A Social Field Model Based on Quantum Phenomenology

Quantum Phenomenological Social Field Theory: A Social Field Model Based on Quantum Phenomenology

From Relational Emergence to the Scientization of Agency Phase

Abstract

This study proposes a social field model grounded in quantum phenomenology, asserting that society is not composed of discrete individuals but rather a continuous field formed by relationships, flows, and interaction intensities. Social behaviors emerge as fluctuations from couplings within the field, with phase changes representing agency, and observation-feedback determining order solidification. The study establishes a mathematical framework, including the social field wave function Ψ(x,t), existence density field ρ(x,t), and relational potential field Φ(x,t), along with nonlinear field evolution equations and an observation-feedback mechanism. This model unifies the description of norm formation, collective action, and social change, providing a physically consistent field-theoretic framework for the social sciences.

Keywords: Quantum Phenomenology, Social Field, Agency, Emergence, Spontaneous Symmetry Breaking

Introduction

Traditional social sciences often assume individuals as decision-making subjects, with society as the aggregate of individual preferences. However, extensive empirical studies reveal that collective behaviors frequently exhibit nonlinear emergent characteristics:

• Crowd effects
• Trend diffusion
• Sudden social transformations

These phenomena are difficult to explain using independent actor models. This study proposes: society is a field, not a collection of particles. Actions are not made independently but generated through interactions.

This perspective aligns with quantum phenomenology:

Phenomena emerge in observation, not fixed prior to measurement.

Theoretical Foundations

This study integrates three core concepts:

1. Society possesses continuous field attributes (Social Field)
2. Interactions form fluctuations and phase couplings (Relation-Induced Waves)
3. Observation and feedback constitute order generation (Phenomenological Determination)

Thus, behavior emerges as ripples from social interactions.

Definition of Social Field Variables

Two fundamental fields are defined:

• Existence Density Field
  ρ(x,t): Describes the local contribution intensity of individuals to the social field
• Relational Potential Field
  Φ(x,t): Describes interaction tensions, normativity, and social resistance

The social field wave function is defined as:

Ψ(x,t) = ρ(x,t) ⋅ e^{i Φ(x,t)}

Interpretation:

|Ψ|² = ρ² represents the intensity of behavioral emergence

Φ is the phase, governing interaction direction and meaning interpretation

Thus:

Existence (density) × Meaning (phase) → Behavior (state)

Field-Theoretic Definition of Agency

Agency is no longer viewed as “freedom independent of society” but as:

ΔΦ(x,t) ≠ 0

Meaning:

Behavior possesses the capacity to alter field phase, thereby reshaping order.

Thus, freedom is not escaping society but redirecting the social wave.

Social Field Dynamics Equations

Behavioral emergence is governed by two forces:

• Normative damping (return to existing order)
• Innovative coupling (formation of new collective trends)

The model adopts a nonlinear diffusion dynamics equation:

∂Ψ/∂t = D ∇² Ψ − α Ψ + β |Ψ|² Ψ

Parameter Meanings:

• D: Efficiency of information and emotion diffusion in networks
• α: Normative suppression intensity (conformity)
• β: Relational amplification coefficient (cohesion resonance)

When β is sufficiently large, the field produces local clustering:

Spontaneous symmetry breaking → Generation of collective action

Observation and Feedback: Phenomenological Mechanism

In the quantum world:

State is established under observation

Society is analogous:

Norms become reality because they are seen

Ψ_observed = M ⋅ Ψ

M is the social observation matrix: media, institutions, public opinion, performance evaluations…

Visibility → Reality

Whoever controls the observation frame shapes facts.

Mathematical Interpretation and Social Implications

Concept	Physical Meaning	Social Correspondence
ρ(x,t)	Mass density	Individual participation, resource investment
Φ(x,t)	Phase	Meaning, values, stance
Ψ(x,t)	Wave function	Behavioral tendency, interaction state
Ψ²	Probability distribution → Ψ² indicates “where particles are most likely observed” Interference effect → Superposition of multiple Ψ alters Ψ² distribution, producing constructive/destructive interference (quantum interference)	In the social field model, Ψ corresponds to “action field” or “strategy field”; Ψ² corresponds to “density of action or strategy occurrence” Interference effect → Interactions among different actions, policies, or decisions in society alter the overall field intensity distribution (Ψ²).
ΔΦ ≠ 0	Phase manipulation	Human agency
∇² Ψ	Diffusion	Social information transmission
Spontaneous symmetry breaking	Energy well formation	Groups, institutions, trends

Concise Proposition:

Humans are sources that feedback and rewrite the field.

Model Application Potential

This model can be applied to:

• Mass movements
• Policy feedback
• Corporate organizational culture
• Meme diffusion
• Network polarization
• Emergent consumer behavior
• Contagious emotions and panic

Enabling quantitative study of topics previously describable only qualitatively.

Conclusion

This study demonstrates:

• Social order is not preset by individual consciousness but emerges from interactions
• Agency is phase variability, reshaping collective direction
• Observation mechanisms determine what becomes reality
• Social sciences can adopt field theory for quantification and simulation

Society is not constituted by people but by relational and meaning fields.

People are not external observers of the field but its shapers.

Future Research Directions

A. More rigorous derivation of Lagrangian and Hamiltonian forms

B. Integration with social network science and Bourdieu’s field theory

C. Numerical simulation and visualization using Python/Julia

D. Empirical data fitting, e.g., crowd sentiment propagation

E. Introduction of multi-field models with dynamic weights and phase entanglement