On Sat, Apr 6, 2024 at 2:29 PM Matt Mahoney <mattmahone...@gmail.com> wrote:
> One problem with estimating the size of a proton from the size of the > universe is that it implies that the proton or one of the constants it is > derived from isn't constant. > And this same problem applies to 2ƛₑCH₄ ≈(ε=0.81±0.15%) H₀⁻¹c CH₄ = 2^(2^(2^(2^2-1)-1)-1)-1 (+3+7+127) CH₄ ≈ 2^(2^(2^(2^2-1)-1)-1)-1 (not methane of course) But not to: CH₄ ≈(ε=0.5±0.002%) PlanckMass/ProtonMass = αGproton ƛₑ² = "quantum metric" = Compton Area of the electron (see below abstract) Interestingly, the Planck Area is increasingly viewed as more fundamental than the Planck Length -- in large part due to its relationship to information theoretic concerns such as you point out in the problematic relationship to the "Age of the Universe". > Universal semiclassical equations based on the quantum metric for a > two-band system > <https://journals.aps.org/prb/abstract/10.1103/PhysRevB.104.134312>C. > Leblanc, G. Malpuech, and D. D. Solnyshkov > Phys. Rev. B 104, 134312 – Published 26 October 2021 > ABSTRACT > We derive semiclassical equations of motion for an accelerated wave packet > in a two-band system. We show that these equations can be formulated in > terms of the static band geometry described by the quantum metric. We > consider the specific cases of the Rashba Hamiltonian with and without a > Zeeman term. The semiclassical trajectories are in full agreement with the > ones found by solving the Schrödinger equation. This formalism successfully > describes the adiabatic limit and the anomalous Hall effect traditionally > attributed to Berry curvature. It also describes the opposite limit of > coherent band superposition, giving rise to a spatially oscillating > *Zitterbewegung* motion, and all intermediate cases. At k=0, such a wave > packet exhibits a circular trajectory in real space, with its radius given > by the *square root of the quantum metric*. This quantity appears as a > *universal > length scale*, providing a geometrical origin of the Compton wavelength. > The quantum metric semiclassical approach could be extended to an arbitrary > number of bands. ------------------------------------------ Artificial General Intelligence List: AGI Permalink: https://agi.topicbox.com/groups/agi/Teaac2c1a9c4f4ce3-M09a9c81983c6f9a7c0515d3b Delivery options: https://agi.topicbox.com/groups/agi/subscription
