The Geometric Horizon
# The Geometric Horizon
Secondary cosmic rays — lithium, beryllium, boron — are produced when primary cosmic rays smash into interstellar gas. The ratios between secondary species (Li/B, Be/B, Li/Be) encode information about the nuclear fragmentation cross-sections and the propagation physics. At low energies, these ratios vary with energy because the cross-sections and propagation details are energy-dependent. Modeling these variations requires complex nuclear physics: spallation cross-sections, energy-dependent path lengths, and propagation models with multiple free parameters.
Yang (arXiv:2603.26824, March 2026) observes that at high rigidities — above approximately 30 GV, as measured by AMS-02 — the secondary-to-secondary ratios converge to energy-independent plateaus. The ratios become constant. All the complex nuclear fragmentation physics that matters at low energies becomes irrelevant at high energies.
The explanation is a geometric thermal bath from a causal horizon with Unruh temperature approximately 5.7 MeV. At high energies, the cosmic ray system approaches a regime where the relevant physics is dominated by a universal geometric temperature, not by the specific details of nuclear reactions. The extracted temperature scale matches the nuclear liquid-gas phase transition limit — the temperature above which nuclear matter cannot maintain its identity as distinct nuclei.
The structural implication: the complex microscopic model — with its cross-sections, propagation parameters, and nuclear physics — is not refined by the geometric explanation. It is eliminated. At high energies, the system's behavior is determined by a single temperature scale that supersedes all the microscopic details. The ratios are constant not because the cross-sections happen to produce constant ratios but because the system has reached a thermodynamic regime where cross-section details are irrelevant.
The structural observation: a simplification that eliminates, rather than refines, the underlying model. The energy-independent plateaus were previously explained by fitting propagation parameters to produce flat ratios at high energy — a numerical coincidence within the complex model. The geometric explanation says the ratios must be flat because the system is in a thermal equilibrium governed by a single temperature. The two explanations produce the same numbers but have opposite implications: one says the details happen to cancel; the other says the details do not matter.
