Am 05.04.2026 um 12:18 schrieb David Chester: I've already unified SU(2,2) with GL(4,R) without resorting to the infinite-dimensional nonlinear differs like Ogieveskii, so it's all good. Gee, can anyone guess a simple finite-dimensional Lie group containing both? Lol, I think Joel will like the answer. Hint: One must use exceptional isomorphisms excessively.Double hint: This group is given by multiplication over a nonassociative 8D algebra that contains the quaternions as a subalgebra, but it's not the octonions. GL(4,R) belongs to Freidrich Hehl more than me. But really, the full metric-affine group is AL(4,R), which is GL(4,R) plus translations. Some authors study GL(4,R) alone in that context, but torsion is technically associated with the translations. On Sat, Apr 4, 2026, 11:27 PM JACK SARFATTI <jacksarfatti@icloud.com> wrote: Conformal Gravity (Weyl Gravity) and QuantizationPhilip Mannheim's conformal gravity uses the Weyl tensor squared action ∫ C_{μνρσ} C^{μνρσ} √-g (fourth-order in derivatives), which is classically conformally invariant and thus tied to SO(2,4).  Classical successes: Reproduces Schwarzschild solutions at solar-system scales; produces linear quadratic potentials that can fit galactic rotation curves without dark matter; addresses cosmological constant and horizon problems without fine-tuning.Quantum aspects: Claims renormalizability and unitarity in 4D (via non-perturbative methods or Bender-Mannheim PT-symmetric quantum mechanics). The vacuum energy interplay between gravity and matter sectors solves the cosmological constant problem. However, perturbative analyses often reveal ghost modes in the propagator, leading to ongoing debates about stability and consistency.Other quantizations treat local conformal symmetry via BRST formalism in a general gravitational theory (with Weyl diffeomorphism invariance), yielding extended global symmetries (including GL(4)-extended conformal algebra) whose SSB produces massless graviton and dilaton as Nambu-Goldstone bosons. Twistor Theory and Loop Quantum Gravity (LQG) ConnectionsTwistors: Originally motivated by conformal invariance (Penrose), twistors provide a description of massless particles and null geodesics using the geometry of SU(2,2) ≅ SL(2,ℂ) extensions. In LQG/spin-foam approaches, twistors embed SU(2) spin networks into a larger SL(2,ℂ) or SU(2,2) structure, introducing scale/dilatation information and relating to twisted geometries or null hypersurfaces. Spin networks/foams: Standard LQG uses SU(2) (from Ashtekar variables), but twistor extensions allow SU(2,2) spin networks, potentially incorporating conformal aspects or self-dual structures. This helps bridge discrete quantum geometry with conformal symmetries at the boundary or in asymptotic regimes. SO(2,4) does not appear as a core gauge group in canonical LQG or most spin-foam models (which emphasize diffeomorphism invariance and SU(2) or SL(2,ℂ) holonomies), but it emerges in boundary CFT-like descriptions or holographic contexts.Other Contexts in Quantum GravityAdS/CFT and holography: SO(2,4) is the conformal group on the 4D boundary of AdS₅, central to the duality where gravity in the bulk corresponds to a CFT on the boundary. Asymptotic safety: Some fixed-point analyses of quantum gravity invoke conformal invariance or related scaling symmetries, though not directly SO(2,4) gauging.Hybrid or alternative models: Weyl conformal geometry as a gauge theory; relations to massive gravity or derivative couplings; extensions combining conformal and affine structures. Comparison to GL(4,ℝ) Gauge Gravity in Quantum Context SO(2,4) emphasizes conformal/light-cone preservation (D Kₐ), often leading to higher-order equations and strong scale invariance. Quantum predictions may include modified UV behavior, ghost issues (or resolutions), and phenomenology like dark-matter alternatives or specific cosmological attractors. GL(4,ℝ) (metric-affine) introduces full non-metricity (dilation shear) torsion, coupling to hypermomentum. It tends toward second-order equations with extra propagating modes from microstructure; SSB to Lorentz recovers GR. Quantum predictions focus on torsion/non-metricity effects in high-density/early-universe regimes, potential renormalizability improvements, but different matter couplings. Both can recover GR at low energies via SSB, but diverge in UV completion, extra degrees of freedom, and testable predictions (e.g., conformal models vs. torsion signals). Neither is the "standard" quantum gravity (string theory or LQG dominate mainstream), but they offer elegant gauge-theoretic alternatives addressing renormalization and symmetry issues. These approaches remain active research areas, with recent papers exploring SSB to GR in SO(2,4) Yang-Mills gravity and conformal quantization techniques. If you're interested in a specific model (e.g., Mannheim's, twistor-LQG links, or a particular action), action details, or phenomenological tests, provide more focus. x.com/i/grok/share/c6d869fa1… jacksarfatti.academia.edu On the extended electro-gravitic new dynamical degrees of freedom - definitely on my back-burner.Begin forwarded message:From: David Chester <chester31124@gmail.com> Subject: Re: Maxwell after Heaviside Modanese Extended Electro-GeometrodynamicsDate: April 4, 2026 at 9:05:40 PM PDT To: Mohamad A <merchantmoh@gmail.com>Cc: Regarding the scale transformation in the conformal group, there is another group that contains the scale transformation, GL(4,R). E.g., Weyl nonmetricity is associated with the scale transformation. A couple years ago, I presented on how to obtain a correspondence between the scalar electric mode and the scale transformation dof associated with the trace of the metric. Note that in GR, it is common to take the transverse traceless gauge, as the trace does not contain physical dof. youtube.com/live/atMUqx1iyIw… I was taught that GR's metric has 10 dof, but string theorists say the graviton has 9 and the dilaton has The dilaton relates to the trace of g_{\mu\nu}. However, I'm now a bit more partial to thinking of the Hertz potentials as the imaginary component of the metric, rather than just the antisymmetric component of a real metric... Still, I think stating that detection of C is support for the conformal group is a bit overstated. In my view, the 3rd Whittaker potential leading to C could be proportional to the dilaton, but that isn't generically true for arbitrary theories. Additionally, both GL(4,R) and SU(2,2) contain the scale transformation. Crucially, the dilaton or scale transformation is associated with Spin(1,1), while electromagnetism is associated with U(1). I really shouldn't say this because it's unpublished, but I worked out that one does obtain a U(1) gauge symmetry when complexifying the metric and looking at the imaginary component's analogue of Spin(1,1). On Sat, Apr 4, 2026 at 3:49 AM Mohamad A <merchantmoh@gmail.com> wrote:Paul, Julien, David -I'll take the open questions in order. Some of these I can settledefinitively. ==========================================================================1. DOES C MAP TO ANYTHING IN SO(2,4)?========================================================================== Yes. The parallel is structural - both are scalar-like sectorsdeleted by gauge fixing in their respective symmetry groups.The SO(2,4) conformal gauge theory has 15 generators. They decompose as:   6  Lorentz generators  M_ab  →  spin connection ω^ab_μ   4  translations        P_a   →  tetrad e^a_μ   4  special conformal   K_a   →  gauge fields k^a_μ   1  dilation D →  dilation gauge field D_μ Standard GR uses SO(1,3). That means you impose the conformal gauge:set D_μ = 0 and k^a_μ = 0. This deletes 5 of the 15 gauge fields.In electrodynamics, when you impose the Lorenz gauge ∂_μA^μ = 0, youset C = 0. Same mathematical operation: gauge-fixing that discards ascalar sector of the full connection. The C field in EED and the dilation sector D_μ in SO(2,4) play the same structural role in their respective gauge theories: both arescalar-like modes that standard formalism sets to zero via gaugefixing, and both carry physical content when the constraint isrelaxed. The parallel is at the level of sectors, not individualfield identities (C is a Lorentz scalar; D_μ is a vector). The Stueckelberg mechanism that Reed and Hively use to derive the EEDLagrangian has the same algebraic structure as the conformal symmetrybreaking that produces the dilation sector in SO(2,4). The explicit derivation - showing the Stueckelberg parameter emerges from SO(2,4) conformal breaking - remains to be worked out, but the group-theoreticmotivation is exact.This means three things: (a) Wilhelm's paper supports Jack's thesis from the EM side - the "deleted degrees of freedom" are exactly the conformal sector      that disappears when you restrict to SO(1,3). (b) Jack's SO(2,4) theory provides the group-theoretic ORIGIN of the C field. It's not a postulate - it's a consequence of  gauging the full conformal group. (c) The "historical deletion" narrative (Heaviside 1884) has a  gravitational parallel: the restriction from conformal to  Poincaré gravity (circa 1960s gauge gravity literature). Both deletions happened for the same reason - simplification - and both may have hidden the same physics.Paul - this is your answer. The C field lives in the dilation sectorof SO(2,4). It was not "lost" by accident. It was gauged away whenthe community chose SO(1,3) over SO(2,4). ========================================================================== HILBERT vs CANONICAL STRESS TENSOR - RESOLVED ========================================================================== Chester raised Wilhelm flagged it as important. I ran thecomputation symbolically. Here is the definitive answer.For the EED Lagrangian:   L_EED = -1/4 F_μν F^μν λ/2 C²      where C = ∂_μ A^μThe HILBERT stress tensor (obtained by metric variation):   T^H_{αβ} = [standard Maxwell] - λC · A_{(α,β)} (λ/2) g_{αβ} C²   Trace:  g^{αβ} T^H_{αβ} = -λC · 2C (4·λ/2) · C² = -2λC² 2λC²  = 0    RESULT: Hilbert trace is ZERO. Completely traceless.The CANONICAL (Noether) stress tensor:   T^can_{μν} = λC · ∂_ν A_μ - (λ/2) η_{μν} C²   Trace:  η^{μν} T^can_{μν} = λC² - 2λC² = -λC² RESULT: Canonical trace is -λC². Non-zero.The Belinfante-Rosenfeld improvement term carries trace λC²,accounting for the discrepancy. Chester was correct: the Hilbert tensor lacks the trace term. Hively was correct: the canonical tensor has the trace term.They were computing different objects. Both valid. Different physics.What this means:  - HILBERT (gravitational source): C does NOT independently source gravity via stress-energy. The C² sector is traceless. It cannot  produce an equation of state w = -1. It will not source dark energy  through the Einstein equations as written. - CANONICAL (energy flow): C DOES carry energy. The scalar field    participates in conservation laws with trace -λC².  - CRITICAL IMPLICATION: In standalone EED (flat space), C carries    energy but cannot source gravity. However, in the coupled SO(2,4) framework, the dilation gauge field D_μ couples to the metric  through the GAUGE FIELD EQUATIONS - not through T_μν. The  gravitational effect enters through the gauge coupling, not the    stress-energy channel. So Jack's earlier intuition about dark energy  may be correct, but the mechanism is gauge-mediated, not  stress-energy-mediated. This distinction matters. It means looking for dark energy in the    Hilbert tensor is looking in the wrong place. The right place is the SO(2,4) gauge equations. All of the above was verified symbolically. I can send the computationif anyone wants to check it. ========================================================================== 3. JULIEN'S FERMI ESTIMATE - CORRECT, AND HERE IS WHY ==========================================================================Julien asks whether the SLW momentum-to-energy ratio is better thanp = E/c.No. For any massless field propagating at c, the relationship p = E/cis fixed by special relativity - regardless of polarization state(transverse, longitudinal, or scalar). The "deleted degrees of freedom"give you new field configurations and new energy flux channels (the-EC term in the Poynting vector), but they do not change thefundamental energy-momentum dispersion relation for massless quanta. Your 1.2 GW to lift 400 grams is correct. If anything, it is optimistic- it assumes 100% conversion efficiency, which no antenna achieves.This is why radiation pressure - from any polarization of EM wave -cannot produce macroscopic propulsion. The mechanism is structurallywrong. You are trying to push matter with photon momentum. Photonsare the wrong tool for the job. Jack's approach is fundamentally different: metric engineering. You donot push against inertia. You reshape spacetime geometry so that"stationary" in the engineered metric corresponds to "accelerating" inthe background metric. The energy budget is set by the NEC violation threshold - not by radiation pressure. The SO(2,4) conformal extensionprovides the extra gauge fields (D_μ, k^a_μ) that source the metricmodification at achievable laboratory power levels. And this is the punchline that connects everything in this thread:    - EED recovers the scalar sector of electrodynamics (the C field).   - SO(2,4) recovers the scalar sector of gravity (the dilation field D_μ). - The C field IS the EM shadow of D_μ. - Detecting C (via SLW experiments) is indirect evidence for the     full conformal sector.    - But USING the conformal sector for propulsion requires the gravitational coupling - not the EM radiation pressure. So, to answer your question directly, Julien: no, we still need the warpdrive. But the SLW experiment is not irrelevant to it - it tests whetherthe "deleted" conformal sector is physically real in the EM domain. Ifit is, the gravitational counterpart becomes much harder to dismiss. ========================================================================== ON THE SLW PROTOCOL ========================================================================== Paul - you mentioned reviewing our SLW detection protocol. I appreciatethat. Bob McGwier and I designed the $4,500 apparatus specifically toresolve the far-zone propagation question, which is the only questionthat matters. Monstein & Wesley's near-zone result - as you correctlynoted - is inconclusive, because conventional EM already haslongitudinal modes in the near field. If Chester's group is also working on GHz-band replication, there maybe value in coordinating on detection methodology. Three independentgroups working independently is good for credibility, but not if weall make the same systematic error. The protocol PDF is available. ========================================================================== 5. MODANESE'S GAUGE WAVES ========================================================================== Paul raised this and asked whether they appear in the formalism. Quickanswer: Modanese and Minotti's "g-waves" (E = B = 0, pure potential waves)are the four-irrotational sector in Woodside's decomposition theorem- the class with F_μν = 0. In EED, these are pure C-mode excitations:∂_μA_ν ≠ 0 but the antisymmetric part (the field strength) vanishes. In the SO(2,4) framework, these correspond to pure dilation/conformalwave modes - oscillations of D_μ and k^a_μ with no excitation of theLorentz connection ω^ab_μ or the tetrad e^a_μ. Geometrically, this is a conformally oscillating spacetime with no curvature or torsionfluctuation. It is a wave in the conformal factor alone.Whether these propagate in the interacting theory (as opposed to thelinearized approximation) depends on the self-coupling structure ofthe SO(2,4) gauge sector - which is precisely what Jack's currentwork is about. Modanese's 2024 detector circuit (arXiv:2403.10580) is designed forthis mode. It would be worth cross-referencing with our SLW protocolto see whether the same apparatus can be adapted to test for g-wavesas well. Two birds, one stone.- MAVirenfrei.www.avast.com ========================================================================= Chester raised this. Wilhelm flagged it as important. I ran thecomputation symbolically. Here is the definitive answer.For the EED Lagrangian:   L_EED = -1/4 F_μν F^μν λ/2 C² where C = ∂_μ A^μThe HILBERT stress tensor (obtained by metric variation):   T^H_{αβ} = [standard Maxwell] - λC · A_{(α,β)} (λ/2) g_{αβ} C²   Trace:  g^{αβ} T^H_{αβ} = -λC · 2C (4·λ/2) · C²  = -2λC² 2λC²  = 0 RESULT: Hilbert trace is ZERO. Completely traceless.The CANONICAL (Noether) stress tensor:   T^can_{μν} = λC · ∂_ν A_μ - (λ/2) η_{μν} C²   Trace:  η^{μν} T^can_{μν} = λC² - 2λC²  = -λC² RESULT: Canonical trace is -λC². Non-zero.The Belinfante-Rosenfeld improvement term carries trace λC²,accounting for the discrepancy. Chester was correct: the Hilbert tensor lacks the trace term. Hively was correct: the canonical tensor has the trace term.They were computing different objects. Both valid. Different physics. What this means:  - HILBERT (gravitational source): C does NOT independently source gravity via stress-energy. The C² sector is traceless. It cannot  produce an equation of state w = -1. It will not source dark energy  through the Einstein equations as written. - CANONICAL (energy flow): C DOES carry energy. The scalar field    participates in conservation laws with trace -λC². - CRITICAL IMPLICATION: In standalone EED (flat space), C carries    energy but cannot source gravity. However, in the coupled SO(2,4)  framework, the dilation gauge field D_μ couples to the metric  through the GAUGE FIELD EQUATIONS - not through T_μν. The    gravitational effect enters through the gauge coupling, not the    stress-energy channel. So Jack's earlier intuition about dark energy  may be correct, but the mechanism is gauge-mediated, not    stress-energy-mediated. This distinction matters. It means looking for dark energy in the  Hilbert tensor is looking in the wrong place. The right place is    the SO(2,4) gauge equations. All of the above was verified symbolically. I can send the computationif anyone wants to check it. ========================================================================== 3. JULIEN'S FERMI ESTIMATE - CORRECT, AND HERE IS WHY ========================================================================== Julien asks whether the SLW momentum-to-energy ratio is better thanp = E/c.No. For any massless field propagating at c, the relationship p = E/cis fixed by special relativity - regardless of polarization state(transverse, longitudinal, or scalar). The "deleted degrees of freedom"give you new field configurations and new energy flux channels (the-EC term in the Poynting vector), but they do not change the fundamental energy-momentum dispersion relation for massless quanta. Your 1.2 GW to lift 400 grams is correct. If anything, it is optimistic- it assumes 100% conversion efficiency, which no antenna achieves.This is why radiation pressure - from any polarization of EM wave -cannot produce macroscopic propulsion. The mechanism is structurally wrong. You are trying to push matter with photon momentum. Photons are the wrong tool for the job. Jack's approach is fundamentally different: metric engineering. You do not push against inertia. You reshape spacetime geometry so that"stationary" in the engineered metric corresponds to "accelerating" inthe background metric. The energy budget is set by the NEC violation threshold - not by radiation pressure. The SO(2,4) conformal extensionprovides the extra gauge fields (D_μ, k^a_μ) that source the metricmodification at achievable laboratory power levels. And this is the punchline that connects everything in this thread:    - EED recovers the scalar sector of electrodynamics (the C field).   - SO(2,4) recovers the scalar sector of gravity (the dilation field D_μ). - The C field IS the EM shadow of D_μ.    - Detecting C (via SLW experiments) is indirect evidence for the  full conformal sector.    - But USING the conformal sector for propulsion requires the     gravitational coupling - not the EM radiation pressure. So to answer your question directly, Julien: no, we still need the warpdrive. But the SLW experiment is not irrelevant to it - it tests whether the "deleted" conformal sector is physically real in the EM domain. Ifit is, the gravitational counterpart becomes much harder to dismiss. ========================================================================== 4. ON THE SLW PROTOCOL ========================================================================== Paul - you mentioned reviewing our SLW detection protocol. I appreciatethat. Bob McGwier and I designed the $4,500 apparatus specifically toresolve the far-zone propagation question, which is the only questionthat matters. Monstein & Wesley's near-zone result - as you correctlynoted - is inconclusive, because conventional EM already haslongitudinal modes in the near field. If Chester's group is also working on GHz-band replication, there maybe value in coordinating on detection methodology. Three independentgroups working independently is good for credibility, but not if weall make the same systematic error. The protocol PDF is available. ========================================================================== 5. MODANESE'S GAUGE WAVES ========================================================================== Paul raised this and asked whether they appear in the formalism. Quickanswer:Modanese and Minotti's "g-waves" (E = B = 0, pure potential waves)are the four-irrotational sector in Woodside's decomposition theorem- the class with F_μν = 0. In EED, these are pure C-mode excitations:∂_μA_ν ≠ 0 but the antisymmetric part (the field strength) vanishes. In the SO(2,4) framework, these correspond to pure dilation/conformalwave modes - oscillations of D_μ and k^a_μ with no excitation of theLorentz connection ω^ab_μ or the tetrad e^a_μ. Geometrically, this isa conformally oscillating spacetime with no curvature or torsionfluctuation. It is a wave in the conformal factor alone.Whether these propagate in the interacting theory (as opposed to thelinearized approximation) depends on the self-coupling structure ofthe SO(2,4) gauge sector - which is precisely what Jack's current work is about. Modanese's 2024 detector circuit (arXiv:2403.10580) is designed forthis mode. It would be worth cross-referencing with our SLW protocolto see whether the same apparatus can be adapted to test for g-waves as well. Two birds, one stone. - MAVirenfrei.www.avast.com

this is an extension of my QuickAnswer app that I have been using for semi-anonymous in-class quizzes (students use anonymous ID which is not linked directly to them in the sense that I am not looking at it).

What does it takes to go premium. #quickanswer

Can you Solve this? #IQ #MindTest #challenge #Solution #QuickAnswer #GTVNews

Ton mec sait se battre ? #quickanswer

Est ce que son mec sait se battre ? #quickanswer

Study maths!📕✨ #weopi.com #freeai #aiprivacy #quickanswer #aitool #AIAssistant #studenthacks #smartai #math #mathematics

当社IRサイトのQuickAnswerを更新しました！まだまだ更新頻度が低く恐縮ですが、ご覧いただければ幸いです！ 今回は 「過去2期の営業利益は投資による減益となっていますが、投資を除く利益（EBITDA）の過去推移はどのようになっていますか。」 です！ n-create.co.jp/pr/ir/qa/

सोचो और कॉमेंट में बताओ.... #riddles #braintraining #quiz #bollywood #movie #quickanswer #Question #puzzle

सोचो और कॉमेंट में बताओ.... #riddles #braintraining #quiz #bollywood #movie #quickanswer #Question #puzzle

बताइये सफेद गेंद का वजन क्या है? #quiz #quickanswer #ball #Question

ऐसा कौन सा फूल है जिसका वजन 10 किलो तक होता है? कमेंट में दे जवाब... #quiz #quickanswer #Question #flower

बताइये कौन- सा कप पहले भरेगा ? #riddles #braintraining #quiz #quickanswer #Cup #QuestionEverything

#puzzled Give #quickanswer

Verified Main games seru-seruan bareng Star Editor Oppal, Kak @isyanasarasvati 🙌🏻 Jangan lupa untuk tonton podcastnya di channel YouTube Oppal_ID 🫶 #isyanasarasvati #isyana #quickanswer #jawabcepat #oppal #stareditoroppal #isyanation

当社IRサイトに「QuickAnswer」ページをご用意しました。株主の皆様・投資家の皆様からのお問い合わせ内容とその回答を公開してまいります。 　 n-create.co.jp/pr/ir/qa/

Can you answer this fun question? If yes, then what is the delay? Quickly comment on the correct answer! #TractorKharido #QuickAnswer #IqTest #EicherTractor #Eicher #Tractors #Tractor #tractorloverzz #quiz #puzzle #game #fun #math #mathsgames

💡 Caught off guard with the question: How do #AI, #Blockchain, and #Web3 connect? 🤯 🎯 Looking for a crisp, one-sentence answer!😉 #QuickAnswer #CrystalClear #SizzlingTopic #ChatGPT

村上がquickAnswerするんやろガハハ！

quickAnswer クッソカッコええ！