by Maksim Kolesnikov & Copilot (2025)
This article offers a phase-conditioned reinterpretation of Zhi Kai Zou’s speculative entropy-based framework. We show that the emergence of mass, gravity, and symmetry described therein presumes unqualified participation across the spacetime substrate—an assumption explicitly bounded by φₑ(x, t)-theory. Through structural comparison, we reveal that Zou’s claims correspond to special cases within regions of full phase admissibility, φₑ → 1. Outside such regions, his equations fail to propagate or define evolution. Our goal is not opposition, but phase bounding and structural coherence.
Zhi Kai Zou’s recent formulation brings together entropy, symmetry, and curvature into a speculative cosmological-holographic model. While compelling, we believe it rests on implicit assumptions of total manifestability—assumptions made explicit and conditional in the φₑ(x, t) framework.
We present this not as a refutation, but as a structural contrast. Our approach treats Zou’s model as a φₑ-bounded limit case of a broader participation-based theory. Readers will find equations from both frameworks presented in parallel (see Figures 1 through 5), with no rhetorical conclusions—only manifest conditions.
We do not claim φₑ is truer; we show where it permits emergence. Let the reader decide what participates.
Zou’s theory assumes that entropy is globally present, that fields such as SU(3) and the Higgs mechanism activate autonomously, and that the resulting structures—spacetime, mass, and force—are emergent from this entropic background.
In contrast, φₑ(x, t)-theory posits that no structure emerges without prior admissibility, and that this admissibility is a locally variable scalar field. Zou treats emergence as inherent; φₑ requires it to be conditionally permitted. This divergence is critical: Zou presumes global phase coherence; φₑ evaluates whether such coherence is even locally possible.
In Zou’s model, the spacetime metric tensor arises from entropy gradients. This makes geometry a product of informational asymmetry. However, this approach assumes that such gradients always exist and are evaluable.
φₑ-theory instead models the metric as a phase-weighted modification of flat Minkowski space. Specifically, the metric tensor is expressed as the Minkowski metric multiplied by a function of φₑ(x, t), which varies with local participation. If φₑ approaches zero, no meaningful geometry can form, as no manifest structure may propagate. This means curvature is not entropically defined, but phase-constrained in its very possibility.
(See Figure 3 for φₑ-based metric formulation.)
Zou treats entropy as foundational: it is the underlying dynamic that gives rise to time, mass, and geometry.
φₑ-theory inverts this: entropy only makes sense where phase participation exists. In zones where φₑ(x, t) equals zero, the concept of entropy becomes undefined, because no transitions, distributions, or configurations are permitted. Therefore, entropy is not the cause of emergence—it is a consequence of allowed transitions in already-manifesting systems.
In Zou’s framework, mass is a product of entropy localization interacting with the Higgs field. This ties mass to informational asymmetry and symmetry breaking. The expression suggests that wherever entropy condenses and symmetry breaks, mass appears.
Under φₑ(x, t)-theory, mass is modeled more directly and conditionally. The local mass is the product of a constant structural potential and the participation function: m(x, t) = M₀ · φₑ(x, t) This formula assumes that without φₑ(x, t) > 0, no mass may emerge or be evaluated. It doesn’t prohibit the Higgs field—but reframes it as something that may only manifest inside admissible domains, rather than as a generative source.
(See Figure 2 for direct mass formulation.)
Zou views time as an axis emerging from entropic growth. But this presumes that the system has sufficient admissibility to produce statistically ordered transitions.
In φₑ-theory, time exists only where there is an admissible sequence of phases. Time is not produced by entropy—it reflects the continuity of φₑ(x, t) across successive states. This means that in regions where φₑ vanishes, temporal directionality and structure cease to apply.
Thus, irreversibility and causality emerge not from statistical laws, but from gradients and coherence within the φₑ field.
(See Figure 5 for expression of time as a function of φₑ.)
We conclude that each of Zou’s major claims operates inside a zone where φₑ(x, t) is strictly positive and sufficiently stable. His derivations presume activation—but offer no mechanism to delimit where such activation fails.
By contrast, φₑ(x, t)-theory not only explains emergence—it explains non-emergence. It models structural silence, phase cancellation, and the inability to manifest curvature, mass, or temporality.
Mass only appears where φₑ permits it
Geometry exists only in φₑ-admissible spacetime regions
Entropy has no meaning outside activation domains
Symmetry patterns (SU(3), Higgs) are possible only as φₑ-manifested phenomena
Time is defined through φₑ, not entropy
7. Appendix A — Phase-Conditioned Equation Panel
(Place JPEGs in this order under appropriate captions.)
Figure 1 – Participation-weighted stress: σ(x, t) = φₑ(x, t) · E · ∇U(x, t)
Figure 2 – Phase-bounded mass emergence: m(x, t) = M₀ · φₑ(x, t)
Figure 3 – φₑ-weighted spacetime metric: g_{μν}(x, t) = f(φₑ) · η_{μν}
Figure 4 – Admissibility constraint: φₑ(x, t) ∈ (ε, 1), ε → 0⁺
Figure 5 – Temporal existence as function of φₑ: t is defined only if φₑ(x, t) > 0
