What have electrons, black holes and Clifford Algebra ever done for us?

  In general relativity, defining "energy" is notoriously difficult. A specific point of confusion often arises in de Sitter space: Why is the quasi-local energy of the horizon exactly double the effective gravitational mass? By imposing a fundamental consistency condition— Horizon Uncertainty—we can re-derive the thermodynamics of the de Sitter horizon. We find that the horizon behaves exactly like a quantum-stretched membrane, where the "factor of two" is simply the result of the Virial Theorem applied to spacetime itself. Horizon Position Uncertainty Whether through holographic arguments, diffusion models, or entanglement entropy, a causal horizon is never sharp. Its position fluctuates. The variance of the horizon position $\Delta x^2$  scales with the geometric mean of the Planck length $L_p$ ​ and the horizon radius $l_{\Lambda}$ ​ :  \begin{equation}     \Delta x^2 = L_P \, l_\Lambda, \qquad L_P = \sqrt{\frac{G\hbar}{c^3}} \end{equation}    W...