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

  Yes , you can define an effective Poisson ratio for the horizon—but only in a very specific, emergent, hydrodynamic sense—and it takes its extremal value. The value you get is not arbitrary; it is forced on you by horizon incompressibility, maximal entropy, and diffusion physics. 1. What a Poisson ratio really measures The Poisson ratio (ν) is defined (in ordinary elasticity) as $$\nu = - \frac{\text{transverse strain}}{\text{longitudinal strain}}.$$ Equivalently, in terms of elastic moduli: $$\nu = \frac{3K - 2\mu}{2(3K + \mu)} \quad \text{(3D bulk)},$$ or $$\nu_{2D} = \frac{K_{2D} - \mu_{2D}}{K_{2D} + \mu_{2D}} \quad \text{(membrane)}.$$ So to even ask for a Poisson ratio, we need: a bulk (or area) modulus (K), a shear modulus (μ). This is where horizons are special. 2. Horizon fluids: what moduli exist? From the membrane paradigm, AdS/CFT, and your own derivations: Horizons have: finite shear viscosity (η), no elastic shear modulus ((μ = 0)), negative bulk ...

  De Sitter space as a thermodynamic equilibrium During both inflation and late-time cosmic acceleration, the Universe is well-approximated by a de Sitter (dS) spacetime with nearly constant curvature radius ($\ell_\Lambda $). Our present Universe may therefore be regarded as a quasi–de Sitter state , possessing a cosmic event horizon (CEH) associated with its vacuum energy density (cosmological constant). A defining feature of de Sitter space is that the cosmological horizon is not merely a causal boundary but a thermodynamic object, endowed with temperature, entropy, and energy. In this context, the total bare (rest) energy associated with the horizon, defined via the Brown–York quasilocal energy, can be written as: \begin{equation} E_0 = 2\, k_B T_{dS} S_{dS} = 2\, m_{CEH} c^2 = 2E_H  \end{equation} This relation is a horizon version of the entanglement first law , from which the Einstein equations themselves can be derived. Here: $S_{dS}$ is the de Sitter entropy (d...

  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...

A 2021 paper by Zurek applied a random walk argument to a black hole horizon.   Credit, Zurek, 2021 Zurek called this a blurring of the horizon (a fuzzy, or uncertain horizon), and also went through some equivalent derivations, which basically supported the idea this length scale is the quantum uncertainty in the position of the BH horizon, aka a dynamic quantum width of an event horizon (a concept which would therefore also apply to the universe's own CEH). The Bekenstein-Hawking entropy gives the number of quantum degrees of freedom that can fluctuate. Below, we step out our own cosmic de-Sitter derivation of the random walk argument, obtaining the same result as Zurek did, so its certainly correct! \begin{equation} \Delta x^2 =2 DT \end{equation} In this equation, $\Delta x$ is the position uncertainty, $D$ is the Einstein diffusion coefficient and $T$ is the time between measurements (aka the relaxation time).    So, lets look at the Einstein diffusion co...

In this post, we introduced the idea that in the presence of a positive cosmological constant, there is a minimum (local) mass $m_{GR}$   McDormand swinging a cosmic light-like mass-energy $m_{GR}$, with a "cosmic string" of radius $l_{\Lambda}$, giving a centripetal force $F_{local}=m_{GR} \ c^2/l_{\Lambda}$.    Let's think about that string for a bit. In fact, a great number of physicists have spent their entire careers tied up unraveling string theory . For a classical string, which lives in D = 10 dimensions, associated with Nambu-Goto action, the the string tension $T_G$ is a local force, or energy per unit length (dimensions $MLT^{-2}$): \begin{equation} \notag T_G = \frac{1}{2\pi \alpha \prime} \end{equation}$\alpha \prime$ is the Regge slope parameter, set here with dimensions of inverse force.  The wavelength of the stringy mass-energy standing wave (such that it does not interfere with itself), is the circumference of the circle, and we know it moves...