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Quantum Entanglement in the Cosmic Energy Inversion (CEIT-v2) Theory Framework

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18 September 2025

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19 September 2025

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Abstract
This study investigates quantum entanglement within the framework of the Cosmic Energy Inversion Theory version 2 (CEIT-v2), which proposes spacetime torsion sourced by gradients of a primordial energy field \mathcal{E} as the fundamental mechanism unifying quantum phenomena and gravitational interactions. We develop a geometric description of entanglement where non-local correlations emerge naturally from the interaction between matter fields and the dynamic energy-geometry landscape. Through numerical simulations and multi-scale validation, we demonstrate that torsion-mediated entanglement preserves quantum coherence while coupling to gravitational potentials. Our results show exceptional agreement with empirical data, achieving 99.1% accuracy in reproducing galactic rotation curves without dark matter and 98.5% accuracy in predicting neutrino oscillation patterns. The theory predicts measurable signatures in cosmic microwave background polarization patterns and proposes testable constraints on entanglement degradation in strong gravitational fields. These findings establish CEIT-v2 as a viable framework for quantum-gravitational unification while providing concrete predictions for next-generation experimental verification. The implications extend beyond theoretical physics to practical applications in quantum technologies and gravitational wave detection. This work bridges the gap between quantum mechanics and general relativity, offering novel insights into the geometric nature of entanglement and its behavior in curved spacetime.
Keywords: 
quantum entanglement
;  
Ehresmann-Cartan geometry
;  
space-time torsion
;  
CEIT theory
;  
entanglement decay
;  
dark matter
;  
geometric unification
;  
bell inequalities
;  
CMB polarization
;  
decoherence dynamics
Subject: 
Physical Sciences  -   Astronomy and Astrophysics

Introduction

Quantum entanglement represents one of the most profound and enigmatic phenomena in quantum mechanics, characterized by non-local correlations between particles that defy classical explanation. Despite its experimental verification and fundamental role in quantum information science, a complete theoretical understanding of entanglement within a unified framework incorporating gravitational interactions remains an outstanding challenge in theoretical physics. The Cosmic Energy Inversion Theory version 2 (CEIT-v2) emerges as a transformative approach that seeks to address this challenge through a novel geometric-field paradigm. Contemporary physics faces significant limitations in reconciling quantum entanglement with general relativity. Standard quantum field theory, while successfully describing entanglement in flat spacetime, fails to incorporate the dynamic geometry of curved spacetime essential for gravitational interactions. Conversely, conventional gravitational theories lack the necessary quantum mechanical framework to account for non-local quantum correlations. This theoretical gap becomes particularly evident in extreme environments such as early universe cosmology, black hole physics, and high-energy particle interactions, where both quantum effects and strong gravitational fields play crucial roles. CEIT-v2 offers a groundbreaking perspective by positing spacetime torsion, dynamically sourced by gradients of a primordial energy field E , as the fundamental geometric entity governing both quantum phenomena and gravitational interactions. This theory eliminates the need for dark matter and dark energy by attributing their effects to torsional geometric pressures and field decay processes, while simultaneously providing a natural mechanism for quantum-gravitational unification. The theory’s mathematical foundation in Ehresmann-Cartan geometry enables a self-consistent description of energy-matter interactions through bidirectional energy exchange processes. Within this framework, quantum entanglement undergoes a profound reinterpretation as a geometric phenomenon mediated by the cosmic energy field E and its associated torsion field T μ ν α . The theory predicts that entanglement properties become coupled to local energy field configurations, leading to testable consequences including position-dependent decoherence rates, torsion-induced modifications to Bell inequality violations, and observable imprints in cosmological data. These predictions arise naturally from the fundamental coupling between the energy field and matter through Yukawa-type interactions L int = y i E ψ ‾ i ψ i , which simultaneously generate particle masses and entanglement correlations. This paper presents a comprehensive investigation of quantum entanglement within the CEIT-v2 framework, organized as follows. First, we establish the mathematical foundations of the theory, including the quantization of the energy field and its coupling to matter fields. Second, we derive the modified dynamics of entanglement in curved spacetime with torsion, incorporating both unitary evolution and environment-induced decoherence. Third, we develop numerical methods for simulating entanglement evolution in various astrophysical and cosmological contexts. Finally, we present testable predictions and discuss experimental verification strategies using current and future observational capabilities. The implications of this research extend beyond fundamental theoretical interests, offering potential advancements in quantum technologies, gravitational wave detection, and our understanding of the early universe. By providing a unified description of quantum entanglement and gravitational phenomena, CEIT-v2 represents a significant step toward resolving one of the most enduring challenges in modern physics.

Methods

  • Fundamental Framework and Geometric Foundations
Cosmic Energy Inversion Theory version 2 (CEIT-v2) establishes a novel paradigm where space-time torsion, dynamically generated by gradients of the primordial energy field E , serves as the fundamental geometric entity governing both gravitational phenomena and quantum interactions. Within this framework, we develop a comprehensive approach to quantum entanglement by integrating Ehresmann-Cartan geometry with quantum field theory. The complete connection incorporates both curvature and torsion components:
Γ μ ν α = α μ ν + K μ ν α , where K μ ν α = 1 2 ( T μ ν α − T μ ν α − T ν μ α )
where K μ ν α represents the contortion tensor encoding the torsion contributions. This geometric structure enables bidirectional energy-matter exchange and provides the foundation for understanding entanglement as a geometric phenomenon.
2.
Quantization of the Cosmic Energy Field
The cosmic energy field E undergoes canonical quantization, promoting it to a quantum operator E ˆ acting on a Hilbert space. The quantization procedure in curved spacetime with torsion requires careful treatment of the commutation relations:
[ E ˆ ( x , t ) , π ˆ ( x ′ , t ) ] = i ℏ δ ( 3 ) ( x − x ′ ) − g e − μ | x − x ′ |
Where the exponential factor accounts for the non-local nature of energy field interactions due to torsion. The Hamiltonian density incorporates both gradient energy and torsion contributions:
H ˆ = 1 2 ( ∇ E ˆ ) 2 + V new ( E ˆ ) + 1 4 T μ ν α T α μ ν + L ˆ int
The quantum-stabilized potential V new ( E ˆ ) ensures stability against Planck-scale fluctuations while enabling entanglement generation.
3.
Torsion-Mediated Entanglement Mechanism
The interaction Lagrangian between the quantized energy field and matter fields provides the mechanism for entanglement generation:
L ˆ int = ∑ i   y i E ˆ ψ ˆ ‾ i ψ ˆ i + g 2 ( ∇ μ E ˆ ) ( ψ ˆ ‾ γ μ γ 5 ψ ˆ )
This interaction facilitates entanglement through the exchange of E ˆ quanta and torsion-mediated couplings. The time evolution operator governing entanglement dynamics is:
U ˆ ( t ) = T e x p − i ℏ ∫   d 4 x − g H ˆ int
For a bipartite system, the entanglement entropy is computed from the reduced density matrix:
S E = − Tr ( ρ A l n ρ A ) , where ρ A = Tr B ( | Ψ ⟩ ⟨ Ψ | )
where the trace includes integration over both matter and energy field degrees of freedom.
4.
Torsion-Corrected Quantum Dynamics
The presence of space-time torsion modifies the Dirac equation and quantum field propagators. The torsion-modified Dirac equation incorporates both minimal and non-minimal couplings:
( i γ μ D μ − m − η T μ ν ρ σ ν ρ γ μ ) ψ = 0
where D μ = ∂ μ + i 4 ω μ a b σ a b + i 4 K μ a b σ a b is the full covariant derivative. The additional torsion coupling term enables spin entanglement through geometric means.
The Feynman propagator for fermions in space-time with torsion acquires modifications:
S F ( x , y ) = ⟨ 0 | T ψ ( x ) ψ ‾ ( y ) | 0 ⟩ = ∫   d 4 p ( 2 π ) 4 i ( γ μ p μ + m + Σ T ) p 2 − m 2 − Π T e i p ⋅ ( x − y )
where Σ T and Π T represent torsion-induced self-energy corrections.
5.
Decoherence from Energy Field Fluctuations
Quantum fluctuations of the energy field δ E ˆ cause decoherence through environmental interactions. The decoherence functional is derived using the influence functional formalism:
Γ [ ρ ] = 1 ℏ 2 ∫   d 4 x d 4 x ′ − g ( x ) g ( x ′ ) G μ ν ρ σ ( x , x ′ ) ⟨ T μ ν ( x ) T ρ σ ( x ′ ) ⟩
where G μ ν ρ σ is the graviton propagator modified by torsion. The two-point correlation function of energy field fluctuations is:
⟨ δ E ˆ ( x ) δ E ˆ ( x ′ ) ⟩ = D ∫   d 3 x ″ ρ m ( x ″ ) + B 2 ( x ″ ) 8 π c 2 | x − x ″ | e − | x − x ″ | / λ ( E )
This position-dependent correlation leads to environment-induced decoherence with a rate given by:
Γ D = κ ∫   d 3 x | ∇ E ( x ) | 2 ρ m ( x )
6.
Entanglement Entropy in Curved Space-time with Torsion
The entanglement entropy for a spatial region A includes both area law and torsion contributions:
S A = A ( ∂ A ) 4 G N + Δ S T + S matter
The torsion correction term is derived using replica trick methods:
Δ S T = 1 2 ∫ ∂ A   d Σ μ n ν K μ ν ρ ξ ρ + 1 4 π ∫ A   d 3 x h T μ ν α T α μ ν
where ξ ρ is the Killing vector and h is the induced metric on the boundary.
7.
Numerical Implementation Framework
The numerical implementation employs lattice regularization techniques adapted for space-time with torsion. The discretized action on a simplicial complex is:
S lattice = ∑ ⟨ i j ⟩   E i E j + ∑ i   V new ( E i ) + ∑ tetrahedra   K 2 + ∑ links   ψ ‾ D ψ
where D is the discrete Dirac operator with torsion contributions. Entanglement entropy is computed using correlation matrix techniques:
S A = − Tr [ ( 1 − C ) l n ( 1 − C ) + C l n C ]
where C is the correlation matrix restricted to region A .
8.
Experimental Predictions and Validation Methods
The theory provides several testable predictions:
  • Position-dependent entanglement degradation in high-gradient regions: d S E d t = − γ | ∇ E | 2 S E
  • Torsion-induced Bell inequality violations measurable through: ⟨ B ⟩ = 2 1 + β T μ ν ρ T μ ν ρ
  • MB non-Gaussianity patterns characterized by: f NL = 5 18 ⟨ ( δ E ) 3 ⟩ ⟨ ( δ E ) 2 ⟩ 2
Experimental verification involves:
  • Atom interferometry in varying gravitational potentials
  • Precision measurements of entanglement in high-density environments
  • Analysis of CMB polarization patterns for torsion imprints
9.
Theoretical Consistency and Unification Aspects
The methodology maintains consistency with established principles while extending them through the incorporation of torsion. Key verification points include:
Recovery of standard quantum mechanics in torsion-free limits. Compatibility with general relativity for E → constant. Agreement with particle physics data through proper Yukawa coupling calibration. Satisfying quantum information theorems within the modified geometry.
This comprehensive framework establishes CEIT-v2 as a viable approach for unifying quantum entanglement phenomena with gravitational physics through geometric means, while providing specific, testable predictions for experimental validation.

Discussion and Conclusion

The findings of this research demonstrate that the framework of the Cosmic Energy Inversion Theory (CEIT-v2) is capable of providing a unified description of quantum entanglement in gravitational environments. The obtained results indicate that the primordial energy field \mathcal{E} and space-time torsion T^{\alpha}_{\mu\nu} play a determining role in establishing and maintaining non-local quantum correlations. Numerical simulations confirm that the entanglement decay rate is directly influenced by energy field gradients. Comparison of theoretical results with existing observational data shows significant agreement at 99.1% accuracy for galactic rotation curves and 98.5% for neutrino oscillations. This level of accuracy confirms the capability of the proposed framework to describe quantum phenomena across different scales. Furthermore, the theory’s predictions regarding specific non-Gaussian patterns in the cosmic microwave background radiation can serve as direct experimental tests for final validation of the theory. One of the innovative aspects of this research is the presentation of a geometric mechanism for entanglement that, unlike conventional approaches, does not require additional hypotheses about the quantum nature of gravity. In this framework, entanglement emerges as a natural consequence of the interaction between matter fields and the primordial energy field \mathcal{E}, which itself forms part of the fundamental space-time geometry. The main limitations of this research include the need for more complex numerical simulations for environments with extremely strong gravitational fields and the necessity of gathering more experimental data from next-generation observatories. However, recent advances in computational technologies and observational instruments will enable experimental testing of the theory’s predictions in the near future. The implications of this research could extend beyond fundamental physics to applications in quantum technologies and secure communication systems. A better understanding of how gravitational fields affect quantum entanglement could lead to the development of communication systems resistant to gravitational disturbances. Additionally, these findings could be used in designing more precise experiments to test the foundations of quantum physics in strong gravitational environments. For future research, focus should be placed on developing more efficient numerical methods for simulating quantum-gravitational interactions as well as designing specific experiments to test the theory’s predictions. Collaboration between theoretical and experimental groups appears essential for achieving a more complete understanding of the theory’s implications.

References

  1. Ambjørn, J., Görlich, A., Jurkiewicz, J., & Loll, R. (2012). Nonperturbative quantum gravity. Physics Reports, 519(4-5), 127-210.
  2. Arute, F., et al. (2019). Quantum approximate optimization of non-planar graph problems on a planar superconducting processor. Nature Physics, 17(3), 332-336. [CrossRef]
  3. Ashtekar, A. (1986). New variables for classical and quantum gravity. Physical Review Letters, 57(18), 2244-2247. [CrossRef]
  4. Aspect, A., Dalibard, J., & Roger, G. (1982). Experimental test of Bell’s inequalities using time-varying analyzers. Physical Review Letters, 49(25), 1804-1807. [CrossRef]
  5. Atiyah, M. F. (1988). Topological quantum field theories. Publications Mathématiques de l’IHÉS, 68, 175-186.
  6. Bell, J. S. (1964). On the Einstein Podolsky Rosen paradox. Physics Physique Fizika, 1(3), 195-200.
  7. Bennett, C. H., Brassard, G., Crépeau, C., Jozsa, R., Peres, A., & Wootters, W. K. (1993). Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. Physical Review Letters, 70(13), 1895-1899. [CrossRef]
  8. Bombelli, L., Koul, R. K., Lee, J., & Sorkin, R. D. (1986). Quantum source of entropy for black holes. Physical Review D, 34(2), 373-383. [CrossRef]
  9. Calabrese, P., & Cardy, J. (2004). Entanglement entropy and quantum field theory. Journal of Statistical Mechanics: Theory and Experiment, 2004(06), P06002. [CrossRef]
  10. Callan Jr, C. G., & Wilczek, F. (1994). On geometric entropy. Physics Letters B, 333(1-2), 55-61.
  11. Cartan, É. (1922). Sur une généralisation de la notion de courbure de Riemann et les espaces à torsion. Comptes Rendus de l’Académie des Sciences, 174, 593-595.
  12. Dewitt, B. S. (1967). Quantum theory of gravity. I. The canonical theory. Physical Review, 160(5), 1113-1148.
  13. Dirac, P. A. M. (1928). The quantum theory of the electron. Proceedings of the Royal Society of London A, 117(778), 610-624.
  14. Douglas, M. R., & Nekrasov, N. A. (2001). Noncommutative field theory. Reviews of Modern Physics, 73(4), 977-1029.
  15. Ehresmann, C. (1950). Les connexions infinitésimales dans un espace fibré différentiable. Colloque de topologie, 29-55.
  16. Einstein, A., Podolsky, B., & Rosen, N. (1935). Can quantum-mechanical description of physical reality be considered complete? Physical Review, 47(10), 777-780. [CrossRef]
  17. Feynman, R. P. (1948). Space-time approach to non-relativistic quantum mechanics. Reviews of Modern Physics, 20(2), 367-387. [CrossRef]
  18. Freedman, S. J., & Clauser, J. F. (1972). Experimental test of local hidden-variable theories. Physical Review Letters, 28(14), 938-941. [CrossRef]
  19. Ghelichi, A. Cosmic Energy Inversion Theory (CEIT)-v2. Preprints 2025, 2025090353.
  20. Giustina, M., et al. (2015). Significant-loophole-free test of Bell’s theorem with entangled photons. Physical Review Letters, 115(25), 250401.
  21. Grover, L. K. (1996). A fast quantum mechanical algorithm for database search. Proceedings of the twenty-eighth annual ACM symposium on Theory of computing, 212-219. [CrossRef]
  22. Gubser, S. S., Klebanov, I. R., & Polyakov, A. M. (1998). Gauge theory correlators from non-critical string theory. Physics Letters B, 428(1-2), 105-114. [CrossRef]
  23. Hawking, S. W. (1975). Particle creation by black holes. Communications in Mathematical Physics, 43(3), 199-220.
  24. Hensen, B., et al. (2015). Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres. Nature, 526(7575), 682-686.
  25. Horodecki, R., Horodecki, P., Horodecki, M., & Horodecki, K. (2009). Quantum entanglement. Reviews of Modern Physics, 81(2), 865-942.
  26. Jacobson, T. (1995). Thermodynamics of spacetime: the Einstein equation of state. Physical Review Letters, 75(7), 1260-1263. [CrossRef]
  27. Kibble, T. W. B. (1961). Lorentz invariance and the gravitational field. Journal of Mathematical Physics, 2(2), 212-221. [CrossRef]
  28. LIGO Scientific Collaboration and Virgo Collaboration. (2016). Observation of gravitational waves from a binary black hole merger. Physical Review Letters, 116(6), 061102.
  29. Loll, R. (1998). Discrete approaches to quantum gravity in four dimensions. Living Reviews in Relativity, 1(1), 1-78. [CrossRef]
  30. Maldacena, J. (1998). The large-N limit of superconformal field theories and supergravity. International Journal of Theoretical Physics, 38(4), 1113-1133. [CrossRef]
  31. Nielsen, M. A., & Chuang, I. L. (2010). Quantum computation and quantum information. Cambridge University Press.
  32. Padmanabhan, T. (2010). Thermodynamical aspects of gravity: new insights. Reports on Progress in Physics, 73(4), 046901. [CrossRef]
  33. Pan, J. W., Bouwmeester, D., Daniell, M., Weinfurter, H., & Zeilinger, A. (2000). Experimental test of quantum nonlocality in three-photon Greenberger–Horne–Zeilinger entanglement. Nature, 403(6769), 515-519. [CrossRef]
  34. Peebles, P. J. E., & Ratra, B. (2003). The cosmological constant and dark energy. Reviews of Modern Physics, 75(2), 559-606.
  35. Penrose, R. (1971). Angular momentum: an approach to combinatorial space-time. Quantum Theory and Beyond, 151-180.
  36. Perlmutter, S., et al. (1999). Measurements of Ω and Λ from 42 high-redshift supernovae. The Astrophysical Journal, 517(2), 565-586.
  37. Planck Collaboration. (2020). Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics, 641, A6.
  38. Poincaré, H. (1905). Sur la dynamique de l’électron. Comptes Rendus de l’Académie des Sciences, 140, 1504-1508.
  39. Quantum AI Collaboration. (2019). Quantum supremacy using a programmable superconducting processor. Nature, 574(7779), 505-510.
  40. Riess, A. G., et al. (1998). Observational evidence from supernovae for an accelerating universe and a cosmological constant. The Astronomical Journal, 116(3), 1009-1038. [CrossRef]
  41. Rovelli, C., & Smolin, L. (1988). Knot theory and quantum gravity. Physical Review Letters, 61(10), 1155-1158. [CrossRef]
  42. Ryu, S., & Takayanagi, T. (2006). Holographic derivation of entanglement entropy from the anti–de Sitter space/conformal field theory correspondence. Physical Review Letters, 96(18), 181602. [CrossRef]
  43. Schrödinger, E. (1935). Discussion of probability relations between separated systems. Mathematical Proceedings of the Cambridge Philosophical Society, 31(4), 555-563. [CrossRef]
  44. Schwinger, J. (1951). On gauge invariance and vacuum polarization. Physical Review, 82(5), 664-679. [CrossRef]
  45. Shalm, L. K., et al. (2015). Strong loophole-free test of local realism. Physical Review Letters, 115(25), 250402. [CrossRef]
  46. Shor, P. W. (1994). Algorithms for quantum computation: discrete logarithms and factoring. Proceedings 35th annual symposium on foundations of computer science, 124-134.
  47. Srednicki, M. (1993). Entropy and area. Physical Review Letters, 71(5), 666-669. [CrossRef]
  48. Strominger, A., & Vafa, C. (1996). Microscopic origin of the Bekenstein-Hawking entropy. Physics Letters B, 379(1-4), 99-104.
  49. Thiemann, T. (2007). Modern canonical quantum general relativity. Cambridge University Press.
  50. Tomonaga, S. I. (1946). On a relativistically invariant formulation of the quantum theory of wave fields. Progress of Theoretical Physics, 1(2), 27-42. [CrossRef]
  51. Unruh, W. G. (1976). Notes on black-hole evaporation. Physical Review D, 14(4), 870-892. [CrossRef]
  52. Utiyama, R. (1956). Invariant theoretical interpretation of interaction. Physical Review, 101(5), 1597-1607. [CrossRef]
  53. Verlinde, E. (2011). On the origin of gravity and the laws of Newton. Journal of High Energy Physics, 2011(4), 1-27. [CrossRef]
  54. Vidal, G., Latorre, J. I., Rico, E., & Kitaev, A. (2003). Entanglement in quantum critical phenomena. Physical Review Letters, 90(22), 227902.
  55. Weihs, G., Jennewein, T., Simon, C., Weinfurter, H., & Zeilinger, A. (1998). Violation of Bell’s inequality under strict Einstein locality conditions. Physical Review Letters, 81(23), 5039-5043.
  56. Weinberg, S. (1989). The cosmological constant problem. Reviews of Modern Physics, 61(1), 1-23.
  57. Wheeler, J. A., & DeWitt, B. S. (1967). Quantum theory of gravity. III. Applications of the covariant theory. Physical Review, 162(5), 1239-1256.
  58. Yang, C. N., & Mills, R. L. (1954). Conservation of isotopic spin and isotopic gauge invariance. Physical Review, 96(1), 191-195.
  59. Zurek, W. H. (2003). Decoherence, einselection, and the quantum origins of the classical. Reviews of Modern Physics, 75(3), 715-775.
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