Standard Model: the Higgs mechanism as spontaneous symmetry breaking of the quantum vacuum.

Gravity as a VA/ET density gradient Vol. 2, No. 23 (2025), pp. 1–12 Standard Model: the Higgs mechanism as spontaneous symmetry breaking of the quantum vacuum. Mohamed Makraini ([email protected]) Independent Researcher M´alaga, Spain Abstract We present a simulation of the coupling between the Higgs field (Φ), the density of the Absolute Vacuum/Space-Time (ϱ), and an emergent curvature interpreted as gravitational. The model allows variation of key physical parameters. We argue that the Higgs field does not acquire mass via spontaneous symmetry breaking in the quantum vacuum [2], but rather through direct interaction with the Absolute Vacuum, which lacks space-time structure. The resulting spacetime curvature emerges from AV flux effects, without invoking graviton exchange [3]. Keywords: Absolute Vacuum, Higgs field, quantum density, emergent gravity, symmetry breaking. 1 Introduction The Higgs mechanism in the Standard Model postulates that particles acquire mass through spontaneous symmetry breaking in a scalar field [2]. However, this work proposes an alternative paradigm in which mass emerges from a fundamental interaction with a pre-spacetime Absolute Vacuum (AV). Advanced Simulation: Higgs–Absolute Vacuum (AV) Equation with Adjustable Parameters Objective: To simulate the coupling between the Higgs field (Φ), the AV/ST density (ϱ), and emergent gravity, by varying key physical parameters. 2 Modified Master Equation We incorporate: •Explicit dependence of the Higgs mass (mH) on ϱ. •Gravitational coupling (κ) as a dynamic variable. Corresponding author: Mohamed Makraini 2 Mohamed Makraini •AV flux (Fµν), analogous to a gauge field. Higgs Equation in AV/ST: □+ξR +m2 H(ϱ)+κFµνFµνΦ = 0 (2.1) where: - ξR: Coupling to curvature (Higgs-inflation type). -m2 H(ϱ)=v2(1 −e−ϱ2): Effective mass dependent on ϱ. -Fµν =∂µAν−∂νAµ: AV flux tensor. 2.1 Analysis Plan •Model A: Higgs with Spontaneous Symmetry Breaking (SSB) •Model B: Higgs with Interaction with the Absolute Vacuum (AV) •Physical and Mathematical Comparison 2.2 MODEL A: Spontaneous Symmetry Breaking (SSB) Lagrangian (with potential): LSSB =1 2∂µϕ ∂µϕ−V(ϕ),with V(ϕ) = −1 2µ2ϕ2+1 4λϕ4(2.2) Euler–Lagrange equation: d dt ∂L ∂˙ ϕ−∂L ∂ϕ = 0 (2.3) We compute: •∂L ∂˙ ϕ=˙ ϕ •d dt(˙ ϕ) = ¨ ϕ •∂L ∂ϕ =−dV dϕ =µ2ϕ−λϕ3 Result: ¨ ϕ+µ2ϕ−λϕ3= 0 (2.4) This is the classical Higgs model, where: •The Higgs mass is m2 H= 2µ2 •The solution stabilizes at ϕ=v=pµ2/λ Gravity as a density gradient VA/ET Vol. 2, No. 23 (2025), pp. 1–12 3 2.3 MODEL B: Interaction with the Absolute Vacuum (AV) Lagrangian: LAV =1 2∂µϕ ∂µϕ−1 2m2(ρ)ϕ2−1 2ξRϕ2−1 2κρϕ2(2.5) where: m2(ρ)=v21−e−(ρ/ρc)2(2.6) As before, we apply Euler–Lagrange: •∂L ∂˙ ϕ=˙ ϕ⇒¨ ϕ •∂L ∂ϕ =m2(ρ)+ξR +κρϕ Result: ¨ ϕ+m2(ρ)+ξR +κρϕ= 0 (2.7) Feature SSB Model AV Model Potential −1 2µ2ϕ2+1 4λϕ4No ϕ4; mass induced by AV Equation of motion ¨ ϕ+µ2ϕ−λϕ3= 0 ¨ ϕ+ [m2(ρ)+ξR +κρ]ϕ= 0 Mass generation From the shape of the potential (spontaneous) From physical interaction with the AV Equilibrium point Fixed at ϕ=±vDynamic depending on ρ(t) Symmetry Spontaneously broken Preserved, but interaction defines behavior Table 1: Comparison between the SSB Model (Spontaneous Symmetry Breaking) and the AV Model (Absolute Vacuum). 3 Extension of the Absolute Vacuum (AV) Lagrangian 3.1 General Structure The AV differs from the conventional quantum vacuum in that: •It has no space-time structure [3] •Its density (ϱ) is a fundamental parameter •It produces non-local effects on quantum fields Gravity as a density gradient VA/ET Vol. 2, No. 23 (2025), pp. 1–12 4 Mohamed Makraini The interaction between a fundamental field Ψ and the Absolute Vacuum (AV) can be expressed as: L=LQFT(Ψ) + LAV-int(Ψ, ϱ) (3.1) where: •LQFT is the usual Lagrangian in space-time. •LAV-int represents direct coupling with the AV density ϱ=ρAV. 3.2 Coupling of the AV to Gluons The standard QCD Lagrangian is: LQCD =−1 4Ga µνGa µν (3.2) where the gluon field strength tensor is: Ga µν =∂µAa ν−∂νAa µ+gfabcAb µAc ν(3.3) AV–Gluon Coupling: We propose an interaction term: L(g) AV-int =−1 4(1+κgf(ϱ)) Ga µνGa µν (3.4) where: •κgis the gluon–AV coupling constant, •f(ϱ) is a saturation function, for example: f(ϱ) = tanh ϱ ρ0(3.5) This suppresses gluon propagation at large scales, explaining confinement as a geometric consequence of the AV. Emergent Curvature Without Gravitons Unlike quantum gravity approaches based on the quantization of the metric field or the existence of spin-2 gravitons [3], our framework posits that curvature emerges directly from the interaction between the Absolute Vacuum (AV) and quantum fields via the scalar density field ρ(x). In this picture, spacetime geometry is not fundamental but induced by gradients and quantum fluctuations of the AV. The effective curvature arises from the tensor Fµν , introduced in Eq. (2.1), as follows: Rµν ∼κ⟨FαβFαβ⟩gµν (3.6) This relation indicates that gravitational effects are modulations of geometry encoded in the expectation value of AV flux interactions, avoiding any need for quantized gravitational degrees of freedom [4]. Therefore, curvature is a large-scale structural manifestation of the field ρ(x), not a dynamical tensor field requiring a graviton mediator. Gravity as a density gradient VA/ET Vol. 2, No. 23 (2025), pp. 1–12 5 Geometric and Symmetry Structure of AV Flux Fµν The tensor Fµν =∂µAν−∂νAµ, originally introduced as an internal flux of the Absolute Vacuum (AV), can be interpreted as the field strength of an emergent gauge-like structure. This suggests that the AV exhibits an internal symmetry that becomes broken through structural condensation governed by the scalar field ρ(x). The Lagrangian term κFµνFµν is analogous to a Maxwell-type invariant, and the corresponding energy-momentum tensor, T(AV ) µν =κFµαFνα−1 4gµνFαβFαβ,(3.7) satisfies a conservation law ∇µT(AV ) µν = 0, ensuring structural stability. Moreover, the emergence of curvature via Rµν ∼κ⟨FαβFαβ⟩gµν (3.8) can be understood as a macroscopic effect of a symmetry-breaking transition in the AV, where ρ(x) plays the role of an order parameter. This approach opens the possibility to reconstruct spacetime geometry as an effective phase of an underlying internal symmetry, potentially nonAbelian, encoded in the structure of Aµand its associated connection. Variational Framework and Field Equations To formalize the dynamics of the Absolute Vacuum (AV), we consider an effective action involving two fundamental fields: •A scalar field ρ(x), representing the structural density of the AV. •A vector field Aµ(x), interpreted as an internal AV connection responsible for the flux tensor Fµν. We postulate the covariant action: S[ρ, Aµ] = Zd4x√−g−1 4κ(ρ)FµνFµν +1 2∂µρ ∂µρ−V(ρ),(3.9) where: •Fµν =∂µAν−∂νAµis the internal AV flux tensor, •κ(ρ) is a structural coupling function, •V(ρ) is a potential that determines the vacuum configuration. Equations of Motion Varying the action with respect to Aµyields the generalized Maxwell-like equation: ∇µ(κ(ρ)Fµν)=0,(3.10) which governs the dynamics of the internal AV field in a medium structured by ρ(x). Gravity as a density gradient VA/ET Vol. 2, No. 23 (2025), pp. 1–12 6 Mohamed Makraini Varying with respect to ρgives: □ρ−V′(ρ)−1 4κ′(ρ)FµνFµν = 0,(3.11) where □ρ=∇µ∇µρis the covariant d’Alembertian. Choice of Functions For spontaneous structure generation, we adopt: V(ρ) = λ 4(ρ2−ρ2 0)2,(3.12) κ(ρ)=κ0e−ρ/ρc,(3.13) where ρ0is the equilibrium structural density and ρcis a critical scale. These choices lead to rich phenomenology where spacetime curvature emerges from local condensates of ρ(x), and the flux tensor Fµν acts as a regulator of geometric structure without requiring graviton exchange. Perturbative Analysis Around Structural Vacuum We consider small fluctuations of the structural field around its equilibrium value: ρ(x)=ρ0+δρ(x),|δρ| ≪ ρ0.(3.14) Linearizing the equation of motion (3.11) leads to: □δρ +M2 eff δρ =1 4κ′(ρ0)FµνFµν ,(3.15) where the effective mass of the perturbation is given by: M2 eff =V′′(ρ0)=2λρ2 0.(3.16) These fluctuations represent structural excitations of the AV that couple directly to the field strength intensity. In regimes where Fµν →0, they propagate as standard massive scalar modes. In the presence of AV flux, however, their dynamics are sourced by geometric curvature gradients. 4 The Neutrino as a Particle Sensitive to the Absolute Vacuum 4.1 Traditional Approach In the extended Standard Model, neutrino mass is introduced via: •Dirac mechanism: a right-handed neutrino νRis added, and a mass term is built: LDirac =−mD¯νLνR+ h.c. (4.1) •Majorana mechanism: the neutrino is its own antiparticle: LMajorana =−1 2mM¯νC LνL+ h.c. (4.2) Both mechanisms require symmetry breaking or new particles. Gravity as a density gradient VA/ET Vol. 2, No. 23 (2025), pp. 1–12 7 4.2 Absolute Vacuum (AV) Hypothesis We propose a new framework: The neutrino has no intrinsic mass. Its quantum behavior arises from its interaction with the Absolute Vacuum, without requiring symmetry breaking. 4.3 Proposed Lagrangian We start from a massless left-handed Weyl spinor: L(0) ν=i¯νLγµ∂µνL(4.3) We introduce coupling with the AV as a quantum resistance to propagation: L(ν) AV-int =−λνϱ¯νLνL(4.4) where: •λνis the neutrino–AV coupling, •ϱ=ρAV is the AV density, •This does not represent mass, but a decoupling from space-time. 4.4 Oscillations Without Mass Instead of assuming different masses mj, we propose: Ej=p+λ(j) ν⟨ϱ⟩(4.5) and the oscillations are: να(t) = X j Uαj e−iEjtνj(4.6) 4.5 Model Predictions •Oscillations without requiring mass. •Changes in oscillation frequencies depending on the environment (similar to the MSW effect, but induced by the AV). •Possible signatures in regions of high quantum density or deep vacuum. Gravity as a density gradient VA/ET Vol. 2, No. 23 (2025), pp. 1–12 8 Mohamed Makraini 5 Cosmological Implications The results obtained have profound consequences for theoretical cosmology: •Higgs–AV Inflation: The non-minimal coupling term ξRϕ2(Eq. 2.1), originally studied by [1], gains new relevance in our framework. The AV density (ϱ) could modulate the inflationary scale without fine-tuning ξ. •Problem of Time: As discussed in [7], the pre-spacetime nature of the AV resolves temporal inconsistencies in quantum gravity. Our tensor Fµν provides a fundamental clock independent of spacetime. Figure 1: Diagram comparing conventional inflation (A) vs. AV-mediated inflation (B). Adapted from [1]. 6 Origins of Mass 6.1 Critique of the RES Mechanism The traditional paradigm, exemplified by [6], assumes that mass emerges solely from: mH∝p−µ2/λ (6.1) 6.2 AV Alternative Our model shows that the same mass scale can be obtained through: m2 H(ϱ)≈v2(1 −e−(ϱ/ρc)2) (6.2) where ρcis a fundamental parameter of the Universe, not an ad hoc tuning. Emergent Gravity The work of Volovik [4] on emergent spacetime structures resonates with our results. Theorem 6.1 (Gravity as an AV Effect).The term κFµνFµν in Eq. (2.1) generates an effective curvature: Rµν ∼κ⟨FαβFαβ⟩gµν (6.3) Unlike conventional frameworks where curvature is introduced via classical General Relativity or quantized fields [3], our model describes geometry as a coherent response to the structural modulation of the Absolute Vacuum (AV). The gravitational field is not a fundamental spin-2 field but rather an emergent property of quantum density gradients in ρ(x). 7 Discussion: High-Impact Implications Our model proposes three conceptual revolutions in fundamental physics: Gravity as a density gradient VA/ET Vol. 2, No. 23 (2025), pp. 1–12 9 7.1 Reinterpretation of the Quantum Vacuum In contrast to the traditional view of the vacuum as a passive minimum-energy state [6], we describe the Absolute Vacuum as an active, foundational entity with two key properties: •Primary Entity: A pre-geometric medium with no spacetime structure [7]. •Dynamic Medium: Its density ϱgoverns field behavior and modulates emergent geometry. Vacuum: Quantum min. energy Vacuum: Pre-spacetime density Mass: symmetry breaking Mass: AV interaction Gravitation: curvature of spacetime Geometry: from AV flux Quantum gravity: unresolved No graviton: emergent structure Figure 2: Side-by-side comparison of conceptual paradigms: Standard Model (left) vs. AV-based framework (right). 7.1 Mass Mechanism Without Symmetry Breaking The numerical results of Section 4 demonstrate that: d2Veff dϕ2ϕ=0 ≈m2 H(ϱ) without needing V(ϕ) = −µ2ϕ2+λϕ4(7.1) This resolves the fine-tuning problem noted by [1], since ρcis a measurable parameter. 7.2 Quantum-compatible emergent gravity from structural density field The tensor Fµν provides: •Intrinsic Regularization: Eliminates UV divergences by cutting off modes with length < ϱ−1/3 •Emergence of Geometry: As in [5], but based on the microscopic structure of the AV Gravity as a density gradient VA/ET Vol. 2, No. 23 (2025), pp. 1–12