New Material Property: 4D Spacetime Energy/Mass Density From QED 0D->4D Einstein-Maxwell Tensor Integrations

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New COMSOL material property of 4D spacetime energy/mass density based on multivariable calculus equations defines computational energy/mass density ranging compressive through rarefactive of central cosmological constant vacuum energy/mass density pressure 𝚲, as shown in GIF. Mathematica® theorem proving operator computationally reproduces QED 0D->4D photon-electron energy, mass, and angular momentum observables to all 31 and 34 decimal places in units of pascals along the perfect fluid metric pressure trace of Einstein-Maxwell spin stress energy momentum density pressure tensor T𝜇𝜈.

Construction of photon matrix element by 4D cylindrical coordinate transverse lemniscate expansion of Poynting energy flux vector energy density volumetric integration ForAll wavelengths computationally reproduces original Einstein-Planck energy observable E = hc/𝜆 and computationally dualistic conversion to mass density reproduces spin angular momentum observable ℏ.

Construction of electron matrix element 4D spherical coordinate expansion is parameterized by the Bohr radius with a conversion to mass density volumetric integration ForAll energy levels n computationally reproduces the electron mass observable and spin angular momentum observable ℏ/2.

Feynman proved spacetime is not differentiable. Nevertheless 4D spacetime energy/mass density distribution landscape is differentiable via Theorem 1 equations as shown in PNG of Mathematica® Proof notebook available on GitHub:

HEP analysis available in Wolfram Notebook Archive:
AI Pattern-Matching CERN LHC Collision Particle Resonance Flow Patterns with Electromagnetic Energy Density Pressure Turbulence

Preprint PDF available on ResearchGate:
General Information Theory 4D Photon-Electron Soliton Gauge Group ForAll Wavelengths and Energy Levels

Wherein Theorem 1 proof establishes the total field formal frame to computationally reproduce all the high-energy experimental particle physics and low energy molecular dynamics full Laplacian spherical harmonics SO(1,3) and further local stress-energy tensor operator product expansions to shorter range higher-energy nuclear configuration observables of periodic table. Recalling Einstein in 1952, “Physical objects are not in space, but these objects are spatially extended. In this way the concept ‘empty space’ loses its meaning.”

Theorem 1 electromagnetic field integrations along the perfect fluid metric pressure trace of T𝜇𝜈 render in pascals; wherein the photon-electron particle-wave observables are negative outward pressure elastic expansions of the 4D spacetime continuum; wherein all multiphysics actuators and sensors mechanical and biological ultimately create and measure pressure. Indeed all scientific measurements ultimately measure total field pressure along the trace of T𝜇𝜈. Accordingly the 4D particle-wave electrodynamics energy/mass density pressure elementary particle-wave integrations extend to multiphysics of viscosity, flow and turbulence relative to actuators, sensors, and the simulation of vapor–liquid interfaces, including both condensation and vaporization processes computationally derived from the spacetime continuum level.

Creating the future of a human-AI aligned 4D spacetime worldview thus has an ultimate computational information basis, regarding which the original QED zero-sized 0D particle model provides no direct information content. However an AI rational agent will be able to process this new 4D spacetime vacuum material property with COMSOL Multiphysics once the LLMs understand multivariable calculus in the analytic domain of machine intelligence formalization; wherein human intelligence computer algebra formalizations, such as Theorem 1 Mathematica® theorem proving operator proof, are a necessary precursor to LLM machine intelligence understanding.


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  • Name:
    David Harness
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