound the five elements field and Shengke field, with the real part as Yang and the virtual part as Yin. If Shengke field always keeps the real number, it is that Yang wood generates Yang fire and Yin wood generates Yin goods. But if Shengke field is also plural, then Yang wood can produce Yang fire, and at the same time, it can also produce some Yin Fire, or even all Yin fire.

However, no matter how we adjust the renormalized Shengke field, we still require the relationshipMust be met.

Of course, this is just a pure brain hole without any theoretical basis, which serves as the theoretical guidance for us to establish the model. We can completely change a set of theories to establish a model, which depends on your own preferences.

The above is only the classical gauge field theory model, and we can certainly consider quantifying it.

The standard quantization scheme is to use the above action quantity as the partition functional, and all fields correspond to the corresponding operators, so that the corresponding quantum process can be calculated:

We put aside the tedious computational details, and only make a simple analysis of the quantized five element Shengke field from the nature.

After quantization, we consider the most common Feynman diagram as an analysis tool. At present, there are mainly two interaction vertices (here, the refolding operation brought by Yin and Yang is considered, and the interaction of Shengke field itself is not considered):

It seems very correct, but there is a problem here: the Shengke field is now the gauge field in the traditional sense, which is true, but the behavior of the five element field has been greatly different. The equation of motion it satisfies is not the traditional active wave equation, but the first-order partial differential equation, it can be converted into the following form:

Here, the former is the propagator of free motion, and the latter is the interaction term. In other words, the top angle interaction of the three lines must be zero.

Therefore, it is very interesting that in the quantum process of generating gram by five elements, there is only four line vertex angle interaction between five elements and no three line vertex angle interaction.

Now, the simplest form of interaction between two five element fields is as follows:

Toy Theory: normative dynamics of Yin Yang and five elements

Feynman diagram sketch of the simplest quantum process (* I can’t find a decent Feynman diagram making tool… *)

The upper and lower straight lines are five element fields, and the red circle in the middle is two Shengke fields.

We can make a comparison between this theory and quantum chromodynamics: in QCD, the gluon in the intermediate gauge field carries one color and one anti color, which changes the color charge of the quark. In our five element Shengke field, the intermediate gauge field is Shengke field, which also carries a “color” and an “inverse color”, such as generating a B and consuming a Q. They are very similar in form, and both have one characteristic: the total amount of all “colors” on a single particle is conserved.

What is really interesting is that there is vacuum energy in the quantized field, that is, the “thread cluster” formed by the five element Shengke field independent of input and output. Because there can be five element fields in this thread group, the properties of other five element fields can be changed.

For example, in the classical case, if there is no Shengke field in space, the corresponding five elements will not change. For example, if there is no field where a generates B, the amount of B will not change even if there are more a elements and more Q elements.

However, after quantization, the situation has changed – there can be five element Shengke fields with random fluctuations in vacuum, which only need to return to nothingness in the time and space constrained by uncertainty. So, for example, now a random fluctuation of a field generating B and an opposite field, because the five element field will not change the Shengke field, but will only be changed by the Shengke field, then the randomly fluctuating Shengke field can act on element a, reducing element Q and increasing element B in space, The B element, which would not have changed, fluctuated due to the vacuum quantum fluctuation. After the action, the Shengke field is annihilated in combination with the corresponding anti field and returns to nothingness.

In the whole process, what we see is that the amount of the five elements has changed for no reason, which was impossible in the classical physical world, but now it may happen because of quantum fluctuations.

Even if there is neither five element field nor Shengke field, the above process can occur: in the vacuum quantum fluctuation, the a field and negative a field are first fluctuated, and then the Shengke field and its inverse field of a generating B are fluctuated. After the quantity is combined, the original zero non attribute Q field is consumed, and the element B is created out of thin air, The unchanged a-field pair and a-born B-field pair return to the void and disappear. What we can see is that element B appears in the vacuum for no reason and consumes element Q as negative.

This is a phenomenon that cannot exist in classical physics after quantization, and its probability is proportional to

Of course, we can also choose to use other methods to construct the field theory describing Yin, Yang and five elements without abiding by the framework of normative field theory. For example, the action quantity is taken as the following form:

The equation of motion given by it is:

Might as well takeFor the most conventionalSo the equation becomes:

As before, we make the matrixIn that way, the Shengke relationship can also be expressed.

Even, we can use scalar gauge fields:

The corresponding equation of motion is():

You see, it can also make the five elements change.

In short, in theory, there are many theoretical models that we can choose as Wuxing Shengke. There is a lot of room for free choice from the basic theoretical framework to some details.

Finally, we would like to emphasize again that all the above is just a toy theory, which is purely for fun and has nothing to do with actual physics. We have no evidence to prove the existence of the above five element field or Shengke field.

However, if you want to write a novel, here gives you a good “theoretical basis”. You can use this as a basis to build your own Yin-Yang and five elements world, which may be very interesting.