Gravity governs the motion of planets, while electromagnetism explains light and the behaviour of charged particles. Modern physics describes these phenomena with extraordinary accuracy. Yet a deeper question remains: why does nature use these particular laws, and why does the spacetime in which they operate have three dimensions of space and one of time?
In a theoretical paper published in Symmetry, Bin Li of the Research Department at Silicon Minds Inc., USA, investigates whether these familiar structures can be selected from more basic requirements. The framework, called reconstruction before dynamics, asks what must be available before physical evolution can be described at all.
The possibility that geometry is emergent also motivated Li’s earlier work, covered in A Different Path to Quantum Gravity. The present paper develops a distinct premetric reconstruction framework with explicitly stated assumptions and conditional mathematical results.
Asking what makes physical laws possible
Conventional theories describe how systems change once the mathematical setting is available. General relativity begins with spacetime geometry; quantum field theory uses fields and symmetries to describe particles and interactions. Reconstruction asks why those starting structures should take their observed forms.
A useful analogy is the grammar of a language. Before a sentence can express a meaningful statement, its elements must fit together consistently. The proposed framework similarly investigates the structural conditions that allow physical objects, measurements and laws to have a consistent meaning.
The approach is called premetric because it starts without assigned distances, durations, light cones or energy densities. It begins with relations, ways of combining them, and distinctions that could become observable. Here, “before” means logically prior. It does not refer to an earlier era on a hidden cosmic clock.
The study proposes a common organizing structure called the neutral parent. This is a mathematical archetype before particle properties and spacetime measurements become defined. Different observable aspects of that common structure are proposed to supply particle records, phase relationships and the shared spacetime platform. The aim is to explain how these ingredients fit together within one reconstruction scheme.
Before asking how the universe evolves, I ask what makes a physical law possible. Reconstruction explores whether the structures we usually assume can themselves be explained.
—Bin Li
Keeping physical identity well defined
At the heart of the study is the Indefinite Reconstruction Stability Principle, or IRSP. In plain language, a candidate physical identity must remain well defined as its reconstruction is continued through every allowed step. Its existence cannot depend on stopping the process at a convenient stage.
The principle also requires independence from invisible bookkeeping. Two mathematical descriptions of the same observable situation must give the same physical conclusions. This does not mean that particles must live forever. A particle can decay while its identity and decay process remain unambiguously defined.
The paper formalizes this requirement by grouping descriptions that agree on the specified observable properties. An exact mathematical theorem states when a reconstruction rule is consistently defined on those groups. Connecting this abstract result to spacetime and physical laws requires further physical assumptions, which the paper identifies explicitly.
From abstract consistency to spacetime geometry
The framework reaches three dimensions of space and one of time through two distinct arguments. One concerns the causal structure that allows disturbances to propagate reliably; the other concerns the total number of dimensions.
For the first, the study requires stability to hold even as the continuum description is refined to shorter scales. Certain mathematical possibilities would make disturbances grow uncontrollably at ever shorter scales. Excluding them constrains the form of propagation. Together with separate assumptions about reciprocal response and the participation of all dimensions, this selects a Lorentzian geometry with one temporal direction.
The dimension argument uses a phase connection, the mathematical structure used to compare phases at nearby locations. Its curvature is represented by a two-form. Requiring the associated basic response to remain well defined when the local metric scale is changed, without introducing an extra compensating field, selects four total dimensions.
Combining the two results gives three spatial dimensions and one temporal dimension. This is a conditional selection: the conclusion follows from the declared stability, response and phase assumptions together, rather than from IRSP alone.
Why loops, phases and symmetry matter
Imagine carrying a reference around a closed loop and comparing it with its starting state. A residual phase change can reveal structure that a purely local comparison misses. This idea is called holonomy and is central to gauge theories.
In the reconstruction framework, specified assumptions about loop detection select codimension-two structure: a structure with two fewer dimensions than its surroundings. Additional assumptions about scalar phase return and smooth holonomy then reconstruct a local U(1) connection, the kind of gauge structure used in electromagnetism.
Reconstructing the laws of electromagnetism and gravity
Once the four-dimensional Lorentzian platform is available, the next question is which leading laws can be built from its own structures. The paper calls this requirement nativeness. An equation cannot quietly introduce an unexplained preferred frame or an extra background tensor just to obtain a desired result.
For the electromagnetic sector, gauge invariance and the stated restrictions on locality, quadratic response and derivative order select the source-free Maxwell law. For gravity, once a measurable metric scale is supplied, locality, coordinate independence and second-order metric dynamics select the Einstein–Hilbert action together with a cosmological term. These are the familiar leading structures of electromagnetism and general relativity.
The proposed contribution is a route to explaining why these mathematical forms arise on the reconstructed platform. The gravitational argument uses an established mathematical classification and depends on additional assumptions about metric scale and matter coupling. Higher-order effects and the numerical values of all physical parameters are not fixed by these law-selection results.
A possible connection to the Standard Model
The study also examines the Standard Model gauge group, which organizes the strong, weak and electromagnetic interactions. Here, the route uses a separate proposed internal structure with blocks of dimensions three and two, linked by a determinant-neutrality condition.
Under these assumptions, the resulting group is S(U(3) × U(2)), equivalent to the Standard Model gauge group with its maximal Z6 quotient. This addresses how its symmetry factors fit together globally. Deriving the assumed internal block structure more fundamentally remains an open task.
What the framework could change
The broader ambition is to turn some familiar starting assumptions of physics into questions with explicit answers and identifiable dependencies. The paper offers a mathematical framework for that investigation while keeping its exact theorems distinct from the physical assumptions connecting them to nature.
This study complements Li’s earlier work on particle mass ratios and electromagnetic coupling, featured in The Science Matters articles A Possible Hidden Pattern Behind the Masses of the Electron, Muon and Tau and A Mathematical Alpha Tower for the Fine Structure Constant. Those studies pursue numerical targets; the present paper examines the structures that make the corresponding physical laws possible.
Further research must derive or test those assumptions and establish observable consequences that distinguish the proposal. The framework may also offer a filter for candidate microscopic descriptions in quantum-gravity research, although applying it to resolve the many possible vacua of string theory remains an open program.
Reference
Li, B. (2026). Reconstruction before dynamics: A premetric framework for selecting physical laws. Symmetry, 18(9), Article 1420. https://doi.org/10.3390/sym18091420
