Erratum: replace CH₄ ≈(ε=0.5±0.002%) PlanckMass/ProtonMass = αGproton with CH₄ ≈(ε=0.5±0.002%) PlanckMass^2/ProtonMass^2 = αGproton
The square term arises due to the fact that gravitation arises in the multiplicative interaction between two masses. On Sun, Apr 7, 2024 at 7:51 PM James Bowery <jabow...@gmail.com> wrote: > > > 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-Mf8e004f6c5d4582f8664a337 Delivery options: https://agi.topicbox.com/groups/agi/subscription
