Jeff Yee’s 2019 work is both insightful and highly commendable. It represents an exceptionally significant advance in the calculation of the fine-structure constant, even though it has only appeared in preprint form to date.

Since 1929, mainstream attempts to explore the mathematical origin of the fine-structure constant have numbered no fewer than 150, with independent investigations by non-professional researchers exceeding 500. Many of these efforts have achieved impressive numerical precision, and some of the relatively better works have incorporated special mathematical constants. Nevertheless, as most of them lack or have no clear physical motivation and rigorous mathematical derivation, these studies, in general, still fall into the category of unfounded numerical fitting. And this situation was not altered until the emergence of Jeff Yee’s work [1].

The core conclusion put forward by Jeff on the fine-structure constant, α, is simply as:

This result achieves a high relative accuracy of +2.2 ppm.

This relation is valuable not only for its concise mathematical form and accurate computational result; more importantly, it was rigorously derived by Jeff from a body-centered cubic-like spherical physical model, based on his deep understanding of electromagnetic wave propagation and his profound insight, which involves no artificial numerical fitting or ad hoc tuning. Given its high precision, this relation is highly likely to reveal the underlying physical reality. All truth is relative. If Jeff’s relation were dismissed as mere coincidence solely because the Standard Model treats α only as a precisely measurable quantity, such a conclusion would be arbitrary and unfair from an impartial historical perspective of scientific development, and would only impede scientific progress. Therefore, Jeff’s relation ought to be accorded its rightful place in scientific discourse. At any rate, to label Jeff’s work as nothing more than a coincidence is rash and scientifically irresponsible.

Based on the guidance of Einstein’s relativity regarding the influences of both uniform and accelerated motions on spatial properties, B. Feng theory posits that time possesses two dimensions and establishes a material framework for five-dimensional spacetime ℝ 5 . According to high-dimensional geometry,

In B. Feng theory [2][3], the relation,

is introduced as an axiomatic boundary condition for the variable-modulus projection, under which the spatial and temporal components of the high-dimensional radius are equivalent. So,

Since an n-dimensional spherical space is equivalent to an (n + 1)-dimensional Euclidean space, the notations S₄ and S₃ can be re-expressed as S 5 and S 4 in the Euclidean space framework, respectively. Thus, the projection coefficient from higher dimensions to lower dimensions can be expressed as:

This represents the idealized variable-modulus or projection result (projection coefficient) in flat space. However, assuming that Einstein’s description of spacetime curvature holds for ℝ 5 , there exists a curvature coefficient k_i that influences the projection. Research within B. Feng theory has revealed a theoretically calculable relation for this curvature coefficient, where, ϑ = π / ( 3 × 2 1 / 2 ) ,

Accordingly, the projection coefficients revised by the curvature coefficients can be written individually as: 64 k 1 / 3 , 3 × 2 1 / 2 π k 2 and then,

and further rewrite it as:

On this basis, B. Feng theory derives the computational formula for the elementary charge and yields the corresponding calculated results,

The result achieves high precision, with an error of q −0.042%.

Substituting this charge calculation formula into the evolved expression of the fine-structure constant defined by Sommerfeld yields its theoretical formula,

Then the result achieves a cumulative error of +0.085%.

It is evident that this is a mathematically precise formula for the fine-structure constant originating from higher dimensions. This first scheme as a derivative of the charge calculation formula rather than a result specifically derived for the study of the fine-structure constant, there is absolutely no premise or motivation for fitting in its derivation. This formula has one-fourth the computational precision of Jeff’s, yet the two are roughly consistent.

Some current astronomical observations (e.g., quasar absorption spectra) suggest that α may vary slightly on cosmological scales. However, the calculations underlying these conclusions still rely on the definition of α, which involves the elementary charge. As such, these analyses inherently involve the physical quantity of electric charge. In contrast, the aforementioned results from B. Feng theory clearly demonstrate that the electric charge itself varies with the properties of spacetime.

From frame ℝ 5 , it is the compactification of five-dimensional space and the derivation of geometric measures are presented as follows:

As a product manifold S 3 × S 1 , it maintains an orientation-agnostic global topological structure under unidirectional constraints. Consequently, symmetry breaking fails to generate a twofold reduction in volume, and the original measure is conserved. Thus, the total effective measure Ω e f f is then had form as,

Perspectives 1 and 2, derived from two distinct higher-dimensional frameworks, independently corroborate Jeff’s findings and lead to the conclusion that the fine-structure constant α is a purely geometric constant.

The measure construction is centered on the five-dimensional compactified structure S 3 × S 1 and involves only S 1 and S 3 . The 2-sphere S 2 , 4-sphere S 4 and others do not participate in the corresponding causal structure or measure composition, hence their measures do not appear in the total measure sum.

In this work, the conventional manifolds S 1 , S 3 , and S ( S 3 × S 1 ) are redefined to denote an unified geometric measure, thus acquiring rigorous dimensionless characteristics, rather than length, area, volume, etc. units, within the same manifold. Therefore, no issue of inconsistent dimensionality arises.

Lastly, I would like to emphasize that, in terms of methodology, perspective 1 focuses on fundamental physical truth through step-by-step projective dimensional reduction from higher dimensions, in which the factors follow innate multiplicative logic; and the perspective 2 of B. Feng theory adopts the high-dimensional compactified topological geometric measure method. By contrast, Jeff’s theory starts directly from observable three-dimensional reality, collects traces left by higher dimensions-like in ordinary 3D space, and restores the intrinsic nature of things through cumulative summation.

As for α, deviations in B. Feng theory (perspective 1) may arise from non‑exhausted higher dimensions, because we cannot exclude the existence of acceleration variation with an extremely small probability. Where then, would errors in Jeff’s theory originate? However, from the results in the perspective 2, no errors arise due to its mathematical rigor. Its only possible source of error is thus identical to that of the perspective 1, the idealized ⁵ model. Minor differences in the resulting error due to different methods or derivation paths are understandable. Clearly, the results demonstrate that the perspective 2 follows a shorter derivation path and is therefore superior.