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

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...

In a previous post we mentioned how the discrepancy in the classical and quantum estimates of the stiffness of space-time was another version of the cosmological constant problem (CCP). You will find some people claiming this is a non-problem , however, the CCP is actually one of the two great naturalness problems in modern physics.  From observations, the cosmological constant $\Lambda \sim 1.3\times10^{-52} \ m^{-2}$. The so-called $10^{121}$ crisis can be expressed as the ratio of the Planck density (from QFT) and the actual observed dark energy density: $\rho_{Planck}/ \rho_{\Lambda}$.  \begin{equation} \rho_{\Lambda} = \frac{\Lambda c^2}{8 \pi G} \ \end{equation}\begin{equation} \rho_{Planck} = \frac{c^5}{\hbar G^2} \end{equation}  The QFT result comes from quantising a 'particle in a box'. However, in 1998 the CKN bound was proposed. CKN realised that if you put particles in a box and heat them, you can only increase their energy so much before the box collapses int...

  The notorious rubber sheet analogy of spacetime teaches one concept and once concept only: Mass-energy causes curvature of space-time.   When a gravitating mass recedes from a region of space-time the curvature diminishes. The field equations of General Relativity don’t have an explicit term for this elastic property, but the framework as a whole does have that property. As very large mass-energies are required to generate gravitational waves (ripples in space-time), the elastic property of space-time is generally regarded as very stiff One other interesting consideration here is that elasticity is an emergent phenomenon. There is a great deal of interest in the idea that gravity is similarly emergent .   In 2018, McDonald quantified the classical stiffness of space-time via Youngs Modulus .  Classical answer: Youngs Modulus of space-time $\sim$ 20 orders of magnitude greater than steel.   DALL.E2 depiction of classical space-time. (Credit SR Anderso...

 In a previous post we introduced the idea that our current Universe has boundary conditions.    Classical 1+1 dS space-time visualized as basketball hoop, with the up/down slam-dunk direction being the time dimension, and the hoop circumference the space dimension.    We also showed a diagram similar to Figure 1 below. Except here, we are once again thinking about the future dS state . Figure 1 . For an observer at O inside the cosmic event horizon (CEH) with radius $l_{\Lambda}$, the universe can be divided into two sub-vacuums, $(A)$ inside the CEH, and $(B)$, outside. The horizon surface $\Sigma$ has entanglement entropy $S_{dS}$ and rest energy $E_H$   Figure 2. The maximum entropy of the Universe (credit: Lineweaver ).   Now, a comoving volume partition of the Universe can be treated as a closed system for which $dS \geq0$. The maximum entropy of a closed system, in this case  ( Figure 2 ) with $L=2 \pi l_{\Lambda}$, the circum...