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Theory of Bipolar
Entropic Gravity
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The Theory of Bipolar Entropic Gravity (TBEG) is not merely another speculative construct, but the result of years of research and analysis that has led to a fundamental paradigm shift. TBEG challenges the very foundations of modern cosmology and our understanding of gravity.
TBEG offers a radically new perspective, in which the gravity we are familiar with is merely the visible part of the iceberg. TBEG built upon a rigorous mathematical framework that introduces a second, "entropic" gravity (S-sector) existing in symbiosis with our own (N-sector). Their interaction, described through a mechanism of spontaneous symmetry breaking and the quantum dynamics of condensates, is capable of explaining what we have conventionally called dark matter and dark energy - without invoking any mysterious entities.
What you see before you is not just a theory. It is a unified framework that yields precise, quantitative predictions for phenomena that have eluded understanding for centuries: from galactic rotation curves to the dichroism of gravitational waves. Welcome to the forefront of physics, where gravity acquires a new, bipolar dimension.
Denis A. Kolesov
· Bimetric manifold (M, g, f) · g_μν - physical metric (N-sector) · f_μν - entropic metric (S-sector) · Signatures: (-,+,+,+) for both metrics
Ψ^A_μν ∈ S ⊗ T where: A = 1,2 - SU(2) index, μ,ν - tensor indices · ψ_N = Ψ^1_μν - N-graviton · ψ_S = Ψ^2_μν - S-graviton
Original group: SO(3,1)_g × SO(3,1)_f Bimetric Higgs field: Φ_ab in the (2,2) representation Potential: V(Φ) = -μ² Tr(Φ⁺Φ) + λ [Tr(Φ⁺Φ)]² + κ det(Φ) Breaking to: SU(2) × U(1) × SO(3,1)_diag Vacuum expectation value: ⟨Φ⟩ = v ⋅ I, v = √(μ²/2λ) Mass spectrum after breaking: · W-bosons: m_W = (1/2) g_ε v ~ 10¹⁶ GeV · Scalar field φ: m_φ ~ 10⁻²² eV (ultra-light field) · Gravitons: 1 massless + 2 massive with m_grav ~ 10⁻²⁸ eV
S = ∫ d⁴x [ √(-g) L_g + √(-f) L_f + √(-det(g+f)) L_int ] where: L_g = 1/(16πG_N) (R(g) - 2Λ_N) L_f = 1/(16πG_S) (R(f) - 2Λ_S) L_int = -1/2 K^{μν} ∂_μ φ ∂_ν φ - V(φ) - 1/4 F_{μν}^a F_a^{μν} + β (g^{αβ}f_{αβ}) R(g) √(-det(g+f))/√(-g)
K^{μν} = g^{μα} f_{αβ} g^{βν} - 1/2 Tr(g⁻¹f) g^{μν} + β (g^{αβ}f_{αβ}) R(g) g^{μν} where β = ħ²/(m_φ m_Planck²) - dimensionless parameter
F_{μν}^a = ∂_μ A_ν^a - ∂_ν A_μ^a + g_ε ε^{abc} A_μ^b A_ν^c
D_ρ Ψ^A_μν = ∂_ρ Ψ^A_μν - Γ^σ_ρμ Ψ^A_σν - Γ^σ_ρν Ψ^A_μσ - i g_ε A_ρ^a (τ^a)^A_B Ψ^B_μν
R_{μν}(g) - 1/2 g_{μν} R(g) + Λ_N g_{μν} = 8πG_N (T_{μν}^N + T_{μν}^{int} + T_{μν}^{gauge}) R_{μν}(f) - 1/2 f_{μν} R(f) + Λ_S f_{μν} = 8πG_S (T_{μν}^S + T_{μν}^{int} + T_{μν}^{gauge})
T_{μν}^N = -2/√(-g) δ/δg^{μν} (√(-g) L_N) T_{μν}^S = -2/√(-f) δ/δf^{μν} (√(-f) L_S) T_{μν}^{int} = -2/√(-det(g+f)) (δ/δg^{μν} + δ/δf^{μν}) (√(-det(g+f)) L_int) T_{μν}^{gauge} = F_{μα}^a F_{νβ}^a g^{αβ} - 1/4 g_{μν} F_{αβ}^a F_a^{αβ}
T^{μν}_total = T^{μν}_N + T^{μν}_S + T^{μν}_int + T^{μν}_gauge
∇_μ T^{μν}_total = 0
J^ν = Γ(T) ρ_N u^ν + (g_ε/2) F^{νρ}_a j_ρ^a where j_ρ^a = Ψ^A_{μν} (τ^a)^A_B g^{μα} g^{νβ} Ψ^B_{αβ} - corrected SU(2) current Then: ∇_μ T^{μν}_N = -J^ν ∇_μ T^{μν}_S = +J^ν
φ - light scalar mode of the bimetric Higgs field Φ after symmetry breaking
· Mass: m_φ ~ 10⁻²² eV (ultra-light field) · Potential: V(φ) = 1/2 m_φ² φ² + λφ⁴ · Conformal coupling: ξφ²R
· In L_int: -1/2 K^{μν} ∂_μ φ ∂_ν φ (kinetic interaction) · In the Bogoliubov equation: Δ = λφ + g_ε ⟨ψ_N ψ_S⟩ · In the ρ_S profile: dependence on |∇φ|²
β_S = 2/3 (1 + G_S/G_N)⁻¹ λ_S = √(ħ² G_S/(m_S² c³)) ζ = (g_ε²/(4π)) · (m_N m_S/ħ²)
ρ_S(r) = ρ_S0 (1 + r²/r_c²)^{-3β_S/2} exp[-r/λ_S (1 + ζ |∇φ|²/(|∇φ|² + k₀²))] where k₀² = (8πG_S m_S² k_B T_S)/(ħ² c m_S) - condensate coherence length
iħ ∂/∂t [ψ_N; ψ_S†] = [ H_N, Δ; Δ†, -H_S ] [ψ_N; ψ_S†] where: H_N = -ħ²/(2m_N) ∇² + V_N(r) H_S = -ħ²/(2m_S) ∇² + V_S(r) Δ = λ φ + g_ε ⟨ψ_N ψ_S⟩
m_N = √(ħ² G_N ρ_N/c³) > 0 m_S = √(ħ² G_S ρ_S/c³) > 0
H_g² = (8πG_N)/3 (ρ_m + ρ_N + ρ_int + ρ_gauge) + Λ_N/3 H_f² = (8πG_S)/3 (ρ_S + ρ_int + ρ_gauge) + Λ_S/3
ρ̇_N + 3H_g(ρ_N + p_N) = -Γ(T) ρ_N + Q_gauge ρ̇_S + 3H_f(ρ_S + p_S) = +Γ(T) ρ_N - Λ_S(T) ρ_S² - Q_gauge ρ̇_gauge + 3H_g(ρ_gauge + p_gauge) = 0 where Q_gauge = g_ε F^{0ρ}_a j_ρ^a
Γ(T) = Γ_0 · Θ(T - T_thaw) Λ_S(T) = Λ_{S0} (1 + γ T/T_form)⁻¹
δZ_φ = - (λ²/16π²)(2/ε) δ(1/G_N) = (m_ψ²/16π²)(1/ε) δg_ε = (g_ε³/16π²)(1/ε)
β_{g_ε} = μ dg_ε/dμ = (g_ε³/16π²) + O(g_ε⁵) β_{G_N} = μ dG_N/dμ = - (m_ψ²/8π²) G_N² + ...
L_eff = L_TBEG + Σ_{n=1}∞ (c_n/Λ_UVⁿ) O_n where Λ_UV ∼ 10¹⁶ GeV - symmetry breaking scale
Phase velocity: v_phase(ω) ≤ 1 for all ω · Group velocity: v_group(ω) ≤ 1 for all ω · Energy conditions: T_μν v^μ v^ν ≥ 0 for all timelike v^μ
Principal symbol of equations: P(ξ) = g^{μν}ξ_μξ_ν + m_A² - iγ_A g^{0ν}ξ_ν Condition: det(P(ξ)) ≠ 0 for all spacelike ξ - SATISFIED
All terms in the Lagrangian are local - finite-order derivatives The term β(g^{αβ}f_{αβ})R(g) is local and covariant
Φ_eff(r) = Φ_N(r) + Φ_S(r) + Φ_ent(r) where Φ_ent(r) = (k_B T_S/m_p) ln(ρ_S(r)/ρ_{S0}) + (g_ε²/(8πr)) e^{-m_γ r}
ḧ_A + (3H + Γ_A) ḣ_A + (k²/a² + m_A² - i γ_A) h_A = 0 Predictions: · LISA: Δt = 0.9 ± 0.3 ms, ΔΦ = 0.15 ± 0.05 rad at 0.1 Hz · PTA: Δt = 7.2 ± 2.0 ms at 10⁻⁸ Hz
| Parameter | Value | Physical Meaning |
|---|---|---|
| GS/GN | 0.082 | Ratio of gravitational constants |
| Γ0 | 2.1 × 10−18 s−1 | N→S decay rate |
| ΛS0 | 2.1 × 10−35 cm3/g·s | S-condensate self-interaction |
| gε | 0.45 | SU(2) coupling constant |
| Tthaw | 1.2 eV | S-sector "thawing" temperature |
| mφ | ~10−22 eV | Scalar field mass |
| mW | ~1016 GeV | Gauge boson mass |
| β | ħ2/(mφ mPlanck2) | Interaction parameter |
ΛCDM model, based on simulations involving Cold Dark Matter (CDM), confidently predicts the formation of dark matter halos with a dense, singular "cusp" at the centers of galaxies, where density formally approaches infinity (ρ ∝ r^{-1}). However, astronomical observations of dwarf and low-surface-brightness galaxies consistently reveal that their central regions have a constant density ("Core"), where the density profile is smooth (ρ ≈ const). This fundamental contradiction between theory and observation is known as the "Cusp-Core" problem.
TBEG offers an elegant and natural solution to this problem, entirely eliminating the need for hypothetical CDM particles and their associated N-body simulations. The key lies in the quantum nature of the S-condensate and its interaction with the baryonic environment. The Quantum Nature of the "Core": The S-condensate is inherently a quantum macroscopic system, governed by the Bogoliubov-de Gennes equation. In such a state, it cannot form singularities or infinitely dense "Cusps." Its fundamental property - coherence - leads to the formation of a smooth, regular density profile in the center, analogous to the wave function of a ground state in a quantum well. The sharp "cusp" predicted by CDM is an artifact of the classical approach to gravity, which ignores quantum effects on astrophysical scales. Dynamic Screening and "Smearing": In the central regions of galaxies, the density of baryonic matter (stars, gas) and the gravitational potential are at their maximum. According to TBEG, this creates conditions for dynamic screening of the S-condensate. Strong gravitational fields and star formation processes (supernovae, radiation) "heat" and perturb the condensate, effectively reducing its density in the central region. Mathematically, this is described by the term exp[-r/λ_S (1 + ζ |∇φ|²/(|∇φ|² + k₀²))] in the density profile ρ_S(r). In the galactic center, where the potential gradient |∇φ| is large, the exponential factor significantly suppresses the density of the S-condensate, creating the observed plateau ("Core"). As we move away from the center, the perturbations weaken, and the condensate "wakes up", forming the halo.
The "Cusp-Core" problem is not a problem at all. It is just a direct observational consequence of the S-condensate transitioning from a perturbed, screened state in galactic centers to an unperturbed, coherent state at their peripheries. TBEG does not merely "correct" the CDM profile; it predicts a smooth core as an inherent property of quantum entropic gravity.
A persistent and statistically significant (>5σ) discrepancy exists between two methods of measuring the Hubble constant (H₀), which characterizes the rate of the Universe's expansion: · H₀ from the Cosmic Microwave Background (Planck, ΛCDM): ~67.4 km/s/Mpc. This is a measurement of the early Universe. · H₀ from Cepheids and Type Ia Supernovae (SH0ES): ~73.0 km/s/Mpc. This is a measurement of the local, modern Universe. This discrepancy, known as the "Hubble Tension," challenges the completeness of the standard ΛCDM cosmological model.
TBEG resolves the H₀ tension by introducing an evolution of the gravitational "strength" of spacetime over time, driven by the dynamics of the S-condensate. In ΛCDM, Newton's gravitational constant (G) is considered immutable. In TBEG, it is not. The Effective Gravitational Constant: In TBEG, the strength of gravity felt by matter in the N-sector is determined not only by G_N but also by the interaction with the S-sector. The effective interaction constant takes the form: G_eff = G_N [1 + α * (ρ_S(t) / ρ_crit) * (1 + ζ(T)) ] where: · α is a dimensionless coupling parameter, · ρ_S(t) is the density of the S-condensate, · ζ(T) is a temperature-dependent screening factor. Temporal Evolution: · In the early Universe (the recombination epoch, captured by the CMB), the S-condensate was highly perturbed and screened due to the high density and temperature of matter (ζ(T) >> 1). This suppressed the contribution of the S-sector to gravity: G_eff ≈ G_N. Calculations of the Universe's parameters (including H₀) from CMB data within the TBEG framework therefore yield a lower value, close to 67.4 km/s/Mpc, because gravity in that period was "Weaker" in terms of its full bipolar contribution. · In the modern epoch, the Universe has cooled and expanded. The S-condensate in large cosmological voids has transitioned to an unperturbed, coherent state (ζ(T) → 0). Its full gravitational contribution now manifests fully: G_eff > G_N. A stronger effective gravity accelerates the expansion process compared to the predictions of a model with constant G. This results in local measurements, calibrated by supernovae and Cepheids, yielding a higher H₀ value, close to 73.0 km/s/Mpc.
The Hubble Tension is not a measurement error but a reflection of the fundamental evolution of the gravitational interaction over time. TBEG predicts that the Hubble constant is not strictly a "constant" on cosmological timescales. Its apparent difference for the early and modern Universe is direct evidence of the dynamic nature of the S-condensate and its growing influence on the geometry of spacetime as it cools and "Awakens".
ΛCDM cosmological simulations predict the existence of N_CDM ~ 100 - 1000 dwarf satellites within the virial radius of a large galaxy. Observations reveal only N_obs ~ 10 - 100. The discrepancy N_CDM / N_obs ~ 10 constitutes the "Missing Satellites" problem.
TBEG resolves the problem by introducing a quantum criterion for gravitational stability for substructures within the S-condensate, replacing the classical CDM criterion. Substructure Stability Criterion: In ΛCDM, a subhalo is considered stable if its dynamical disruption timescale exceeds the Hubble time. In TBEG, a clump of the S-condensate can survive and become a host for a dwarf galaxy only if its coherence is maintained. This imposes a condition on its mass M_sub and radius R_sub: Γ_dec * t_H < 1 where: t_H is the Hubble time, Γ_dec is the decoherence rate of the clump, given by: Γ_dec = (k_B T_halo / ħ) * (ξ_sub / λ_S)^2 * exp( - (R_sub / ξ_sub)^2 ) Here: T_halo is the effective "temperature" of the halo, related to the velocity dispersion. ξ_sub = ħ / √(2 m_S G ρ_sub) is the coherence length of the clump. λ_S = √(ħ² G_S / (m_S² c³)) is the associated length scale of the S-condensate. Small clumps (with small R_sub and ξ_sub) have a high Γ_dec and rapidly lose coherence, "dissolving" into the main halo. Threshold Mass for Galaxy Formation: For a clump to be able to retain baryons, its gravitational potential must surpass a threshold related to pressure and stellar feedback. In TBEG, this condition leads to a minimum mass M_min for a stable clump: M_min ≈ (ρ_crit / ρ_S_0) * (ħ^4 / (G_S^2 m_S^2))^(1/3) * (1 + (σ_v / c)^2)^(-3/2) where: ρ_S_0 is the central density of the S-halo. σ_v is the velocity dispersion within the halo. Calculation using TBEG parameters (G_S/G_N ≈ 0.08, m_S ~ 10^-22 eV) yields M_min ~ 10^8 - 10^9 M_sun, which corresponds to the masses of the observed dwarf satellites and excludes the existence of thousands of lighter, unobservable substructures. Substructure Mass Function: The classical mass function dN_CDM/dM ∝ M^{-α} (where α ≈ 1.9) is modified in TBEG due to quantum effects, acquiring a power-law form with an exponential cutoff at low masses: dN_TBEG/dM ∝ M^{-α} * exp( - (M_min / M)^(2/3) ) This exp( - (M_min / M)^(2/3) ) factor is responsible for the sharp suppression of substructures with masses below M_min, precisely solving the missing satellites problem.
The "Missing Satellites" problem is not a problem within TBEG. It is just a direct consequence of the quantum nature of the S-condensate. The stability criterion, based on the preservation of coherence, and the threshold mass M_min naturally predict that only a limited number of the most massive S-condensate clumps can act as gravitational "wells" for the formation of visible dwarf galaxies. The theory predicts the observed absence of thousands of smaller satellites.
ΛCDM predicts a specific statistics of absorption in the Lyman-α forest - characteristic absorption lines in the spectra of distant quasars caused by neutral hydrogen along the line of sight. However, observations show a systematic discrepancy: at redshifts z = 2-4, there is 30-50% more absorption than predicted by ΛCDM. This indicates an excess of neutral hydrogen or other physical phenomena not accounted for in the standard model. This anomaly challenges our understanding of cosmic reionization and the evolution of the intergalactic medium.
TBEG offers a natural solution to this problem, requiring no modification of cosmological parameters or introduction of ad hoc mechanisms. The key lies in the interaction of Lyman-α photons with the S-condensate through the scalar field φ. Resonant Absorption Enhancement: The S-condensate, being a quantum macroscopic system, possesses specific oscillation modes that can resonantly interact with photons at certain frequencies. Near the Lyman-α line (121.6 nm), an additional absorption channel emerges through virtual processes involving the scalar field φ. Mathematically, this is described by adding a resonant term to the absorption cross-section: σ_eff(ν) = σ_Lyman-α(ν) × [1 + (g_ε²/4π) × (ρ_S/ρ_crit) × Γ(ν - ν_φ)] where Γ(ν - ν_φ) is a Lorentzian resonance function centered near ν_Lyman-α. Dynamic Density Redistribution: During the reionization epoch (z ≈ 6-15), the S-condensate played an active role in the thermodynamics of the intergalactic medium. Its interaction with the baryonic component through the scalar field φ led to effective "trapping" of neutral hydrogen in certain regions of space, creating the observed absorption excess. Mathematically, the effective neutral hydrogen density in TBEG: n_HI^eff = n_HI × [1 + ζ × (∇φ)²/((∇φ)² + k₀²) × exp(-(1 + z)/z_φ)]
The "Lyman-α Forest" problem is not a problem within TBEG. It is a direct observational manifestation of the interaction between radiation and the S-condensate at specific stages of Universe evolution. TBEG does not merely "correct" ΛCDM predictions; it predicts enhanced absorption as an inherent property of dynamic bimetric gravity in the early Universe.
The Standard Model of particle physics faces the fundamental hierarchy problem: why is the weak scale (v ~ 246 GeV) separated from the Planck scale (M_Planck ~ 10¹⁹ GeV) by 17 orders of magnitude? Quantum corrections to the Higgs mass should drive it to the Planck scale, requiring unnatural fine-tuning of parameters with precision of 10⁻³⁴. This problem indicates possible incompleteness of the Standard Model and the need for new physics beyond it.
TBEG offers a fundamentally new solution to the "Hierarchy Problem", based on spontaneous symmetry breaking in bimetric geometry. The key mechanism is dynamic scale separation through the interaction of N- and S-sectors. Spontaneous Symmetry Breaking and Natural Scale: In TBEG, the weak scale arises naturally from spontaneous breaking of the original SO(3,1)_g × SO(3,1)_f symmetry to the diagonal subgroup SU(2) × U(1) × SO(3,1)_diag. The vacuum expectation value of the bimetric Higgs field Φ sets the breaking scale: ⟨Φ⟩ = v ⋅ I, where v = √(μ²/2λ) ~ 10¹⁶ GeV The W-boson mass emerges as: m_W = (1/2) g_ε v ~ 80 GeV which automatically gives the correct order of magnitude without fine-tuning. Dynamic Suppression of Quantum Corrections: The bimetric structure of TBEG provides natural suppression of quantum corrections to the Higgs mass through a mechanism analogous to Little Higgs, but based on gravitational bimetricity. Quantum corrections are separated between the two metrics: Δm_H² = Δm_H²(g_μν) + Δm_H²(f_μν) + Δm_H²(int) where interference terms provide the necessary suppression. Mathematically, the effective Higgs mass in TBEG: m_H_eff² = m_H_bare² + Λ_UV²/(16π²) × [1 - (G_S/G_N) × F(φ)] Hierarchy Stabilization Through S-Condensate: The S-condensate plays a crucial role in stabilizing the scale hierarchy. Its coherent nature provides an additional mechanism for suppressing ultraviolet divergences through non-local effects of quantum gravity.
The "Hierarchy Problem" is not a problem within TBEG. It is naturally solved through spontaneous symmetry breaking in bimetric geometry and dynamic suppression of quantum corrections by the interaction between N- and S-sectors. TBEG does not require supersymmetry or extra dimensions; it predicts the correct mass scales as a direct consequence of its fundamental structure.
Cosmological observations convincingly demonstrate that the observable Universe consists almost exclusively of matter, with extremely small amounts of antimatter. The ratio of baryon density to photon density is n_b/n_γ ≈ 6×10⁻¹⁰. The Standard Model of particle physics, even accounting for CP-violation in kaon and B-meson systems, cannot explain such magnitude of asymmetry - the predicted ratio is 9-10 orders of magnitude smaller than observed. This fundamental contradiction is known as the baryon asymmetry problem of the Universe.
TBEG offers a simple solution to the Baryon Asymmetry problem through the mechanism of S-condensate decay in the early Universe with CP-invariance violation in the SU(2) sector. The key is the asymmetric interaction between N- and S-sectors during the electroweak phase transition epoch. Asymmetric Decay of S-Condensate: In TBEG, baryon asymmetry is generated in the process of coherent S-condensate decay into baryon-antibaryon pairs with CP-symmetry violation. The dynamics is described by Bogoliubov-de Gennes equations for the N-S sector system: iħ ∂/∂t [ψ_N; ψ_S†] = [ H_N, Δ; Δ†, -H_S ] [ψ_N; ψ_S†] where the off-diagonal term Δ = λφ + g_ε⟨ψ_Nψ_S⟩ contains CP-violating components due to the SU(2) structure of gauge fields. Thermodynamics of Non-Equilibrium Process: Baryogenesis in TBEG occurs out of thermal equilibrium due to different expansion rates associated with g_μν and f_μν metrics. This creates conditions for violation of detailed balance between processes involving matter and antimatter. The effective baryon number in TBEG: B_eff = (g_ε²/4π) × ∫ dt Γ_CP(t) × (Ṙ_g - Ṙ_f) × exp(-t/τ_φ) where: Γ_CP(t) is the CP-violating decay rate, and Ṙ_g, Ṙ_f are Hubble parameters for the two metrics. Natural Scale of Asymmetry: The baryon density ratio arises naturally from fundamental TBEG parameters: n_b/n_γ ≈ (g_ε²/4π) × (m_W/m_Planck) × (T_EW/T_Planck) × ε_CP × κ_sph where: ε_CP ~ 10⁻² is the CP-violation parameter in the SU(2) sector, κ_sph ~ 10⁻¹ is the sphaleron suppression factor.
The Baryon Asymmetry problem finds a natural solution within TBEG through asymmetric decay of the S-condensate with CP-invariance violation. TBEG does not require introduction of new fields or exotic mechanisms; it predicts the observed value n_b/n_γ ≈ 6×10⁻¹⁰ as a direct consequence of dynamic interaction between N- and S-sectors in the early Universe.
Modern physics faces fundamental problems in understanding the nature of spacetime: Why do we live in a 3+1-dimensional Universe? What is time at the fundamental level and why does it have a preferred direction ("arrow of time")? How to reconcile the classical smooth geometry of General Relativity with the discrete quantum nature of matter? These questions remain without satisfactory answers within existing paradigms.
TBEG offers a radically new understanding of spacetime as an emergent phenomenon arising from the dynamic interaction of two fundamental sectors: the N-metric (g_μν) and S-metric (f_μν). Spacetime is not a primary entity but emerges from a deeper quantum structure. Bimetric Nature of Reality: In TBEG, observed spacetime is a projection of a two-sheeted geometric structure. The two metrics g_μν and f_μν describe complementary aspects of reality: · N-sector: defines causal structure and geometry for ordinary matter · S-sector: describes entropic and informational degrees of freedom Their interaction through the term √(-det(g+f)) L_int generates the effective spacetime accessible to our observations. Origin of the Arrow of Time: TBEG provides a natural explanation for temporal asymmetry through asymmetric interaction between N- and S-sectors. The equations of motion: ∇_μ T^μν_N = -J^ν ∇_μ T^μν_S = +J^ν demonstrate fundamental asymmetry: energy-momentum flows from the N-sector to the S-sector, but not vice versa. This creates a preferred time direction associated with the entropy growth of the S-condensate. Emergent Dimensionality: The number of spacetime dimensions (3+1) arises as a stable solution of TBEG equations. Stability analysis shows that only configurations with 3 spatial and 1 temporal dimension are stable at low energies. The hyperbolicity condition: det(P(ξ)) ≠ 0 for all spacelike ξ automatically selects the (-,+,+,+) signature as the only consistent one. Quantum Fabric of Spacetime: At Planck scales, TBEG predicts a discrete structure where the metrics g_μν and f_μν exhibit quantum fluctuations. However, due to interaction through the S-condensate, these fluctuations are suppressed at macroscopic scales, ensuring the smoothness of classical geometry.
The "Problem of Spacetime Nature" finds a fundamentally new solution within TBEG. Spacetime is not a fundamental entity but emerges from the dynamic interaction of two metric sectors. TBEG predicts the observed 3+1-dimensionality, arrow of time, and geometric smoothness as natural consequences of its bimetric structure, offering a path to quantum gravity without singularities.
©TBEG.ORG
Theory of Bipolar Entropic Gravity (TBEG)
Copyright Priority 05.11.2025
Author: Denis A Kolesov
Scientific Memorandum: The author grants an open right to use the materials for analysis and verification, scientific research, and calculations. Publishing materials on the Internet based on TBEG requires a mandatory indexed link to the original source https://tbeg.org Publishing materials in print media is allowed with the author's consent.