What question did this study set out to answer?

The research aims to derive a unified theory connecting spacetime, matter, and their interactions using kinetic principles.

March 28, 2026Open Access

Chrono-Kinetic Gravity: A Unified Theory of Spacetime, Matter, and Interactions from the Kinetics of the "Time Budget"

Key Points

The research aims to derive a unified theory connecting spacetime, matter, and their interactions using kinetic principles.
Developed a classical distribution function on the light cone in flat Minkowski space.
Introduced maximum entropy and thermodynamic stability to derive Maxwell and Einstein actions.
Modeled the collision integral in successive steps including relaxation approximations.
Applied the Chapman–Enskog method to derive effective actions for gauge fields.
Identified a hierarchy of relaxation times for gravitational and electroweak sectors.
Derived masses for WW and ZZ bosons and described the emergence of massless photons.
Provided numerical values for parameters matching observed particle masses.
Demonstrated the emergence of fermionic matter as topological skyrmions with suppressed masses.

Abstract

I present a complete derivation of a unified theory based on a classical distribution function T(x,k)T(x,k) on the light cone in flat Minkowski space. The lowest moments of this distribution generate scalar (dark energy), vector (gauge fields), and tensor (graviton) degrees of freedom. By imposing maximum entropy and thermodynamic stability, I derive the Maxwell and Einstein actions. The collision integral CTCT is modelled in successive steps: a relaxation (BGK) approximation, a modified version with a projector that ensures zero relaxation for transverse-traceless modes, and extensions to include spinor (SU(2)×U(1)SU(2)×U(1)) and colour (SU(3)cSU(3)c) indices. The spectrum of the linearized collision operator exhibits a hierarchy of relaxation times: a Planckian scale τgravτgrav for the gravitational sector, and much larger times τ0,τ1τ0,τ1 for the electroweak sector. Using the Chapman–Enskog method I derive the effective action for gauge fields. Finite τ1τ1 generates masses for the WW and ZZ bosons, while the massless photon emerges as a linear combination of the singlet and triplet fields after mixing (the Weinberg mechanism). Matching the observed masses mW=80.4 GeVmW=80.4GeV, mZ=91.2 GeVmZ=91.2GeV and the Weinberg angle sin⁡2θW=0.231sin2θW=0.231 gives numerical values τ0≈1.75×1017tPlτ0≈1.75×1017tPl, τ1≈1.32×1017tPlτ1≈1.32×1017tPl. The electroweak scale λEW=cτ0≈2.8×10−18 mλEW=cτ0≈2.8×10−18m is thus naturally separated from the Planck scale λgrav∼lPlλgrav∼lPl. Fermionic matter (electrons, quarks) emerges as topological skyrmions of the long‑wavelength order parameter U(x)∈SU(2)U(x)∈SU(2), with masses exponentially suppressed relative to MPlMPl. The theory avoids gravitational singularities through a transition to a ballistic regime when the Knudsen number exceeds unity, and provides a concrete basis for further predictions, including modifications of the gravitational wave spectrum and possible variations of Newton's constant at small distances.

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