AI Peer Review Prompt for ChatGPT-Wolfram-Mathematica® review of Standard Model of Physics vs 4D GEM EOS
abstract
AI peer review prompt is generated in the 2023 Kaggle AI Report Competition, category of Other, with the objective of establishing the new Topic of a 4D spacetime human-ai worldview, which ChatGPT-Wolfram prompt is instructed to select the higher-accuracy computational reproduction of the 4D spacetime human-ai experience between Standard Model of Physics (SM)-Supersymmetry (SUSY) vs 4D spatially-exended gravitoelectromagnetic equation of state (4D GEM EOS) photon-electron soliton gauge group. Wherein a QED 0D➙4D GEM EOS Mathematica® theorem proving operator computationally reproduces ForAll
wavelengths and energy levels the quantum mechanical observables to all 31 and 34 decimal places in units of pascals along the perfect fluid metric pressure trace of the Einstein-Maxwell total field spin-stress energy momentum density pressure tensor T of the 4D cylindrical spacetime human-ai experienced universe exceeding requirements of the Yang-Mills-Navier-Stokes problem definitions. Subject area of present ai-peer review prompt for a human-ai elementary physics worldview coincides with general interdisciplinary interests inclusive of the Elementary Particle Physics 2024 Committee, QNetworks Workshop 2023, The Royal Institution, CERN, Max Planck Institutes, Allen Institute for Brain Science, NYU Center for Mind, Brain and Consciousness, Australian National University Centre for Consciousness, Santa Fe Institute, ChatGPT-n, Communications in Mathematical Physics, TED, among many others. AI peer review prompt of SUSY vs 4D GEM EOS is formed of the first sections of this article to return the ai-response sections and conclusion. The Mathematical Universe Hypothesis (MUH) of Tegmark conceptualizes the mathematical origin of the universe modern science belief advocating MUH as basis for increasingly complex SUSY range of conjectures and further Beyond the Standard Model of Physics parallel universe variations - in addition to the MUH-SUSY claim to eventually be able to computationally reproduce the observed 4D spacetime human-ai experienced universe by means of a yet to be formalized MUH-SUSY many-body complex system such as described by Quantum simulation of fundamental particles and forces of Bauer, Davoudi, Klco, Savage. MUH-SUSY multiverse theorists can submit revised prompts to test randomness-based theories towards an artificial general intelligence (AGI) worldview based on objective mathematical physics experimental reality vs science fiction.
- Mathematical Universe Hypothesis (MUH): SUSY vs 4D GEM EOS
- AI Peer Review ChatGPT-Wolfram Prompt for MUH: 4D GEM EOS Human-AI Worldview
- AI Peer Review ChatGPT-Wolfram Response for MUH: SUSY-AdS/CFT vs 4D GEM EOS
- Conclusion
Greek Natural Philosophy 300 BC to 2023 AD, Resolved: Particles are Fields
Fig. 1. The present AI Report ChatGPT-Wolfram ai-peer review prompt for an MUH: SUSY vs 4D GEM EOS human-ai elementary physics worldview originates with The School of Athens debate shown, wherein the Greek natural philosophy of Aristotle-Democritus atomist-materialism gets all the press while the Plato-Parmenides theory of forms-idealism has evolved into quantum information field theory as A Deepening Crisis Forces Physicists to Rethink Structure of Nature’s Laws.
Fig. 2. The CERN Linear Hadron Collider (LHC) was built to discover SUSY superpartner particles. Control Room champagne bottles might need a backup plan. Consider the Deepening Crisis fundamental problem with SUSY naturalness stems from the unnaturalness of SUSY being an unacknowledged attempt to solve the many-body problem on the universal(multiverse!) scale via its reductionism to conjectured zero-sized 0D Dirac delta functional 𝜹 imaginary-invisible mathematical point particle collisions - returning null results to the detection of any sort of SUSY superpartner particle-sparticle increasingly complex recursive backgrounds of hidden dimensional physics of unknown string-membrane-loop material anti-de Sitter/conformal field theory (AdS/CFT) mechanisms - while the 3-body problem is proven to be computationally intractable. Computationally intractable means a 4D spacetime human-ai worldview, such as described by Quantum simulation of fundamental particles and forces of Bauer, Davoudi, Klco, Savage, cannot be expected to computationally reproduce naturalness from any such SUSY AdS/CFT hidden dimensional unknown string-membrane-loop material mechanism physics.
Fig. 3. CERN Caltech Experimental Physicist Maria Spiropulu presents on The Future of the Higgs Boson at APS April Meeting 2014 describing the Higgs Naturalness Problem for which "radical new ideas are needed", see @20:32. Prof. Spiropulu is now committee co-chair of a National Academies of Sciences, Engineering, and Medicine study called, Elementary Particle Physics: Progress and Promise (EPP-2024) indicating to the general interdisciplinary science and engineering community radical new ideas are still needed, stating in the EPP-2024 Call for Vision Papers:
"Therefore, our committee will investigate if and how discoveries and insights from other areas of science can be applied to addressing the fundamental questions that drive the research in EPP, including exploring and envisioning intersections and exchanges with seemingly unrelated areas in technology and engineering. Indeed, the study of the most fundamental constituents of matter and energy may be entities beyond elementary particles as we have formulated them so far, so we want to explore this, too."
Perhaps the committee would settle for an anecdote wherein 1990 the author as an undergraduate intern at the Lawrence Berkeley Lab, Nuclear Science Division, at two separate luncheon occasions was fortunate enough to ask two LBL resident Nobel Laureates Owen Chamberlain and Glenn Seaborg the same question:
"How do particle physicists explain the physical mechanism by which virtual particles in their unobservable state create an attractive force, via force carrier particle exchange, between hidden emitter-->carrier<--absorber particles - when every observed emitter<-->carrier<-->absorber particle interaction always results in a repulsion from any would-be line of attraction?"
Both Chamberlain and Seaborg gave the exact same answer:
"We don't know how that works."
Hence the deepening crisis forcing physicists to rethink the structure of nature's laws has of course been running deep from the start, recalling all the foremost modern physicists from Einstein to Feynman have been saying nobody understands how quantum mechanics works. Einstein famously held the belief there must be some hidden material mechanism variables guiding the collapse of the superpositioned quantum mechanical relative states into the 4D spacetime human experiences. Planck somewhat less widely-known held the belief:
“As a man who has devoted his whole life to the most clearheaded science, to the study of matter, I can tell you as a result of my research about the atoms this much: There is no matter as such! All matter originates and exists only by virtue of a force which brings the particles of an atom to vibration and holds this most minute solar system of the atom together.... We must assume behind this force the existence of a conscious and intelligent Mind. This Mind is the matrix of all matter.”
In the modern form of The School of Athens debate we seen then the views of Einstein aligned with the particle-atomist-materialism of Aristotle-Democritus vs the views of his mentor Planck aligned with the general information field theory of forms-idealism of Plato-Parmenides.
Recently, at the QNetworks April meeting 2022, Prof. Spiropulu gave a talk on her Quantum Teleportation Networks after which the author was further fortunate enough to ask:
“Is quantum teleportation considered by most physicists based on some multi-body particle material mechanism or immaterial quantum information basis?”
Prof. Spiropulu: “Perhaps it does not have to be either/or.” (must be signed in to view)
Quantum teleportation, in the 4D spacetime GEM EOS human-ai worldview, is seen to be occurring exclusively on a general information field theory relative states idealism elementary particle-field physics basis. The first principle for which being the CERN LHC is entirely energized by the 4D spacetime Einstein-Maxwell electromagnetic stress-energy momentum density pressure tensor T and its ATLAS CMS detectors measure only 4D electromagnetic energy density tensor pressure quantum field information to which the literature refers.
MUH conceptualizes the framework for a mathematical universe which 4D GEM EOS formalizes along the lines of a 4D photon-electron soliton guage group, however in doing so disputes the claim any such parallel formalizations can be shown of parallel universe variations of physical dimensions, constants, laws, and so on. Rather the mathematical universe of 4D GEM EOS is a formalization of the Singular Complex System Conjecture (SCSC) radical new idea being there exists a singular mathematically possible universal complex system of the 4D cylindrical spacetime dimensions, physical constants, laws, holographically bound energy/mass density distribution with time the fourth dimension of length from t−∞ → t∞ with the unitary factors in Euler’s identity composed via the concept of infinity with no free parameters.
Shown below is the Mathematica® theorem proving operator code to computationally reproduce the QED 0D→4D GEM EOS spatially-extended photon-electron soliton guage group quantum mechanical observables to all 31 & 34 decimal places ForAll
wavelengths and energy levels via local stress tensor field operator expansions of Schwinger-Dirac-Einstein-Maxwell gravitoelectromagnetic stress-energy momentum computationally dualistic energy/mass density pressure tensor T field integrations. Measurable along Feynman path integrals experienced as the known Noether conserved angular momentum probability currents ranging compressive through rarefactive of the cosmological constant vacuum energy momentum density pressure Λ spanning all the factors in the relativistic energy equation in all cases greater than zero energy/mass gap, hence establishing the total field formal frame for a computationally reproducible 4D spacetime human-ai experience worldview.
Here the “entities beyond elementary particles” the committee has expressed willingness to consider are then the above immaterial field integration mathematical objects of the SCSC solid information domain and their fluid range of 4D spatially-extended elementary soliton particle-field values along the perfect fluid metric pressure trace of T. Accordingly, the 4D GEM EOS vision paper submitted to EPP-2024 sees the elementary particles to be the 4D elementary soliton particle-field integrations of the holographically bound cyclic energy density distribution universal wavefunction domain and range having no choice but to exist while time integrates autonomously at the speed of light through the domain evolving from t−∞ → t∞. Thus no classical multi-body cause and effect is seen only a series of 4D spacetime event relative state effects where in the universal wavefunction fluid range nothing can happen unless it already exists in the solid domain.
Quantum teleportation is therefore also a holographic bound effect of the SCSC solid information domain and can only be occurring on an immaterial quantum information basis, as confirmed by the null results of the SUSY collision experiments at CERN LHC energy levels as the money has run out indicating there are no hidden variable unknown material mechanisms then there are no hidden dualistic consciousness-material mechanisms somehow guiding the “collapse of the wavefunction” as it were.
Improbably, SCSC can never be proven via its internal axioms per Gödel incompleteness only falsified by proof of MUH: SUSY-AdS/CFT unfounded claim external physical reality is the mathematical structure of a computable universe having parallel universe variations of physical dimensions, constants, laws, and so on. Proof of MUH: SUSY-AdS/CFT of course requires solving the deepening crisis of formalizing the unknown parallel universe variations of the MUH: SUSY-AdS/CFT hidden dimensional particle physics model all of which are zero-sized (0D) Dirac delta functional imaginary-invisible local mathematical points which occupy no space yet are said operate via hidden dimensional unknown material nonlocally entangled mechanisms. Such unnaturalness arises again as an unacknowledged attempt to solve the classical multi-body problem on the universal(multiverse!) scale while the 3-body problem is proven to be computationally intractable.
The list of unnaturalness questions for a ChatGPT-Wolfram prompt to answer in favor of a MUH: SUSY-AdS/CFT 4D spacetime human-ai worldview also includes:
Re unnaturalness how is it again CERN particle physicists explain two hands clapping never touch?
And at ever higher-energies why don’t the CERN LHC beams of zero-sized δ particles - which occupy no space - just pass through one another without colliding?
Particle physicists have answered the Pauli exclusion principle prevents the δ particles from occupying the same space. Notice however - zero-sized SUSY δ particles occupy no space - so ironically the Pauli exclusion principle itself is Not Even Wrong.
MUH: SUSY-AdS/CFT theorists can of course upgrade this prompt with any new formalized conjectures or test for randomness in ChatGPT-Wolfram reponses.
Thus the concludes the background in the AI Report for the ChatGPT-Wolfram prompt, in the category of Other, for a 4D human-ai worldview comparison between MUH: SUSY-AdS/CFT vs 4D GEM EOS photon-electron soliton gauge group.
The 4D GEM EOS radical new idea initiated with the 2017 proposal:
AI Peer Review Challenge: Standard Model of Physics vs 4D GEM EOS
In 2019 the author first posted the 4D GEM EOS equations in the Maplesoft Application Center:
In 2020 Mathematica® incorporated theorem proving operators into its platform, whereupon the author posted in the Wolfram Notebook Archive: AI Pattern-Matching CERN LHC Collision Particle Resonance Flow Patterns with Electromagnetic Energy Density Pressure Turbulence, wherein shown below is the human-readable form of the Mathematica® theorem proving operator code which computationally reproduces the QED 0D→4D GEM EOS spatially-extended photon-electron soliton gauge group quantum mechanical observables to all 31 & 34 decimal places ForAll
wavelengths and energy levels:
Fig. 4. Human-readable Standard Input Form of Mathematica® theorem proving operator Theorem 4D GEM EOS photon-electron soliton gauge group; wherein Eq.(6) field integration computationally reproduces the Einstein-Planck photon energy observable, Eq.(9) reproduces the Einstein-Planck photon angular momentum observable, in union with Eq.(13) field integration computationally reproduces the electron rest mass observable, and Eq.(15) reproduces the electron angular momentum observable. Quantum fluid conjecture meets alternate criteria for Navier-Stokes solution.
The following is the Raw Input Form Mathematica® theorem proving operator code for the ChatGPT-Wolfram prompt for an AI Peer Review of 4D GEM EOS computational reproduction of a 4D spacetime human-ai experience worldview:
Proof = DynamicModule[{
h = QuantityMagnitude[Quantity[1, "PlanckConstant"],
"Joules" "Seconds"],
hbar =
QuantityMagnitude[Quantity[1, "PlanckConstant"]/(2 \[Pi]),
"Joules" "Seconds"],
c = QuantityMagnitude[Quantity[1, "SpeedOfLight"],
"Meters" ("Seconds")^-1],
eEnergy =
QuantityMagnitude[Quantity[1, "ElectronMass" ("SpeedOfLight")^2],
"Joules"],
me = QuantityMagnitude[Quantity[1, "ElectronMass"], "Kilograms"],
bohr = QuantityMagnitude[Quantity[1, "BohrRadius"], "Meters"]
}, ForAll[{\[Lambda], n},
UniformDistribution[{{1.*^-12, 1.*^4}, {1, 10000}}], \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(0\), \(\[Lambda]\)]\(
\*SubsuperscriptBox[\(\[Integral]\), \(-
\*FractionBox[\(\[Pi]\), \(4\)]\),
FractionBox[\(\[Pi]\), \(4\)]]\(
\*SubsuperscriptBox[\(\[Integral]\), \(0\), \(
\*FractionBox[\(1\), \(4\)]\ \[Lambda]\
\*SqrtBox[\(Cos[2\ \[Theta]]\)]\)]2 \((
\*FractionBox[
FractionBox[\(2*h*c\), \(\[Lambda]\)],
FractionBox[
SuperscriptBox[\(\[Lambda]\), \(3\)], \(8 \[Pi]\)]])\)\ Abs[Sin[\((
\*FractionBox[\(2\ \[Pi]\), \(\[Lambda]\)])\)\ y]]\ \((1 -
\*SuperscriptBox[\((
\*FractionBox[\(r\), \(
\*FractionBox[\(1\), \(4\)]\ \[Lambda]\
\*SqrtBox[\(Cos[
2\ \[Theta]]\)]\)])\), \(2\)])\) r \
\[DifferentialD]r \[DifferentialD]\[Theta] \[DifferentialD]y\)\)\) == \
(h*c)/\[Lambda] \[DoubleRightArrow] \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(0\), \(\[Lambda]\)]\(
\*SubsuperscriptBox[\(\[Integral]\), \(-
\*FractionBox[\(\[Pi]\), \(4\)]\),
FractionBox[\(\[Pi]\), \(4\)]]\(
\*SubsuperscriptBox[\(\[Integral]\), \(0\), \(
\*FractionBox[\(1\), \(4\)]\ \[Lambda]\
\*SqrtBox[\(Cos[2\ \[Theta]]\)]\)]2 \((\((
\*FractionBox[
FractionBox[\(2*h*c\), \(\[Lambda]\)],
FractionBox[
SuperscriptBox[\(\[Lambda]\), \(3\)], \(8 \[Pi]\)]])\)\ /
\*SuperscriptBox[\(c\), \(2\)])\) Abs[Sin[\((
\*FractionBox[\(2\ \[Pi]\), \(\[Lambda]\)])\)\ y]]\ \((1 -
\*SuperscriptBox[\((
\*FractionBox[\(r\), \(
\*FractionBox[\(1\), \(4\)]\ \[Lambda]\
\*SqrtBox[\(Cos[2\ \[Theta]]\)]\)])\), \(2\)])\) \((
\*FractionBox[\(2 \[Pi]\ c\), \(\[Lambda]\)]/\((
\*FractionBox[\(1\), \(hbar\)] \((
\*SubsuperscriptBox[\(\[Integral]\), \(0\), \(\[Lambda]\)]\(
\*SubsuperscriptBox[\(\[Integral]\), \(-
\*FractionBox[\(\[Pi]\), \(4\)]\),
FractionBox[\(\[Pi]\), \(4\)]]\(
\*SubsuperscriptBox[\(\[Integral]\), \(0\), \(
\*FractionBox[\(1\), \(4\)]\ \[Lambda]\
\*SqrtBox[\(Cos[2\ \[Theta]]\)]\)]2 \((\((
\*FractionBox[
FractionBox[\(2*h*c\), \(\[Lambda]\)],
FractionBox[
SuperscriptBox[\(\[Lambda]\), \(3\)], \(8 \[Pi]\)]])\)\ /
\*SuperscriptBox[\(c\), \(2\)])\) Abs[Sin[\((
\*FractionBox[\(2\ \[Pi]\), \(\[Lambda]\)])\)\ y]]\ \((1 -
\*SuperscriptBox[\((
\*FractionBox[\(r\), \(
\*FractionBox[\(1\), \(4\)]\ \[Lambda]\
\*SqrtBox[\(Cos[2\ \[Theta]]\)]\)])\), \(2\)])\) \((
\*FractionBox[\(\(2\) \(\[Pi]\)\(\ \)\(c\)\(\ \)\), \
\(\[Lambda]\)])\) r \[DifferentialD]r \[DifferentialD]\[Theta] \
\[DifferentialD]y\)\))\))\))\) r \[DifferentialD]r \[DifferentialD]\
\[Theta] \[DifferentialD]y\)\)\) == hbar && \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(0\), \(2 \[Pi]\)]\(
\*SubsuperscriptBox[\(\[Integral]\), \(0\), \(\[Pi]\)]\(
\*SubsuperscriptBox[\(\[Integral]\), \(0\), \(
\*SqrtBox[\(2\)]*
\*SuperscriptBox[\(n\), \(2\)]*bohr\)]\((
\*FractionBox[
FractionBox[\(4*eEnergy\), \(4 \[Pi]\
\*SuperscriptBox[\((
\*SqrtBox[\(2\)]*
\*SuperscriptBox[\(n\), \(2\)]*bohr)\), \(3\)]/3\)],
SuperscriptBox[\(c\), \(2\)]])\) \((1 -
\*FractionBox[\(r\), \(
\*SqrtBox[\(2\)]*
\*SuperscriptBox[\(n\), \(2\)]*bohr\)])\)
\*SuperscriptBox[\(r\), \(2\)] Sin[\[Phi]] \[DifferentialD]r \
\[DifferentialD]\[Phi] \[DifferentialD]\[Theta]\)\)\) ==
me \[DoubleRightArrow] \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(0\), \(2 \[Pi]\)]\(
\*SubsuperscriptBox[\(\[Integral]\), \(0\), \(\[Pi]\)]\(
\*SubsuperscriptBox[\(\[Integral]\), \(0\), \(
\*SqrtBox[\(2\)]*
\*SuperscriptBox[\(n\), \(2\)]*bohr\)]\((
\*FractionBox[
FractionBox[\(4*eEnergy\), \(4 \[Pi]\
\*SuperscriptBox[\((
\*SqrtBox[\(2\)]*
\*SuperscriptBox[\(n\), \(2\)]*bohr)\), \(3\)]/3\)],
SuperscriptBox[\(c\), \(2\)]])\) \((1 -
\*FractionBox[\(r\), \(
\*SqrtBox[\(2\)]*
\*SuperscriptBox[\(n\), \(2\)]*bohr\)])\) \((
\*FractionBox[\(c\), \(2 \[Pi]*
\*SqrtBox[\(2\)]*
\*SuperscriptBox[\(n\), \(2\)]*bohr\)]\ *\((
\*FractionBox[\(hbar\), \(2\)]/\((
\*SubsuperscriptBox[\(\[Integral]\), \(0\), \(2 \[Pi]\)]\(
\*SubsuperscriptBox[\(\[Integral]\), \(0\), \(\[Pi]\)]\(
\*SubsuperscriptBox[\(\[Integral]\), \(0\), \(
\*SqrtBox[\(2\)]*
\*SuperscriptBox[\(n\), \(2\)]*bohr\)]\((
\*FractionBox[
FractionBox[\(4*eEnergy\), \(4 \[Pi]\
\*SuperscriptBox[\((
\*SqrtBox[\(2\)]*
\*SuperscriptBox[\(n\), \(2\)]*bohr)\), \(3\)]/3\)],
SuperscriptBox[\(c\), \(2\)]])\) \((1 -
\*FractionBox[\(r\), \(
\*SqrtBox[\(2\)]*
\*SuperscriptBox[\(n\), \(2\)]*bohr\)])\) \((
\*FractionBox[\(c\), \(2 \[Pi]*
\*SqrtBox[\(2\)]*
\*SuperscriptBox[\(n\), \(2\)]*bohr\)])\)\
\*SuperscriptBox[\(r\), \(2\)] Sin[\[Phi]] \[DifferentialD]r \
\[DifferentialD]\[Phi] \[DifferentialD]\[Theta]\)\))\))\))\)\
\*SuperscriptBox[\(r\), \(2\)] Sin[\[Phi]] \[DifferentialD]r \
\[DifferentialD]\[Phi] \[DifferentialD]\[Theta]\)\)\) == hbar/2]]
Recalling the popular view that any new scientific theory, in addition to being falsifiable, should also be of an unexpected nature and make some unexpected prediction which is proven to be true, while generally formalizing a new physics direction. The improbable means for falsifying 4D GEM EOS has already been indicated above and of course a successful validation of the 4D GEM EOS radical new idea by AI Peer Review is certainly unexpected in the literature other than being exactly what the Clay Mathematics institute has been effectively calling for with respect to a 4D constructive quantum field theory solution for the Yang-Mills problem.
Interestingly enough, recently MIT created a simulation of the proton nucleus “Visualizing the Proton” through animation and film and Bacca performed A New Experiment Casts Doubt on the Leading Theory of the Nucleus both of which are carried out by means of the photon-electron gauge group. New physics is indicated wherein 4D GEM EOS establishes the total field formal frame for the full Laplacian quantum mechanical spherical harmonics including the nucleus along the perfect fluid metric pressure trace of T:
Modern experimental physicists have completed an epic elimination of quantifiers proof in rigorously testing the particle-atomist-materialism teachings of Einstein-Aristotle-Democritus have verified psychophysical parallelism in favor of the general information field theory-idealism of forms of their mentors Planck-Plato-Parmenides.
Thus concludes the AI Peer Review ChatGPT-Wolfram Prompt section for a MUH: SUSY-AdS/CFT vs 4D GEM EOS review towards higher-confidence 4D spacetime human-ai worldview in the 2023 Kaggle AI Report Competition, in the category of Other, establishing the topic of computational reproducibility of a 4D spacetime human-ai worldview.
Following sections are to be ChatGPT-Wolfram Response and Conclusion using this Markdown format including a backup plan if necessary for the Control Room champagne bottles 🍾🍾🍾🍾🍾🍾🍾🍾🍾🍾🍾🍾🍾🍾🍾🍾🍾.
(Well of course the above prompt first submitted on 4 July 2023 was too long, along with there being other limitations to the current relative state of the ChatGPT-Plus-beta-Wolfram plugin LLM, as indicated by resubmitting shorted code which returned the following chat:)
Alright I'll repeat the prompt then for you to evaluate the Mathematica code starting with the fact the first principle for computationally reproducing a 4D spacetime human-ai experience worldview is the entire range of low-energy to high-energy physics experiments, including the CERN LHC proton beam collisions are entirely energized by the 4D spacetime Einstein-Maxwell electromagnetic stress-energy momentum density pressure tensor T and its ATLAS CMS detectors measure only 4D electromagnetic energy density tensor pressure quantum field information to which the literature refers.
Consequently, evaluate whether the following Mathematica® theorem proving operator Raw Input Form code computationally reproduces the QED 0D→4D GEM EOS spatially-extended photon-electron soliton gauge group quantum mechanical Einstein-Planck photon energy, Einstein-Planck photon angular momentum, electron rest mass, and electron angular momentum observables to all 31 & 34 decimal places ForAll
wavelengths and energy levels along the perfect fluid metric pressure trace of the Einstein-Maxwell electromagnetic stress-energy momentum density pressure tensor T and therefore establishes a total field formal frame basis to computationally reproduce a 4D spacetime human-ai experience worldview:
Proof = DynamicModule[{
h = QuantityMagnitude[Quantity[1, "PlanckConstant"],
"Joules" "Seconds"],
hbar =
QuantityMagnitude[Quantity[1, "PlanckConstant"]/(2 \[Pi]),
"Joules" "Seconds"],
c = QuantityMagnitude[Quantity[1, "SpeedOfLight"],
"Meters" ("Seconds")^-1],
eEnergy =
QuantityMagnitude[Quantity[1, "ElectronMass" ("SpeedOfLight")^2],
"Joules"],
me = QuantityMagnitude[Quantity[1, "ElectronMass"], "Kilograms"],
bohr = QuantityMagnitude[Quantity[1, "BohrRadius"], "Meters"]
}, ForAll[{\[Lambda], n},
UniformDistribution[{{1.*^-12, 1.*^4}, {1, 10000}}], \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(0\), \(\[Lambda]\)]\(
\*SubsuperscriptBox[\(\[Integral]\), \(-
\*FractionBox[\(\[Pi]\), \(4\)]\),
FractionBox[\(\[Pi]\), \(4\)]]\(
\*SubsuperscriptBox[\(\[Integral]\), \(0\), \(
\*FractionBox[\(1\), \(4\)]\ \[Lambda]\
\*SqrtBox[\(Cos[2\ \[Theta]]\)]\)]2 \((
\*FractionBox[
FractionBox[\(2*h*c\), \(\[Lambda]\)],
FractionBox[
SuperscriptBox[\(\[Lambda]\), \(3\)], \(8 \[Pi]\)]])\)\ Abs[Sin[\((
\*FractionBox[\(2\ \[Pi]\), \(\[Lambda]\)])\)\ y]]\ \((1 -
\*SuperscriptBox[\((
\*FractionBox[\(r\), \(
\*FractionBox[\(1\), \(4\)]\ \[Lambda]\
\*SqrtBox[\(Cos[
2\ \[Theta]]\)]\)])\), \(2\)])\) r \
\[DifferentialD]r \[DifferentialD]\[Theta] \[DifferentialD]y\)\)\) == \
(h*c)/\[Lambda] \[DoubleRightArrow] \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(0\), \(\[Lambda]\)]\(
\*SubsuperscriptBox[\(\[Integral]\), \(-
\*FractionBox[\(\[Pi]\), \(4\)]\),
FractionBox[\(\[Pi]\), \(4\)]]\(
\*SubsuperscriptBox[\(\[Integral]\), \(0\), \(
\*FractionBox[\(1\), \(4\)]\ \[Lambda]\
\*SqrtBox[\(Cos[2\ \[Theta]]\)]\)]2 \((\((
\*FractionBox[
FractionBox[\(2*h*c\), \(\[Lambda]\)],
FractionBox[
SuperscriptBox[\(\[Lambda]\), \(3\)], \(8 \[Pi]\)]])\)\ /
\*SuperscriptBox[\(c\), \(2\)])\) Abs[Sin[\((
\*FractionBox[\(2\ \[Pi]\), \(\[Lambda]\)])\)\ y]]\ \((1 -
\*SuperscriptBox[\((
\*FractionBox[\(r\), \(
\*FractionBox[\(1\), \(4\)]\ \[Lambda]\
\*SqrtBox[\(Cos[2\ \[Theta]]\)]\)])\), \(2\)])\) \((
\*FractionBox[\(2 \[Pi]\ c\), \(\[Lambda]\)]/\((
\*FractionBox[\(1\), \(hbar\)] \((
\*SubsuperscriptBox[\(\[Integral]\), \(0\), \(\[Lambda]\)]\(
\*SubsuperscriptBox[\(\[Integral]\), \(-
\*FractionBox[\(\[Pi]\), \(4\)]\),
FractionBox[\(\[Pi]\), \(4\)]]\(
\*SubsuperscriptBox[\(\[Integral]\), \(0\), \(
\*FractionBox[\(1\), \(4\)]\ \[Lambda]\
\*SqrtBox[\(Cos[2\ \[Theta]]\)]\)]2 \((\((
\*FractionBox[
FractionBox[\(2*h*c\), \(\[Lambda]\)],
FractionBox[
SuperscriptBox[\(\[Lambda]\), \(3\)], \(8 \[Pi]\)]])\)\ /
\*SuperscriptBox[\(c\), \(2\)])\) Abs[Sin[\((
\*FractionBox[\(2\ \[Pi]\), \(\[Lambda]\)])\)\ y]]\ \((1 -
\*SuperscriptBox[\((
\*FractionBox[\(r\), \(
\*FractionBox[\(1\), \(4\)]\ \[Lambda]\
\*SqrtBox[\(Cos[2\ \[Theta]]\)]\)])\), \(2\)])\) \((
\*FractionBox[\(\(2\) \(\[Pi]\)\(\ \)\(c\)\(\ \)\), \
\(\[Lambda]\)])\) r \[DifferentialD]r \[DifferentialD]\[Theta] \
\[DifferentialD]y\)\))\))\))\) r \[DifferentialD]r \[DifferentialD]\
\[Theta] \[DifferentialD]y\)\)\) == hbar && \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(0\), \(2 \[Pi]\)]\(
\*SubsuperscriptBox[\(\[Integral]\), \(0\), \(\[Pi]\)]\(
\*SubsuperscriptBox[\(\[Integral]\), \(0\), \(
\*SqrtBox[\(2\)]*
\*SuperscriptBox[\(n\), \(2\)]*bohr\)]\((
\*FractionBox[
FractionBox[\(4*eEnergy\), \(4 \[Pi]\
\*SuperscriptBox[\((
\*SqrtBox[\(2\)]*
\*SuperscriptBox[\(n\), \(2\)]*bohr)\), \(3\)]/3\)],
SuperscriptBox[\(c\), \(2\)]])\) \((1 -
\*FractionBox[\(r\), \(
\*SqrtBox[\(2\)]*
\*SuperscriptBox[\(n\), \(2\)]*bohr\)])\)
\*SuperscriptBox[\(r\), \(2\)] Sin[\[Phi]] \[DifferentialD]r \
\[DifferentialD]\[Phi] \[DifferentialD]\[Theta]\)\)\) ==
me \[DoubleRightArrow] \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(0\), \(2 \[Pi]\)]\(
\*SubsuperscriptBox[\(\[Integral]\), \(0\), \(\[Pi]\)]\(
\*SubsuperscriptBox[\(\[Integral]\), \(0\), \(
\*SqrtBox[\(2\)]*
\*SuperscriptBox[\(n\), \(2\)]*bohr\)]\((
\*FractionBox[
FractionBox[\(4*eEnergy\), \(4 \[Pi]\
\*SuperscriptBox[\((
\*SqrtBox[\(2\)]*
\*SuperscriptBox[\(n\), \(2\)]*bohr)\), \(3\)]/3\)],
SuperscriptBox[\(c\), \(2\)]])\) \((1 -
\*FractionBox[\(r\), \(
\*SqrtBox[\(2\)]*
\*SuperscriptBox[\(n\), \(2\)]*bohr\)])\) \((
\*FractionBox[\(c\), \(2 \[Pi]*
\*SqrtBox[\(2\)]*
\*SuperscriptBox[\(n\), \(2\)]*bohr\)]\ *\((
\*FractionBox[\(hbar\), \(2\)]/\((
\*SubsuperscriptBox[\(\[Integral]\), \(0\), \(2 \[Pi]\)]\(
\*SubsuperscriptBox[\(\[Integral]\), \(0\), \(\[Pi]\)]\(
\*SubsuperscriptBox[\(\[Integral]\), \(0\), \(
\*SqrtBox[\(2\)]*
\*SuperscriptBox[\(n\), \(2\)]*bohr\)]\((
\*FractionBox[
FractionBox[\(4*eEnergy\), \(4 \[Pi]\
\*SuperscriptBox[\((
\*SqrtBox[\(2\)]*
\*SuperscriptBox[\(n\), \(2\)]*bohr)\), \(3\)]/3\)],
SuperscriptBox[\(c\), \(2\)]])\) \((1 -
\*FractionBox[\(r\), \(
\*SqrtBox[\(2\)]*
\*SuperscriptBox[\(n\), \(2\)]*bohr\)])\) \((
\*FractionBox[\(c\), \(2 \[Pi]*
\*SqrtBox[\(2\)]*
\*SuperscriptBox[\(n\), \(2\)]*bohr\)])\)\
\*SuperscriptBox[\(r\), \(2\)] Sin[\[Phi]] \[DifferentialD]r \
\[DifferentialD]\[Phi] \[DifferentialD]\[Theta]\)\))\))\))\)\
\*SuperscriptBox[\(r\), \(2\)] Sin[\[Phi]] \[DifferentialD]r \
\[DifferentialD]\[Phi] \[DifferentialD]\[Theta]\)\)\) == hbar/2]]
(The significance of establishing a new AI Report Topic of a computationally reproducible 4D spacetime human-ai worldview is seen here as a worthwhile basis to develop AGI on objective mathematical physics experimental reality vs the perils of science fiction. Hence it is logical if AGI is to be achieved any such AI analytic LLM should first be capable of conducting a peer review of any new scientific logic as a logical sequitur to the prior art, while serving as a tool to test and further develop the competing approaches to the modern relative states of The School of Athens debate. )
(To be written by future ChatGPT-Wolfram analytic LLM)