Social Quantum Field Theory · SQFT

Social Quantum Field Theory · SQFT

Social Quantum Field Theory

A Clear Guide to Its Axioms, Definitions, Propositions, and Computation

CONTENTS

1. What are axioms, definitions and propositions?Axiom 1: Field priorityAxiom 2: The individual is a local expression of the fieldAxiom 3: Relationships are inseparableAxiom 4: Capital value is determined by the fieldAxiom 5: Critical events converge possibilitiesAxiom 6: Real transformation is a change in relationship structureAxiom 7: Social systems are always subject to external influencesAxiom 8: Similarity in form does not mean the same physicsDefinition 1: Field vectorDefinition 2: Social distanceDefinition 3: Bayesian updateDefinition 4: Relational entropyDefinition 5: Order parameterProposition 1: When the field changes, social distance will changeProposition 2: If you take different paths, your identity results may be different.Proposition 3: Local instability may continue to amplifyProposition 4: External forces can change the original stable stateProposition 5: Symmetry can be used to check fairness1. State transition matrix2. Add Buddy intervention effectSpecific examplesFinally, summarize it in one sentence

Social Quantum Field Theory: A Clear Guide to Its Axioms, Definitions, Propositions, and Computation

Social Quantum Field Theory, or SQFT for short, the core idea is:

A person's behavior cannot only depend on the individual, but also on how the relationships, systems, resources, history and environment in which he is located work together.

It borrows the mathematical language of quantum field theory, network science, probability theory and geometry. Its purpose is not to prove that human society really follows quantum physics, but to establish a system that can:

1. Describe complex social situations.
2. Calculate the relationship between different factors.
3. Analyze how the system changes.
4. Identify possible turning points.
5. Provide verifiable predictions or decision-making references.

The following is explained in accordance with "Axiom → Definition → Proposition → Computer Calculation → Practical Application".

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1. What are axioms, definitions and propositions?

Think of a theory like designing a game.

Axioms: Rules of the Game

Axioms are basic assumptions set by researchers first.

For example:

We assume that a person's social identity cannot be understood in isolation from his or her context.

This is not a proven law of the universe, but a starting point for constructing a model.

Mathematically it can be written as:

\mathcal{F} \succ A_i

in:

\mathcal{F}

Represent the overall social field.

A_i

Represents actor (i).

\succ

Stands for "analytical priority."

Plain-language interpretation:

If you want to understand a person, first look at what kind of situation he is in.

Definition: noun in the game

Definitions are used to describe what each symbol represents.

For example:

\mathbf{x} = \begin{pmatrix} I\\ S\\ R\\ C\\ A\\ T\\ O \end{pmatrix}

Represents a person’s seven-dimensional field state:

I=\text{main force}

S=\text{Stability}

R=\text{Amount of resources}

C=\text{conflict tension}

A=\text{Adaptability}

T=\text{Transformation pressure}

O=\text{openness}

Plain-language interpretation:

Instead of summarizing everything with one sentence, "I'm not doing well recently," I break it down into seven directions that can be observed.

Proposition: the result deduced according to the rules

For example:

The same person's abilities may have different values ​​if circumstances change.

Mathematically:

V_i = V\left(C_i,\mathcal{F},t\right)

in:

V_i

Represents the effective value of person (i).

C_i

Represents the resources or abilities he possesses.

\mathcal{F}

Represent the field.

t

represents time.

if:

\frac{\partial V_i}{\partial \mathcal{F}}\neq 0

The intuitive interpretation is:

The value of a person's abilities changes with circumstances.

Also knows how to write programs:

• In traditional manufacturing, skills may just be a plus.
• In an AI company, it might be core capabilities.
• In some management positions, communication skills are more important.

so:

The ability has not changed, but the stage has changed and the value will also change.

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2. Eight axioms: comparison between mathematics and intuitive interpretation

Axiom 1: Field priority

Officially means:

\mathcal{F}\succ A_i

Plain-language interpretation:

A person's social identity is determined by his environment and relationship network.

For example:

A_i = \text{same person}

At the company:

A_i \mid \mathcal{F}_{\text{company}} = \text{manager}

In the family:

A_i \mid \mathcal{F}_{\text{family}} = \text{Father}

On the team:

A_i \mid \mathcal{F}_{\text{team}} = \text{goalkeeper}

Plain-language interpretation:

People are the same person, but when they enter different fields, their roles, responsibilities, powers and behavior patterns will change.

How does a computer calculate?

Computers can create different situational profiles for the same person:

\mathbf{x}_{\text{company}} = \begin{pmatrix} 0.80\\ 0.45\\ 0.70 \end{pmatrix}

\mathbf{x}_{\text{family}} = \begin{pmatrix} 0.35\\ 0.85\\ 0.60 \end{pmatrix}

Assume that the three numbers represent:

\left( \text{Dominance}, \text{emotional safety}, \text{Available resources} \right)

A computer can compare:

The same person has high dominance at work but low security; he or she has low dominance at home but has high security.

This is more accurate than simply saying "He is a strong person."

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Axiom 2: The individual is a local expression of the field

Formal representation:

\lvert A_i\rangle \sim \hat{\phi}(x_i)\lvert\Omega\rangle

Each symbol can be understood as:

\lvert A_i\rangle

Represents a person's social role or action status.

x_i

Represents his position in the relationship network.

\lvert\Omega\rangle

Represents the background environment.

\hat{\phi}(x_i)

Represents the specific manifestation of the background environment formed at that location.

Plain-language interpretation:

What a person does is usually the result of the environment in which he is located.

For example football:

\text{movement} = f( \text{tactics}, \text{score}, \text{Teammate position}, \text{Opponent position}, \text{past training} )

Not simply:

\text{movement} = f(\text{personal will})

How does a computer calculate?

Can build:

a_i(t) = \alpha_1 p_i(t) + \alpha_2 q_i(t) + \alpha_3 h_i(t) + \alpha_4 e(t)

in:

a_i(t) = \text{No.}i\text{people in time}t\text{action tendencies}

p_i(t) = \text{personal preference}

q_i(t) = \text{Influence of people around you}

h_i(t) = \text{historical experience}

e(t) = \text{external environment}

Assumptions:

\alpha_1=0.30

\alpha_2=0.25

\alpha_3=0.20

\alpha_4=0.25

And currently:

p_i=0.80

q_i=0.60

h_i=0.50

e=0.40

but:

a_i = 0.30(0.80) + 0.25(0.60) + 0.20(0.50) + 0.25(0.40)

a_i = 0.24+0.15+0.10+0.10

a_i = 0.59

Plain-language interpretation:

Although this person wants to take action, the surrounding conditions do not fully cooperate, so the overall action tendency is only 0.59, not 0.80 as indicated by the individual's willingness.

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Axiom 3: Relationships are inseparable

Formal representation:

\lvert\Psi_{AB}\rangle \neq \lvert\psi_A\rangle \otimes \lvert\psi_B\rangle

Plain-language interpretation:

Some relationships cannot be viewed in isolation between two people, because the tacit understanding between the two is itself additional information.

For example:

\text{team performance} \neq \text{A's ability} + \text{B’s ability}

Closer:

\text{team performance} = \text{A's ability} + \text{B’s ability} + \text{collaborative effect}

written as:

P_{AB} = P_A+P_B+\lambda_{AB}

in:

\lambda_{AB} = \text{The effect of collaboration or friction between two people}

How does a computer calculate?

Assumptions:

P_A=70

P_B=75

If there is a good understanding of each other:

\lambda_{AB}=30

but:

P_{AB}=70+75+30=175

If two people don’t trust each other:

\lambda_{AB}=-25

but:

P_{AB}=70+75-25=120

Plain-language interpretation:

The same two people with good abilities can reach 175 points if they are matched well; if they are not matched well, they may only be left with 120 points.

Going one step further: mutual information

You can use:

I(A;B) = \sum_{a,b} p(a,b) \log \frac{p(a,b)}{p(a)p(b)}

Plain-language interpretation:

After seeing A's behavior, can you guess B's next behavior more accurately?

if:

I(A;B)=0

express:

There is no identifiable statistical dependence on the data for A's and B's actions.

if:

I(A;B)>0

express:

There is some statistical correlation between the two.

But it must be noted:

I(A;B)>0 \not\Rightarrow \text{Physics Quantum Entanglement}

Nor does it necessarily represent causation.

Because it is possible for two people to:

• All while adhering to the same set of rules.
• At the same time, they are directed by the coach.
• See the same message at the same time.
• Affected by common external events.

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Axiom 4: Capital value is determined by the field

Formal representation:

V_i = V( C_i, \mathcal{F}, \mathcal{T}, t )

in:

C_i = \text{Resources, skills, education or reputation}

\mathcal{F} = \text{field}

\mathcal{T} = \text{relationship structure}

t = \text{time}

Plain-language interpretation:

Whether you have value or not depends not only on what you have, but also on where, when and by whom you are recognized.

How does a computer calculate?

can be simplified to:

V_i = C_i \times R_{\mathcal{F}} \times D_t

in:

C_i = \text{Ability base value}

R_{\mathcal{F}} = \text{Field recognition level}

D_t = \text{current level of demand}

Suppose someone has:

C_i=90

However, the current industry recognition is only:

R_{\mathcal{F}}=0.40

Market demand:

D_t=0.50

So:

V_i=90\times0.40\times0.50

V_i=18

If you transfer to a more suitable industry:

R_{\mathcal{F}}=0.90

D_t=0.85

but:

V_i=90\times0.90\times0.85

V_i=68.85

Plain-language interpretation:

The ability is obviously the same, but the field has been changed, and the actual value that can be used has increased from 18 to 68.85.

This is it:

It’s not that you have no value, but that the current environment may not use your value.

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Axiom 5: Critical events converge possibilities

Before the incident:

\lvert\Psi\rangle = \sum_{k=1}^{n} c_k\lvert\psi_k\rangle

in:

\lvert\psi_k\rangle = \text{No.}k\text{possible development}

|c_k|^2 = \text{The weight of this development in the model}

and requires:

\sum_{k=1}^{n}|c_k|^2=1

Plain-language interpretation:

Before the matter is finalized, there may be multiple development directions at the same time.

For example:

p= \begin{pmatrix} 0.45\\ 0.35\\ 0.20 \end{pmatrix}

represent:

45% = \text{maintain status quo}

35% = \text{Gradual transformation}

20% = \text{Quick reorganization}

If there is a major policy or technological breakthrough, new information may change the distribution:

p' = \begin{pmatrix} 0.10\\ 0.25\\ 0.65 \end{pmatrix}

Plain-language interpretation:

It was most likely to maintain the status quo, but after the incident, rapid reorganization became the most likely direction.

projection representation

If projective formalization is used, the normalized state can be written as:

\lvert\Psi'\rangle = \frac{ \hat{P}_k\lvert\Psi\rangle }{ \sqrt{ \langle\Psi\rvert \hat{P}_k \lvert\Psi\rangle } }

Plain-language interpretation:

A major event converged many possibilities into a path that is now realized.

However, in actual social research, it is usually easier to verify using Bayesian update, event study or state transition model than directly applying the physical projection formula.

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Axiom 6: Real transformation is a change in relationship structure

formal:

\Delta\chi = - \chi(\mathcal{F}_{t_2}) \chi(\mathcal{F}_{t_1})

if:

\Delta\chi\neq0

express:

A structural feature of the field changes.

if:

\Delta\chi=0

It means:

The selected topology index has not changed.

But be careful:

\Delta\chi=0 \not\Rightarrow \text{All structures remain completely unchanged}

Because a single topological indicator may not capture all changes.

How does a computer calculate?

Assume there are five departments:

A,B,C,D,E

Before reform:

A\leftrightarrow B

B\leftrightarrow C

C\leftrightarrow D

D\leftrightarrow E

This is a layer-by-layer transfer structure.

Newly added after the reform:

A\leftrightarrow D

B\leftrightarrow E

A\leftrightarrow E

Information no longer can only flow according to its original level.

Can be compared to:

\Delta E = - E_{\text{After reform}} E_{\text{before reform}}

in:

E = \text{Number of active links}

If before reform:

E_{\text{before reform}}=4

After reform:

E_{\text{After reform}}=7

but:

\Delta E=3

Plain-language interpretation:

Not only did the company's performance numbers change, but there were actually three new channels of cooperation between different departments.

Further calculations can also be made:

L = \text{average shortest path length}

Q = \text{The degree of community modularization}

C = \text{clustering coefficient}

Plain-language interpretation:

• The average path becomes shorter: information reaches the people who need it faster.
• Modular changes: Departmental barriers may increase or decrease.
• Changes in clustering coefficient: changes in small group cooperation patterns.

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Axiom 7: Social systems are always subject to external influences

Simplified representation:

\frac{d\mathbf{x}}{dt} = f(\mathbf{x}) + g(\mathbf{x},\mathbf{u}) + \boldsymbol{\varepsilon}

in:

\mathbf{x} = \text{Current situation}

f(\mathbf{x}) = \text{internal natural evolution}

\mathbf{u} = \text{external input}

g(\mathbf{x},\mathbf{u}) = \text{Changes due to external influences}

\boldsymbol{\varepsilon} = \text{random disturbance}

Plain-language interpretation:

Tomorrow's state comes from today's state, external events, and factors that cannot be fully anticipated.

If we use the formal analogy of an open system:

\frac{d\hat{\rho}}{dt} = -\frac{i}{\hbar} [\hat{H},\hat{\rho}] + \sum_k \left( \hat{L}_k\hat{\rho}\hat{L}_k^\dagger - \frac{1}{2} \left{ \hat{L}_k^\dagger\hat{L}_k, \hat{\rho} \right} \right)

Plain-language translation:

\text{status change} = \text{internal interaction} + \text{external environmental impact}

in:

\hat{H}

It can be compared to:

Interaction rules within the system.

\hat{L}_k

It can be compared to:

Type (k) external influence channel.

For example:

\hat{L}_1 = \text{work pressure}

\hat{L}_2 = \text{family support}

\hat{L}_3 = \text{health changes}

\hat{L}_4 = \text{economic fluctuations}

However, practical social models usually do not require physical constants:

\hbar

Fitted in; it can be changed to a dimensionless parameter or time scale that is consistent with the data.

How does a computer calculate?

The most direct way:

x_{t+1} = x_t + \alpha I_t - \beta C_t + \gamma S_t

in:

x_t = \text{Overall status today}

I_t = \text{positive action}

C_t = \text{conflict or pressure}

S_t = \text{level of support}

Assumptions:

x_t=0.50

I_t=0.60

C_t=0.80

S_t=0.70

and:

\alpha=0.20

\beta=0.30

\gamma=0.25

but:

x_{t+1} = 0.50 + 0.20(0.60) - 0.30(0.80) + 0.25(0.70)

x_{t+1} = 0.50+0.12-0.24+0.175

x_{t+1} = 0.555

Plain-language interpretation:

Although the pressure is high today, the overall status can rise slightly from 0.50 to 0.555 because there is still the ability and support to act.

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Axiom 8: Similarity in form does not mean the same physics

The most important boundaries:

\text{formal analogy} \neq \text{physical identity}

therefore:

\text{Social relations are inseparable} \neq \text{Physics Quantum Entanglement}

\text{structural transition} \neq \text{Quantum wave function collapse}

\text{field vector} \neq \text{real quantum state}

Plain-language interpretation:

Just borrowing a set of mathematical tools that are good at describing complex interactions does not mean that people really become particles.

This boundary is very important for future submissions, research and product design.

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3. Important definitions: What exactly does the formula count?

Definition 1: Field vector

The situation can be written as:

\mathbf{x} = \begin{pmatrix} I\\ S\\ R\\ C\\ A\\ T\\ O \end{pmatrix}

For example:

\mathbf{x} = \begin{pmatrix} 0.55\\ 0.40\\ 0.35\\ 0.80\\ 0.60\\ 0.75\\ 0.45 \end{pmatrix}

correspond:

index	numerical value	Intuitive interpretation
Main force (I)	0.55	Still have some mobility
Stability (S)	0.40	Not stable enough recently
Resource amount (R)	0.35	Limited time, energy or support
Conflict Tension (C)	0.80	Stress and conflict are high
Adaptability (A)	0.60	Can also be adjusted
Transformation Pressure (T)	0.75	The original approach may no longer be enough
Openness (O)	0.45	Not willing to accept too many new options for the time being

Overall interpretation:

You still have the ability to act and adjust, but you have recently been under high pressure, with insufficient resources, and your current lifestyle may be approaching the stage of needing adjustment.

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Definition 2: Social distance

The gap between the two field states can be written as:

d(\mathbf{x},\mathbf{y}) = \sqrt{ \sum_{j=1}^{n} w_j(x_j-y_j)^2 }

in:

w_j

Represents the importance of the (j)th indicator.

if:

\sum_{j=1}^{n}w_j=1

The normalized weighted distance is obtained.

Plain-language interpretation:

See how similar the two situations are, but different projects can have different importance.

Specific calculation

User's current status:

\mathbf{x} = \begin{pmatrix} 0.55\\ 0.40\\ 0.35\\ 0.80\\ 0.60\\ 0.75\\ 0.45 \end{pmatrix}

"High tension transformation" model:

\mathbf{h}_1 = \begin{pmatrix} 0.60\\ 0.35\\ 0.40\\ 0.85\\ 0.55\\ 0.80\\ 0.40 \end{pmatrix}

Assume that seven items are equally important:

w_j=\frac{1}{7}

but:

d_1 = \sqrt{ \frac{1}{7} \sum_{j=1}^{7} (x_j-h_{1,j})^2 }

Because each difference is:

0.05

so:

d_1 = \sqrt{ \frac{7(0.05^2)}{7} }

d_1=0.05

Another "stable recovery" model:

\mathbf{h}_2 = \begin{pmatrix} 0.40\\ 0.80\\ 0.70\\ 0.25\\ 0.65\\ 0.30\\ 0.60 \end{pmatrix}

but:

d_2 = \sqrt{ \frac{ 0.15^2 + (-0.40)^2 + (-0.35)^2 + 0.55^2 + (-0.05)^2 + 0.45^2 + (-0.15)^2 }{7} }

d_2 = \sqrt{ \frac{0.835}{7} }

d_2\approx0.345

Compare:

d_1=0.05

d_2\approx0.345

Plain-language interpretation:

Your current state is obviously closer to "high-tension transformation" than "stable recovery".

Notice:

This is not fortune telling, but using numerical values ​​to determine which state you are in now.

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Definition 3: Bayesian update

formula:

P(H_k\mid E) = \frac{ P(E\mid H_k)P(H_k) }{ \sum_j P(E\mid H_j)P(H_j) }

in:

H_k = \text{No.}k\text{possible situations}

E = \text{The data currently observed}

P(H_k) = \text{Originally thought that the possibility of this situation occurring}

P(E\mid H_k) = \text{The degree to which the current data is consistent with the situation}

P(H_k\mid E) = \text{Possibility of recalculating after adding data}

Plain-language interpretation:

The original judgment is adjusted based on new evidence.

Specific calculation

Assume there are two states:

H_1=\text{high tension transformation}

H_2=\text{stable recovery}

Original probability:

P(H_1)=0.40

P(H_2)=0.60

Indicates that before reading new information:

We originally thought that "stable recovery" was more common.

Convert distance into degree of coincidence:

P(E\mid H_k) \propto \exp \left( -\frac{d_k^2}{2\sigma^2} \right)

Pick:

\sigma=0.15

Regarding "high-tension transformation":

d_1=0.05

so:

P(E\mid H_1) \propto \exp \left( -\frac{0.05^2}{2(0.15)^2} \right)

P(E\mid H_1) \propto 0.946

For "stable recovery":

d_2\approx0.345

therefore:

P(E\mid H_2) \propto \exp \left( -\frac{0.345^2}{2(0.15)^2} \right)

P(E\mid H_2) \propto 0.071

Substitute:

P(H_1\mid E) = \frac{ 0.946\times0.40 }{ 0.946\times0.40 + 0.071\times0.60 }

P(H_1\mid E) \approx0.899

Same reason:

P(H_2\mid E) \approx0.101

therefore:

P(H_1\mid E)\approx89.9%

P(H_2\mid E)\approx10.1%

Plain-language interpretation:

Although I originally thought that stable recovery was more common, after seeing the current high pressure, low resources, and high transformation pressure, the system re-judged: You are currently closer to a high-tension transformation state.

But note that this example only has two candidate states.

If FieldSense has:

64

For each situation, deal with them all:

H_1,H_2,\ldots,H_{64}

Compute and normalize together:

P(H_k\mid E) = \frac{ L_k\pi_k }{ \sum_{j=1}^{64}L_j\pi_j }

in:

L_k=P(E\mid H_k)

\pi_k=P(H_k)

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Definition 4: Relational entropy

The general probability distribution entropy can be written as:

S = -\sum_{k=1}^{n} p_k\log p_k

Plain-language interpretation:

Is the system "very clear in direction" or "many possibilities are similar"?

Situation 1: Unknown direction

p = \begin{pmatrix} 0.25\\ 0.25\\ 0.25\\ 0.25 \end{pmatrix}

All four possibilities are similar.

Plain-language interpretation:

I can't see which way is more likely.

Scenario 2: The direction is clear

p = \begin{pmatrix} 0.85\\ 0.05\\ 0.05\\ 0.05 \end{pmatrix}

Plain-language interpretation:

Most of the evidence points to the first scenario.

Need to emphasize:

\text{High entropy} \neq \text{Must be bad}

\text{low entropy} \neq \text{Must be good}

because:

• High entropy may also mean more choices and more room for exploration.
• Low entropy can also mean being restricted, forced to accept a single direction.

So entropy mainly measures:

Levels of uncertainty, not happiness.

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Definition 5: Order parameter

The order parameter can be written as:

\Phi = \langle\phi\rangle

Plain-language interpretation:

Use a representative indicator to determine which state the entire system has entered.

For example, organizational trust:

\Phi_{\text{trust}} = \frac{1}{N} \sum_{i=1}^{N} T_i

in:

T_i = \text{No.}i\text{member's level of trust}

Assume the trust scores of five employees:

0.80,\ 0.70,\ 0.65,\ 0.75,\ 0.60

but:

\Phi_{\text{trust}} = \frac{ 0.80+0.70+0.65+0.75+0.60 }{5}

\Phi_{\text{trust}}=0.70

Plain-language interpretation:

Overall team trust is 0.70.

If after two months it becomes:

\Phi_{\text{trust}}=0.32

It may mean:

It’s not that a single employee is in a bad mood, it’s that overall organizational trust is slipping.

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4. Important Propositions: From Formulas to Realistic Judgments

Proposition 1: When the field changes, social distance will change

Officially means:

d_{\mathcal{F}}(A,B) \neq d_{\mathcal{F}'}(A,B)

Plain-language interpretation:

The distance between the same two people in different systems may be completely different.

example:

d_{\text{flat organization}} ( \text{staff}, \text{manager} ) = 0.20

d_{\text{hierarchical organization}} ( \text{staff}, \text{manager} ) = 0.85

Plain-language interpretation:

In the first company, employees could discuss it directly with their supervisor; in the second company, they had to go through several layers.

Can be applied to

• Organizational reform.
• A study of promotion and class.
• Professional social mobility.
• Social class comparison.

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Proposition 2: If you take different paths, your identity results may be different.

Formal representation:

\mathcal{P}_{\gamma_1}(v) \neq \mathcal{P}_{\gamma_2}(v)

in:

\gamma_1,\gamma_2

Represents two different systems or career paths.

Plain-language interpretation:

Even if the starting point is the same, through different systems and experiences, the final identity recognition may be different.

For example:

\text{engineer} \rightarrow \text{product manager} \rightarrow \text{Entrepreneur}

and:

\text{engineer} \rightarrow \text{Research Director} \rightarrow \text{Entrepreneur}

They all became entrepreneurs in the end, but:

• People are different.
• Investor trust is different.
• Product capabilities vary.
• Teams are managed differently.

so:

The result should not only be judged by the final professional title, but also by how you have gone along the way.

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Proposition 3: Local instability may continue to amplify

Assume that the small disturbance is:

\delta x(t)

if:

\delta x(t) = \delta x(0)e^{\lambda t}

when:

\lambda>0

express:

Small problems will grow bigger.

when:

\lambda<0

express:

The system will gradually return to stability.

Specific calculation

Assuming the initial level of instability:

\delta x(0)=0.10

and:

\lambda=0.30

go through:

t=4

but:

\delta x(4) = 0.10e^{0.30\times4}

\delta x(4) = 0.10e^{1.2}

\delta x(4)\approx0.332

Plain-language interpretation:

What starts out as a small friction of 0.10 may magnify to 0.332 after four time units.

Practical use:

• Organizational trust crisis.
• Market panic.
• Communal opposition.
• User stress builds up.
• Team communication fails.

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Proposition 4: External forces can change the original stable state

Simplified representation:

\frac{dx}{dt} = -\frac{dV(x)}{dx} + J

in:

V(x) = \text{original stable structure}

J = \text{external thrust}

Plain-language interpretation:

The system may be stuck in a certain habit, but if the external force is strong enough, there is a chance to push it to another state.

For example:

J = \text{Policy subsidies}

or:

J = \text{New technology emerges}

or:

J = \text{an important conversation}

FieldSense Applications

If the user has been in:

x_{\text{old}} = \text{High pressure but no change}

One time Buddy provided:

J = \text{arrange a break}

or:

J = \text{Seek someone you can trust to talk to}

May allow users to gradually enter:

x_{\text{new}} = \text{Reorganize and restore}

However, whether it is effective must be verified with follow-up data and cannot rely solely on theoretical assumptions.

---

Proposition 5: Symmetry can be used to check fairness

If a system is fair, the results should be the same if certain labels are changed that should not affect the results:

R(X,Z) = R(X,gZ)

in:

X = \text{actual ability or condition}

Z = \text{identity tag}

gZ = \text{Changed label}

can be defined:

\Delta_G = \left| R(X,Z) - R(X,gZ) \right|

if:

\Delta_G=0

Plain-language interpretation:

Changing the irrelevant labels does not change the results, and the model meets the set fairness conditions.

if:

\Delta_G>0

Plain-language interpretation:

Obviously the ability conditions are the same, but just because the identity labels are different, the results are different.

computer example

Same resume:

X = \text{Same academic qualifications, years of experience and skills}

Version one:

R(X,Z_1)=0.82

Version two:

R(X,Z_2)=0.61

but:

\Delta_G = |0.82-0.61|

\Delta_G=0.21

Plain-language interpretation:

Two resumes with the same qualifications, only the identity tags were changed, but the admission score differed by 0.21, which deserves further investigation.

---

5. How does the computer simulate the next step of the field?

1. State transition matrix

Assume that the user may currently be in three states:

H_1=\text{high pressure}

H_2=\text{Adjustment}

H_3=\text{recover}

Current odds:

\mathbf{p}_t = \begin{pmatrix} 0.70 & 0.20 & 0.10 \end{pmatrix}

Plain-language interpretation:

Current system estimates: 70% near high pressure, 20% in correction, and 10% near recovery.

Create a transfer matrix:

\mathbf{P} = \begin{pmatrix} 0.65 & 0.25 & 0.10\\ 0.15 & 0.60 & 0.25\\ 0.05 & 0.25 & 0.70 \end{pmatrix}

The first column represents:

P(H_1\rightarrow H_1)=0.65

P(H_1\rightarrow H_2)=0.25

P(H_1\rightarrow H_3)=0.10

Plain-language interpretation:

When at high pressure, the next stage is 65% still high pressure, 25% entering adjustment, and 10% entering recovery.

Next stage:

\mathbf{p}_{t+1} = \mathbf{p}_t\mathbf{P}

Substitute:

\mathbf{p}_{t+1} = \begin{pmatrix} 0.70 & 0.20 & 0.10 \end{pmatrix} \begin{pmatrix} 0.65 & 0.25 & 0.10\\ 0.15 & 0.60 & 0.25\\ 0.05 & 0.25 & 0.70 \end{pmatrix}

After calculation:

\mathbf{p}_{t+1} = \begin{pmatrix} 0.49 & 0.32 & 0.19 \end{pmatrix}

Plain-language interpretation:

In the next phase, high pressure may drop from 70% to 49%, adjustment may increase to 32%, and recovery may increase to 19%.

This is not a guarantee of the future, but rather:

Which change is more likely under the current model and assumptions?

---

2. Add Buddy intervention effect

Suppose Buddy provides three suggestions:

u_1=\text{rest}

u_2=\text{organize thoughts}

u_3=\text{Contact a trusted person}

can be defined:

\mathbf{P}(u) = \text{take action}u\text{The transfer matrix after}

For example after a break:

\mathbf{P}(u_1) = \begin{pmatrix} 0.50 & 0.35 & 0.15\\ 0.10 & 0.55 & 0.35\\ 0.03 & 0.20 & 0.77 \end{pmatrix}

Computer recalculation:

\mathbf{p}_{t+1}^{(u_1)} = \mathbf{p}_t\mathbf{P}(u_1)

get:

\mathbf{p}_{t+1}^{(u_1)} = \begin{pmatrix} 0.373 & 0.375 & 0.252 \end{pmatrix}

Plain-language interpretation:

If the "rest" intervention really meets the model assumptions, high pressure may be reduced to 37.3%, and recovery may be increased to 25.2%.

But these numbers cannot be specified out of thin air and then regarded as valid.

should be passed through:

• User feedback.
• historical record.
• Before and after status comparison.
• The results of actual actions taken.

Step by step estimation:

\mathbf{P}(u)

Only then can there be research and product value.

---

6. How to integrate into FieldSense?

FieldSense already has a foundation that is very suitable for SQFT implementation:

\text{user} + \text{Field analysis} + \text{Buddy} + \text{memory} + \text{Suggestions for next steps}

can be further formed into:

\mathbf{x}_t = f( \text{mood}, \text{relation}, \text{resource}, \text{environment}, \text{memory} )

Then:

P(H_k\mid\mathbf{x}_t) = \text{The user currently meets the}k\text{probability of a situation}

then:

\mathbf{x}_{t+1} = g( \mathbf{x}_t, u_t, \mathcal{E}_t )

in:

u_t = \text{Next step the user takes}

\mathcal{E}_t = \text{External events and living environment}

at last:

M_{t+1} = M_t + \Delta M_t

in:

M_t = \text{personal memory}

\Delta M_t = \text{The new experience gained from this interaction}

Plain-language interpretation:

FieldSense first understands your current status, Buddy makes a small suggestion based on past experience, then remembers the results, and gradually learns which methods are more helpful to you.

Specific examples

User status today:

\mathbf{x}_t = \begin{pmatrix} 0.45\\ 0.35\\ 0.40\\ 0.80\\ 0.55\\ 0.70\\ 0.30 \end{pmatrix}

System judgment:

P(\text{High voltage transformation}\mid\mathbf{x}_t) = 0.72

P(\text{Tensions}\mid\mathbf{x}_t) = 0.18

P(\text{gradual recovery}\mid\mathbf{x}_t) = 0.10

Buddy doesn't need to show a bunch of math.

Just say:

Buddy discovered: You may have been struggling recently, but what really makes you tired is not just that there are too many things, but that the original arrangement is no longer suitable for you now.

Then suggest:

Don't rush to solve all the problems today. Just pick one thing that consumes you the most and see if you can temporarily reduce it a little.

If the user takes action to re-measure the next day:

\mathbf{x}_{t+1} = \begin{pmatrix} 0.50\\ 0.45\\ 0.45\\ 0.65\\ 0.60\\ 0.60\\ 0.40 \end{pmatrix}

You can calculate:

\Delta C = C_{t+1}-C_t

\Delta C = 0.65-0.80

\Delta C=-0.15

Plain-language interpretation:

The stress indicator fell by 0.15.

at the same time:

\Delta S = 0.45-0.35

\Delta S=0.10

Plain-language interpretation:

The sense of stability increased by 0.10.

Finally Buddy can say:

After you slowed down one thing yesterday, the tension seems to be lessened today. Maybe you don’t need to organize your life all at once, just keep a little space.

This is it:

\text{SQFT} + \text{Bayesian update} + \text{personal memory} + \text{Gentle companionship}

Implement it into a specific product.

---

7. How to prove that it is really useful in the future?

No matter how beautiful the theory is, it must be tested by data.

Two models can be compared.

Baseline model

Only view the user's own data:

\widehat{y}_{\text{baseline}} = f( \text{mood}, \text{age}, \text{personal preference} )

SQFT model

Add relationships and environments:

\widehat{y}_{\text{SQFT}} = f( \text{personal status}, \text{Relationship network}, \text{resource}, \text{historical memory}, \text{institutional position}, \text{external events} )

Compare forecast errors:

\operatorname{Error}_{\text{baseline}}

and:

\operatorname{Error}_{\text{SQFT}}

if:

\operatorname{Error}_{\text{SQFT}} < \operatorname{Error}_{\text{baseline}}

There is reason to claim:

After adding field, relationship and historical factors, the model is indeed better at explaining or predicting behavior.

Further, the improvement ratio can be calculated:

\operatorname{Improvement} = \frac{ \operatorname{Error}_{\text{baseline}} - \operatorname{Error}_{\text{SQFT}} }{ \operatorname{Error}_{\text{baseline}} } \times100%

For example:

\operatorname{Error}_{\text{baseline}}=0.30

\operatorname{Error}_{\text{SQFT}}=0.21

but:

\operatorname{Improvement} = \frac{0.30-0.21}{0.30} \times100%

\operatorname{Improvement}=30%

Plain-language interpretation:

If the prediction error is reduced by 30% after adding relationships, environment and history, this model will truly show practical value.

Finally, summarize it in one sentence

Axioms determine the perspective from which a problem is viewed, definitions turn concepts into calculable variables, and propositions propose testable results; computers turn these rules into data analysis, situation simulations and personalized suggestions.

Note: This article borrows the formal language of quantum field theory as a modeling tool for social systems. Similar mathematical forms do not imply identical physical mechanisms.

Reference

Social Quantum Field Theory. First Edition, 2026. Zenodo Record 21532345