Physics: On the Theory of Entropicity (ToE) and Google’s Quantum Core Breakthrough Experiment on the Observer Effect: The Theory of Entropicity (ToE) Offers Insights and Inroads on the Quantum Measurement Problem

Physics: On the Theory of Entropicity (ToE) and Google’s Quantum Core Breakthrough Experiment on the Observer Effect

The Theory of Entropicity (ToE) Offers Insights and Inroads on the Quantum Measurement Problem

by John Onimisi Obidi

In the Theory of Entropicity (ToE), first formulated and further developed by John Onimisi Obidi,[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35] [36][37][38][39][40][41][42][43][44][45][46][47][48] [49] [50] [51] [52] [53] [54] [55] [56] [57] [58] [59] [60] [61] [62] [63] [64] [65] [66] [67] [68] [69] [70] [71] [72] [73] [74] [75] [76] [77] [78] [79] [80] [81] [82] [83] [84] [85] [86] [87] [88] [89] [90] [91][92] [93] [94] [95] [96] the observer is embedded within the entropy field [as already hinted at by recent observations from Google’s Quantum Core Breakthrough Experiment on the Observer Effect]. The observer becomes an active par-ticipant in the orchestra, symphony and drama of existence in the participatory Universe[See Expository Note Below]. Collapse occurs when entropy exchange exceeds the observability threshold, governed by Obidi’s Criterion of Entropic Observability.

Expository Note: It was John Archibald Wheeler who introduced the concept of the ”participatory universe,” in which he argued that observers (or participants) are not merely passive recorders of events but actively contribute to bringing the universe into being. This notion is a key part of his participatory anthropic principle and is also linked to his famous phrase ”it from bit,” which emphasizes that information — fundamentally shaped by observation — is at the core of physical reality. But as Obidi has already explained in his Centennial Paper on Einstein and Bohr Reconciled, among other works, it is entropy that shapes information, and it is entropy that is at the core of physical reality. Thus, for ToE, it is no longer ”it from bit,” but ”bit from it.”

The Vuli–Ndlela Integral’s weighting by “classical action + entropies” has profound consequences: it imposes strict constraints on allowable quantum trajectories, replacing the unconstrained superposition of paths with an entropy-constrained existential selection principle. Interference between paths that would lead to wildly different entropy outcomes is suppressed, effectively limiting the superposition principle to those branches that respect the second law of thermodynamics. To illustrate, imagine a quantum system with two possible evolutions: Path A leads to a very low-entropy final state, Path B leads to a higher-entropy final state (perhaps because Path B entangles the system with many environmental degrees of freedom). In standard quantum theory, if both paths are dynamically allowed, they would in principle interfere.

In ToE, however, the entropy weighting in GVNI (Generalized Vuli-Ndlela Integral) biases the probability amplitude in favor of the higher entropy Path B, consistent with an “entropic arrow of time” dictated by the Vuli-Ndlela Integral Bound. If Path A’s entropy output is too low (violating entropic expectations), its contribution to ZGVNI may be exponentially damped. Thus, even at the level of virtual quantum amplitudes, entropy enforces an arrow: quantum histories that do not produce sufficient entropy are edged out by those that do. This concept is closely related to the idea of “einselection” (environment-induced superselection) in decoherence theory, wherein environmental entanglement causes certain preferred states (usually those that minimize entropy production or information leakage) to emerge. However, ToE differs by positing an intrinsic entropy field guiding this selection, rather than merely a phenomenological environment tracing-out. A concrete key equation arising in ToE is the definition of a local entropy potential associated with the quantum state. Given any wavefunction ψ(x, t) (for simplicity, non-relativistic), ToE defines an entropy density functional s(x, t) and a corresponding potential Λ(x, t).

One formulation is as follows: First, we recollect that the probability density in formal literature is given by: ρ(x, t) = |ψ(x, t)|² The entropy density functional is then given by the Shannon-like formula as earlier shown by John Obidi in Einstein and Bohr Reconciled[April 2025]: s(x, t) = −kB ρ(x, t) ln[ρ(x, t)] , where kB is Boltzmann’s constant. The corresponding entropic potential is thus defined as the functional derivative of s(x, t) with respect to ρ(x, t) [also shown by John Obidi in Einstein and Bohr Reconciled[April 2025]: Λ(x, t) = δs/δρ(x, t) = − kB[ln(ρ(x, t)) + 1] Remembering our earlier expression for the probability density, we can therefore write the above expression for the entropic potential in the general form: Λ(x, t) = − kBln|(ψ(x, t)|² + C] , where, as usual, |ψ(x, t)|² is the probability density and C is a constant offset. This Λ(x, t) is essentially a Shannon entropy per unit volume (up to constants), since −kB ln |ψ| 2 would be the contribution to information entropy at point x and time t.

References

1. Obidi, J.O. Theory of Entropicity(ToE) On Geometry and Space-Time Curvature. Encyclopedia. Available online: https://encyclopedia.pub/entry/59142 (accessed on 15 October 2025)
2. The Theory of Entropicity (ToE) On the Geometry of Existence and the Curvature of Space-Time: A Brief Overview of the Conceptual and Mathematical Evolution of the Theory of Entropicity (ToE) https://open.substack.com/pub/johnobidi/p/the-theory-of-entropicity-toe-on-fe2?r=1yk33z&utm_campaign=post&utm_medium=web&showWelcomeOnShare=false
3. The Theory of Entropicity (ToE) On the Geometry of Existence and the Curvature of Space-Time: A Brief Overview of the Conceptual and Mathematical Evolution of the Theory of Entropicity (ToE) https://medium.com/@jonimisiobidi/the-theory-of-entropicity-toe-on-the-geometry-of-existence-and-the-curvature-of-space-time-cff8e2e7f7c8
4. On the Conceptual and Mathematical Foundations of the Theory of Entropicity (ToE): An Alternative Path toward Quantum Gravity and the Unification of Physics https://open.substack.com/pub/johnobidi/p/on-the-conceptual-and-mathematical-9df?utm_source=share&utm_medium=android&r=1yk33z
5. On the Conceptual and Mathematical Foundations of the Theory of Entropicity (ToE): An Alternative Path toward Quantum Gravity and the Unification of Physics https://johnobidi.substack.com/p/on-the-conceptual-and-mathematical-9df
6. On the Conceptual and Mathematical Foundations of the Theory of Entropicity (ToE): An Alternative Path toward Quantum Gravity and the Unification of Physics https://medium.com/@jonimisiobidi/on-the-conceptual-and-mathematical-foundations-of-the-theory-of-entropicity-toe-an-alternative-20030186d0eb
7. “The Discovery of the Entropic α-Connection: How the Theory of Entropicity (ToE) Transformed…“ by John Onimisi Obidi on Medium: https://medium.com/@jonimisiobidi/the-discovery-of-the-entropic-%CE%B1-connection-how-the-theory-of-entropicity-toe-transformed-6e4e524dead7
8. Obidi, J.O. Evolutionary Introduction to the Theory of Entropicity(ToE). Encyclopedia. Available online: https://encyclopedia.pub/entry/59129 (accessed on 13 October 2025)
9. An Introduction to the Theory of Entropicity (ToE): On the Evolution of its Conceptual and Mathematical Foundations (Part I) https://open.substack.com/pub/johnobidi/p/an-introduction-to-the-theory-of?utm_source=share&utm_medium=android&r=1yk33z
10. “An Introduction to the Theory of Entropicity (ToE):“ by John Onimisi Obidi on Medium: https://medium.com/@jonimisiobidi/an-introduction-to-the-theory-of-entropicity-toe-9041c28a6d3a
11. Obidi, J.O. On David Sigtermans and Obidi’s Theory of Entropicity(ToE). Encyclopedia. Available online: https://encyclopedia.pub/entry/59128 (accessed on 13 October 2025)
12. Obidi, John Onimisi (2025). On the Conceptual and Mathematical Foundations of the Theory of Entropicity (ToE): An Alternative Path toward Quantum Gravity and the Unification of Physics. https://doi.org/10.6084/m9.figshare.30337396.v1
13. Obidi, J.O. Conceptual and Mathematical Foundations of Theory of Entropicity(ToE). Encyclopedia. Available online: https://encyclopedia.pub/entry/59127 (accessed on 13 October 2025)
14. “Sean Collins and the Mjolnir (A137) Lattice Dynamics: A Brief Introductory Note on Its Importance…“ by John Onimisi Obidi on Medium: https://medium.com/@jonimisiobidi/sean-collins-and-the-mjolnir-a137-lattice-dynamics-a-brief-introductory-note-on-its-importance-246b6749a2ac
15. Physics:Einstein’s Relativity from Obidi’s Theory of Entropicity(ToE). (2025, August 30). HandWiki, . Retrieved 12:19, August 30, 2025 from https://handwiki.org/wiki/index.php?title=Physics:Einstein%27s_Relativity_from_Obidi%27s_Theory_of_Entropicity(ToE)&oldid=3742784
16. Physics:Time Dilation, Length Contraction in the Theory of Entropicity (ToE). (2025, August 30). HandWiki, . Retrieved 10:01, August 30, 2025 from https://handwiki.org/wiki/index.php?title=Physics:Time_Dilation,_Length_Contraction_in_the_Theory_of_Entropicity_(ToE)&oldid=3742771
17. Physics:Insights from the No-Rush Theorem in the Theory of Entropicity(ToE). (2025, August 1). HandWiki, . Retrieved 09:43, August 30, 2025 from https://handwiki.org/wiki/index.php?title=Physics:Insights_from_the_No-Rush_Theorem_in_the_Theory_of_Entropicity(ToE)&oldid=3741840
18. Physics:The Cumulative Delay Principle(CDP) of the Theory of Entropicity(ToE). (2025, August 11). HandWiki, . Retrieved 09:40, August 30, 2025 from https://handwiki.org/wiki/index.php?title=Physics:The_Cumulative_Delay_Principle(CDP)_of_the_Theory_of_Entropicity(ToE)&oldid=3742101
19. Physics:Theory of Entropicity(ToE), Time Quantization and the Laws of Nature. (2025, August 1). HandWiki, . Retrieved 09:34, August 30, 2025 from https://handwiki.org/wiki/index.php?title=Physics:Theory_of_Entropicity(ToE),_Time_Quantization_and_the_Laws_of_Nature&oldid=3741802
20. Book:Conceptual and Mathematical Treatise on Theory of Entropicity(ToE). (2025, August 30). HandWiki, . Retrieved 09:31, August 30, 2025 from https://handwiki.org/wiki/index.php?title=Book:Conceptual_and_Mathematical_Treatise_on_Theory_of_Entropicity(ToE)&oldid=3742769
21. Physics:Gravity from Newton and Einstein in the Theory of Entropicity(ToE). (2025, August 7). HandWiki, . Retrieved 09:19, August 30, 2025 from https://handwiki.org/wiki/index.php?title=Physics:Gravity_from_Newton_and_Einstein_in_the_Theory_of_Entropicity(ToE)&oldid=3742006
22. Physics:Randomness and Determinism Unified in the Theory of Entropicity(ToE). (2025, August 13). HandWiki, . Retrieved 09:17, August 30, 2025 from https://handwiki.org/wiki/index.php?title=Physics:Randomness_and_Determinism_Unified_in_the_Theory_of_Entropicity(ToE)&oldid=3742233
23. Physics:Relativity from Fundamental Postulate of Theory of Entropicity(ToE). (2025, August 30). HandWiki, . Retrieved 09:13, August 30, 2025 from https://handwiki.org/wiki/index.php?title=Physics:Relativity_from_Fundamental_Postulate_of_Theory_of_Entropicity(ToE)&oldid=3742766
24. Physics:Artificial Intelligence Formulated by the Theory of Entropicity(ToE). (2025, August 27). HandWiki, . Retrieved 03:59, August 27, 2025 from https://handwiki.org/wiki/index.php?title=Physics:Artificial_Intelligence_Formulated_by_the_Theory_of_Entropicity(ToE)&oldid=3742591
25. Physics:Curved Spacetime Derived from Obidi’s Theory of Entropicity(ToE). (2025, August 29). HandWiki, . Retrieved 09:01, August 30, 2025 from https://handwiki.org/wiki/index.php?title=Physics:Curved_Spacetime_Derived_from_Obidi%27s_Theory_of_Entropicity(ToE)&oldid=3742730
26. Physics:Information and Energy Redistribution in Theory of Entropicity(ToE). (2025, August 30). HandWiki, . Retrieved 09:05, August 30, 2025 from https://handwiki.org/wiki/index.php?title=Physics:Information_and_Energy_Redistribution_in_Theory_of_Entropicity(ToE)&oldid=3742765
27. Obidi, John Onimisi (2025). Master Equation of the Theory of Entropicity (ToE). Encyclopedia. https://encyclopedia.pub/entry/58596
28. Obidi, John Onimisi. Corrections to the Classical Shapiro Time Delay in General Relativity (GR) from the Entropic Force-Field Hypothesis (EFFH). Cambridge University. (11 March 2025). https://doi.org/10.33774/coe-2025-v7m6c
29. Obidi, John Onimisi. How the Generalized Entropic Expansion Equation (GEEE) Describes the Deceleration and Acceleration of the Universe in the Absence of Dark Energy. Cambridge University. (12 March 2025). https://doi.org/10.33774/coe-2025-6d843
30. Obidi, John Onimisi. The Theory of Entropicity (ToE): An Entropy-Driven Derivation of Mercury’s Perihelion Precession Beyond Einstein’s Curved Spacetime in General Relativity (GR). Cambridge University. (16 March 2025). https://doi.org/10.33774/coe-2025-g55m9
31. Obidi, John Onimisi. The Theory of Entropicity (ToE) Validates Einstein’s General Relativity (GR) Prediction for Solar Starlight Deflection via an Entropic Coupling Constant η. Cambridge University. (23 March 2025). https://doi.org/10.33774/coe-2025-1cs81
32. Obidi, John Onimisi (25 March 2025). “Attosecond Constraints on Quantum Entanglement Formation as Empirical Evidence for the Theory of Entropicity (ToE)”. Cambridge University. https://doi.org/10.33774/coe-2025-30swc
33. Obidi, John Onimisi. Einstein and Bohr Finally Reconciled on Quantum Theory: The Theory of Entropicity (ToE) as the Unifying Resolution to the Problem of Quantum Measurement and Wave Function Collapse. Cambridge University. (14 April 2025). https://doi.org/10.33774/coe-2025-vrfrx
34. Obidi, John Onimisi . “On the Discovery of New Laws of Conservation and Uncertainty, Probability and CPT-Theorem Symmetry-Breaking in the Standard Model of Particle Physics: More Revolutionary Insights from the Theory of Entropicity (ToE)”. Cambridge University. (14 June 2025). https://doi.org/10.33774/coe-2025-n4n45
35. Obidi, John Onimisi. A Critical Review of the Theory of Entropicity (ToE) on Original Contributions, Conceptual Innovations, and Pathways towards Enhanced Mathematical Rigor: An Addendum to the Discovery of New Laws of Conservation and Uncertainty. Cambridge University.(2025–06–30). https://doi.org/10.33774/coe-2025-hmk6n
36. Physics:HandWiki Master Index of Source Papers on Theory of Entropicity(ToE). (2025, September 9). HandWiki, . Retrieved 17:33, September 9, 2025 from https://handwiki.org/wiki/index.php?title=Physics:HandWiki_Master_Index_of_Source_Papers_on_Theory_of_Entropicity(ToE)&oldid=3743060
37. Philosophy:Obidi’s Agile Manifesto in Publishing of Revolutionary Ideas. (2025, September 9). HandWiki, . Retrieved 17:37, September 9, 2025 from https://handwiki.org/wiki/index.php?title=Philosophy:Obidi%27s_Agile_Manifesto_in_Publishing_of_Revolutionary_Ideas&oldid=3743065
38. Physics:Entrodynamic Bellman Equation of AI RL in Theory of Entropicity(ToE). (2025, September 10). HandWiki, . Retrieved 14:46, September 10, 2025 from https://handwiki.org/wiki/index.php?title=Physics:Entrodynamic_Bellman_Equation_of_AI_RL_in_Theory_of_Entropicity(ToE)&oldid=3743125
39. Why language models hallucinate | OpenAI. (September 2025). https://openai.com/index/why-language-models-hallucinate/
40. Physics:On the Phenomenological Foundations of the Theory of Entropicity(ToE). (2025, September 15). HandWiki, . Retrieved 05:06, September 15, 2025 from https://handwiki.org/wiki/index.php?title=Physics:On_the_Phenomenological_Foundations_of_the_Theory_of_Entropicity(ToE)&oldid=3743204
41. Wikipedia contributors. (2025, May 7). Entropic uncertainty. In Wikipedia, The Free Encyclopedia. Retrieved 00:34, September 20, 2025, from https://en.wikipedia.org/w/index.php?title=Entropic_uncertainty&oldid=1289229404
42. Pawłowski, M. (2020). Entropy in Foundations of Quantum Physics. Entropy, 22(3), 371 https://doi.org/10.3390/e22030371
43. Physics:Entropy as Foundation of Quantum Mechanics in Theory of Entropicity. (2025, September 20). HandWiki, . Retrieved 01:29, September 20, 2025 from https://handwiki.org/wiki/index.php?title=Physics:Entropy_as_Foundation_of_Quantum_Mechanics_in_Theory_of_Entropicity&oldid=3743315
44. Physics:The Theory of Entropicity (ToE) as a New Foundation for Cybersecurity. (2025, September 20). HandWiki, . Retrieved 02:29, September 20, 2025 from https://handwiki.org/wiki/index.php?title=Physics:The_Theory_of_Entropicity_(ToE)_as_a_New_Foundation_for_Cybersecurity&oldid=3743326
45. Physics:A Brief Introduction to the Theory of Entropicity(ToE) for Research. (2025, September 20). HandWiki, . Retrieved 08:55, September 20, 2025 from https://handwiki.org/wiki/index.php?title=Physics:A_Brief_Introduction_to_the_Theory_of_Entropicity(ToE)_for_Research&oldid=3743334
46. Physics:The Theory of Entropicity(ToE) and Competing Theories in Physics. (2025, September 23). HandWiki, . Retrieved 06:05, September 23, 2025 from https://handwiki.org/wiki/index.php?title=Physics:The_Theory_of_Entropicity(ToE)_and_Competing_Theories_in_Physics&oldid=3743374
47. Physics:Mathematical Formulation of the Theory of Entropicity(ToE). (2025, September 23). HandWiki, . Retrieved 08:47, September 23, 2025 from https://handwiki.org/wiki/index.php?title=Physics:Mathematical_Formulation_of_the_Theory_of_Entropicity(ToE)&oldid=3743383
48. Physics:Theory of Entropicity(ToE) Applied in Materials and Energy Systems. (2025, September 25). HandWiki, . Retrieved 19:42, September 25, 2025 from https://handwiki.org/wiki/index.php?title=Physics:Theory_of_Entropicity(ToE)_Applied_in_Materials_and_Energy_Systems&oldid=3743397
49. A Brief Note On the Theory of Entropicity(ToE) and its General Implications — Substack https://open.substack.com/pub/johnobidi/p/a-brief-note-on-the-theory-of-entropicitytoe?r=1yk33z&utm_campaign=post&utm_medium=web&showWelcomeOnShare=true
50. The Theory of Entropicity(ToE) Explains Mass, Time Dilation, Length, Speed of Light, etc.(Part 1) — Substack https://open.substack.com/pub/johnobidi/p/the-theory-of-entropicitytoe-explains?utm_source=share&utm_medium=android&r=1yk33z
51. The Theory of Entropicity(ToE) Explains Mass, Time Dilation, Length, Speed of Light, etc.(Part 2) — Substack https://open.substack.com/pub/johnobidi/p/the-theory-of-entropicitytoe-explains-51c?utm_source=share&utm_medium=android&r=1yk33z
52. Correspondence Between the Theory of Entropicity(ToE) and the Idea of the Aether and the Higgs Field Mechanism in the Standard Model of Particle Physics https://open.substack.com/pub/johnobidi/p/correspondence-between-the-theory?utm_source=share&utm_medium=android&r=1yk33z
53. Physics:Theory of Entropicity(ToE), Idea of Aether and Higgs Field Mechanism. (2025, September 28). HandWiki, . Retrieved 23:39, September 28, 2025 from https://handwiki.org/wiki/index.php?title=Physics:Theory_of_Entropicity(ToE),_Idea_of_Aether_and_Higgs_Field_Mechanism&oldid=3743493
54. Physics:Higgs Field Mechanism and Aether in the Theory of Entropicity(ToE). (2025, September 29). HandWiki, . Retrieved 18:54, September 29, 2025 from https://handwiki.org/wiki/index.php?title=Physics:Higgs_Field_Mechanism_and_Aether_in_the_Theory_of_Entropicity(ToE)&oldid=3743520
55. Physics:Path to an Entropic Field Equation in the Theory of Entropicity(ToE). (2025, September 29). HandWiki, . Retrieved 20:04, September 29, 2025 from https://handwiki.org/wiki/index.php?title=Physics:Path_to_an_Entropic_Field_Equation_in_the_Theory_of_Entropicity(ToE)&oldid=3743523
56. The Limit of the Speed of Light © is a Consequence of [Thermodynamic] Entropy Rather Than the Geometry of Einstein’s Theory of Relativity. By John Onimisi Obidi on Medium: https://medium.com/@jonimisiobidi/the-limit-of-the-speed-of-light-c-is-a-consequence-of-thermodynamic-entropy-rather-than-the-6ee6c04aae60
57. The Limit of the Speed of Light © is a Consequence of [Thermodynamic] Entropy Rather Than the Geometry of Einstein’s Theory of Relativity. https://open.substack.com/pub/johnobidi/p/the-limit-of-the-speed-of-light-c?utm_source=share&utm_medium=android&r=1yk33z
58. Physics:The Emergence of the Speed of Light in the Theory of Entropicity(ToE). (2025, September 30). HandWiki. Retrieved 06:37, September 30, 2025 from https://handwiki.org/wiki/index.php?title=Physics:The_Emergence_of_the_Speed_of_Light_in_the_Theory_of_Entropicity(ToE)&oldid=3743551
59. How Does the Theory of Entropicity(ToE) Describe Nature in Modern Physics? https://medium.com/@jonimisiobidi/how-does-the-theory-of-entropicity-toe-describe-nature-in-modern-physics-ae5739a15e7c
60. How Does the Theory of Entropicity(ToE) Describe Nature in Modern Physics? https://open.substack.com/pub/johnobidi/p/how-does-the-theory-of-entropicitytoe?utm_source=share&utm_medium=android&r=1yk33z
61. Physics:How the Theory of Entropicity(ToE) Describes Nature in Physics. (2025, October 2). HandWiki, . Retrieved 00:10, October 2, 2025 from https://handwiki.org/wiki/index.php?title=Physics:How_the_Theory_of_Entropicity(ToE)_Describes_Nature_in_Physics&oldid=3743579
62. So, Why Do Objects or Bodies or Particles Move At All? Explained By The Theory of Entropicity(ToE) https://open.substack.com/pub/johnobidi/p/so-why-do-objects-or-bodies-or-particles?utm_source=share&utm_medium=android&r=1yk33z
63. So, Why Do Objects or Bodies or Particles Move At All? Explained By The Theory of Entropicity(ToE) https://medium.com/@jonimisiobidi/so-why-do-objects-or-bodies-or-particles-move-at-all-2749d400a026
64. The Theory of Entropicity and the Laws of Newton https://en.everybodywiki.com/The_Theory_of_Entropicity_and_the_Laws_of_Newton
65. The Theory of Entropicity(ToE) Explains Motion and the Laws of Newton https://en.everybodywiki.com/The_Theory_of_Entropicity(ToE)_Explains_Motion_and_the_Laws_of_Newton
66. How The Theory Of Entropicity(ToE) Explains Newton’s Laws Of Motion And Einstein’s Theory Of Spacetime Curvature https://open.substack.com/pub/johnobidi/p/how-the-theory-of-entropicitytoe?r=1yk33z&utm_campaign=post&utm_medium=web&showWelcomeOnShare=true
67. How The Theory Of Entropicity(ToE) Explains Newton’s Laws Of Motion And Einstein’s Theory Of Spacetime Curvature https://medium.com/@jonimisiobidi/how-the-theory-of-entropicity-toe-explains-newtons-laws-of-motion-and-einstein-s-theory-of-2dbd601786a0
68. Obidi, John Onimisi. “Theory of Entropicity(ToE) Explains Newton and Einstein” Encyclopedia, https://encyclopedia.pub/entry/59079 (accessed October 03, 2025)
69. The Theory of Entropicity(ToE) Re-interprets Newton’s Gravitation and Einstein’s Relativity Under One Unifying Principle https://open.substack.com/pub/johnobidi/p/the-theory-of-entropicitytoe-re-interprets?utm_source=share&utm_medium=android&r=1yk33z
70. The Theory of Entropicity(ToE) Re-interprets Newton’s Gravitation and Einstein’s Relativity Under One Unifying Principle https://medium.com/@jonimisiobidi/the-theory-of-entropicity-toe-re-interprets-newtons-gravitation-and-einstein-s-relativity-under-aafa8bb6ce95
71. Obidi, John Onimisi. “Theory of Entropicity(ToE) Reinterprets Newton and Einstein” Encyclopedia, https://encyclopedia.pub/entry/59081 (accessed October 03, 2025)
72. Physics:The Obidi Action in the Theory of Entropicity(ToE). (2025, October 3). HandWiki, . Retrieved 17:12, October 3, 2025 from https://handwiki.org/wiki/index.php?title=Physics:The_Obidi_Action_in_the_Theory_of_Entropicity(ToE)&oldid=3743585
73. Obidi, John Onimisi. “The Obidi Action in the Theory of Entropicity(ToE)” Encyclopedia, https://encyclopedia.pub/entry/59083 (accessed October 03, 2025)
74. Physics:Pre-geometric Origin of Obidi Action in Theory of Entropicity(ToE). (2025, October 3). HandWiki, . Retrieved 21:34, October 3, 2025 from https://handwiki.org/wiki/index.php?title=Physics:Pre-geometric_Origin_of_Obidi_Action_in_Theory_of_Entropicity(ToE)&oldid=3743593
75. Amari, Shun-ichi (1985). Differential-Geometrical Methods in Statistics. Lecture Notes in Statistics. 28. Springer-Verlag. ISBN 978–0387909683. Retrieved 2025–10–03.
76. Čencov, Nikolai N. (1982). Statistical Decision Rules and Optimal Inference. Translations of Mathematical Monographs. 53. American Mathematical Society. ISBN 978–0821830979. Retrieved 2025–10–03.
77. Amari, Shun-ichi. *Differential-Geometrical Methods in Statistics*. Lecture Notes in Statistics, vol. 28. New York: Springer-Verlag, 1985. ISBN 978–0387909683. https://link.springer.com/book/10.1007/978-1-4612-5056-2 (accessed October 3, 2025).
78. Čencov, Nikolai N. *Statistical Decision Rules and Optimal Inference*. Translations of Mathematical Monographs, vol. 53. Providence, RI: American Mathematical Society, 1982. ISBN 978–0821830979. https://bookstore.ams.org/mmono-53 (accessed October 3, 2025).
79. Amari, Shun-ichi. *Differential-Geometrical Methods in Statistics*. Lecture Notes in Statistics, vol. 28. New York: Springer-Verlag, 1985. ISBN 978–0387909683. https://link.springer.com/book/10.1007/978-1-4612-5056-2 (accessed October 3, 2025).
80. Čencov, Nikolai N. *Statistical Decision Rules and Optimal Inference*. Translations of Mathematical Monographs, vol. 53. Providence, RI: American Mathematical Society, 1982. ISBN 978–0821830979. https://bookstore.ams.org/mmono-53 (accessed October 3, 2025).
81. Amari, Shun-ichi; Hiroshi Nagaoka (2000). Methods of Information Geometry. Translations of Mathematical Monographs. 191. American Mathematical Society and Oxford University Press. ISBN 978–0821805312. Retrieved 2025–10–03.
82. Amari, Shun-ichi, and Hiroshi Nagaoka. *Methods of Information Geometry*. Translations of Mathematical Monographs, vol. 191. Providence, RI: American Mathematical Society and Oxford University Press, 2000. ISBN 978–0821805312. https://bookstore.ams.org/translations-191 (accessed October 3, 2025)
83. Physics:Pre-Geometric Origin of Obidi Action in Theory of Entropicity(ToE). (2025, October 4). HandWiki, . Retrieved 01:47, October 4, 2025 from https://handwiki.org/wiki/index.php?title=Physics:Pre-Geometric_Origin_of_Obidi_Action_in_Theory_of_Entropicity(ToE)&oldid=3743611
84. On the Mathematical Foundations of the Theory of Entropicity(ToE): A Qualitative Odyssey and Roadmap https://open.substack.com/pub/johnobidi/p/on-the-mathematical-foundations-of?utm_source=share&utm_medium=android&r=1yk33z
85. On the Mathematical Foundations of the Theory of Entropicity(ToE): A Qualitative Odyssey and Roadmap https://medium.com/@jonimisiobidi/on-the-mathematical-foundations-of-the-theory-of-entropicity-toe-a-qualitative-odyssey-and-aeb2f754addc
86. On The Uniqueness of the Theory of Entropicity (ToE) With Respect to Other Competing Theories in Modern Theoretical Physics https://medium.com/@jonimisiobidi/on-the-uniqueness-of-the-theory-of-entropicity-toe-with-respect-to-other-competing-theories-in-29e409de7177
87. On The Uniqueness of the Theory of Entropicity (ToE) With Respect to Other Competing Theories in Modern Theoretical Physics https://open.substack.com/pub/johnobidi/p/on-the-uniqueness-of-the-theory-of?utm_source=share&utm_medium=android&r=1yk33z
88. Physics:Rényi Entropy Derived from Obidi’s Theory of Entropicity(ToE). (2025, October 6). HandWiki, . Retrieved 05:56, October 6, 2025 from https://handwiki.org/wiki/index.php?title=Physics:R%C3%A9nyi_Entropy_Derived_from_Obidi%27s_Theory_of_Entropicity(ToE)&oldid=3743623
89. Physics:The Theory of Entropicity(ToE) On a New Path to Quantum Gravity. (2025, October 6). HandWiki, . Retrieved 16:39, October 6, 2025 from https://handwiki.org/wiki/index.php?title=Physics:The_Theory_of_Entropicity(ToE)_On_a_New_Path_to_Quantum_Gravity&oldid=3743629
90. The Theory of Entropicity ToE: On a New Path Toward Quantum Gravity https://open.substack.com/pub/johnobidi/p/the-theory-of-entropicity-toe-on?utm_source=share&utm_medium=android&r=1yk33z
91. Sean Collins (February, 2025). On the Theory of Mjolnir (A137) Lattice Dynamics by Sean Collins: Collected Unpublished Works and Communications with John Onimisi Obidi (Unpublished). Self-archived manuscript and materials.
92. Physics:Sean Collins’ Path-Integral Mapping of the Mjolnir(A137)Lattice. (2025, October 7). HandWiki, . Retrieved 20:13, October 7, 2025 from https://handwiki.org/wiki/index.php?title=Physics:Sean_Collins%27_Path-Integral_Mapping_of_the_Mjolnir(A137)Lattice&oldid=3743664
93. Physics:Potency of Sean Collins’ Path Integral Formulation of QM Dynamics. (2025, October 8). HandWiki, . Retrieved 04:28, October 8, 2025 from https://handwiki.org/wiki/index.php?title=Physics:Potency_of_Sean_Collins%27_Path_Integral_Formulation_of_QM_Dynamics&oldid=3743680
94. On the Potency of Sean Collins’ Mjolnir (A137) Lattice Dynamics Path Integral Formulation of Quantum Mechanics and Its Incorporation Into the Conceptual and Mathematical Foundations of the Theory of Entropicity (ToE) https://open.substack.com/pub/johnobidi/p/on-the-potency-of-sean-collins-mjolnir?utm_source=share&utm_medium=android&r=1yk33z
95. “On the Potency of Sean Collins’ Mjolnir (A137) Lattice Dynamics Path Integral Formulation of…“ by John Onimisi Obidi on Medium: https://medium.com/@jonimisiobidi/on-the-potency-of-sean-collins-mjolnir-a137-lattice-dynamics-path-integral-formulation-of-6ec8ac23e7ab
96. Obidi, John Onimisi (2025–10–07). “On the Conceptual and Mathematical Foundations of the Theory of Entropicity (ToE): An Alternative Path toward Quantum Gravity”. doi:10.6084/m9.figshare.30327445.v1.
97. HandWiki contributors, "Physics:On the Theory of Entropicity (ToE)," HandWiki, https://handwiki.org/wiki/index.php?title=Physics:On_the_Theory_of_Entropicity_(ToE)&oldid=3821075 (accessed November 8, 2025).
98. Medium: Physics: On the Theory of Entropicity (ToE) and Google’s Quantum Core Breakthrough Experiment on the Observer Effect: The Theory of Entropicity (ToE) Offers Insights and Inroads on the Quantum Measurement Problem. https://medium.com/@jonimisiobidi/physics-on-the-theory-of-entropicity-toe-and-googles-quantum-core-breakthrough-experiment-on-e6b1930976c

Comparative Analysis Between John Onimisi Obidi’s Theory of Entropicity (ToE) and Waldemar Marek Feldt’s FELDT-HIGGS Universal Bridge (F-HUB) Theory: From Information Fields to Entropic Dynamics: Evaluating Competing Foundations for a Post-Einsteinian Physics in Our Understanding of Nature and Reality

Last updated: November 8, 2025

Comparative Analysis Between John Onimisi Obidi’s Theory of Entropicity (ToE) and Waldemar Marek Feldt’s FELDT-HIGGS Universal Bridge (F-HUB) Theory

From Information Fields to Entropic Dynamics: Evaluating Competing Foundations for a Post-Einsteinian Physics in Our Understanding of Nature and Reality

Introduction

In the unfolding landscape of twenty-first-century theoretical physics, the search for unifying principles that can reconcile quantum mechanics, gravitation, and thermodynamics has become a defining intellectual frontier. Among the emerging frameworks that attempt to move beyond the limitations of Einstein’s geometric spacetime and the probabilistic formalism of quantum theory are two bold proposals: John Onimisi Obidi’s Theory of Entropicity (ToE) and Waldemar Marek Feldt’s FELDT-HIGGS Universal Bridge (F-HUB) Theory. Though they arise from different philosophical and mathematical traditions, both theories converge on a striking intuition — that the universe is not fundamentally mechanical or geometric but informational and entropic in nature. Yet, each articulates this intuition through distinct first principles, mathematical architectures, and ontological hierarchies.

Obidi’s Theory of Entropicity (ToE) reconceptualizes entropy as the primary causal field of reality — a continuous, dynamical, and universal force that governs the emergence of mass, motion, and spacetime itself. In ToE, the second law of thermodynamics is not a constraint but a generative principle: the universe evolves by maximizing entropy through a self-organizing, time-asymmetric process encoded in the Obidi Action and the Vuli Ndlela Integral. These foundational equations establish a variational framework in which gravitational attraction, relativistic kinematics, and quantum probability all arise as manifestations of entropy’s drive toward optimal reconfiguration. The speed of light is reinterpreted as the maximum rate of entropic information redistribution, making relativity an emergent property of entropy rather than an imposed geometric invariant. Through this lens, time dilation, length contraction, and mass increase are natural consequences of entropy’s finite update speed — an idea that recasts the very meaning of motion and causality.

Feldt’s FELDT-HIGGS Universal Bridge (F-HUB) theory, by contrast, situates its foundation in the interaction between quantum information and the Higgs field. It envisions a universe in which mass, gravity, and spacetime emerge from a deeper informational substrate governed by an algebraic “master equation” linking entropy, mass, Boltzmann’s constant, and the Higgs contribution. While F-HUB shares ToE’s conviction that entropy and information underlie physical reality, it treats these quantities primarily as structural descriptors of the informational network from which spacetime geometry arises. Its focus lies in revealing how the Higgs mechanism — long regarded as the source of mass in the Standard Model — may itself be a by-product of informational symmetry breaking at the quantum level.

The contrast between the two theories is profound. ToE presents a field-theoretic and variational model in which entropy behaves as a real, continuous field that evolves dynamically across spacetime, generating curvature, energy, and motion. F-HUB, on the other hand, offers a phenomenological and algebraic bridge between information and physics, using the Higgs interaction as a unifying element but without yet formulating a full-fledged field equation. Where ToE generalizes thermodynamics into a universal causal law, F-HUB embeds thermodynamic and informational relations within an existing physical ontology. The former is thus a first-principles reconstruction of physics from entropy; the latter, an informational extension of known physics.

This comparative study examines the philosophical foundations, mathematical formalisms, and physical implications of both frameworks. It traces their shared origins in information theory and thermodynamics, analyzes their divergent formulations of entropy, and evaluates how each theory addresses the perennial questions of mass generation, gravitational attraction, relativistic invariance, and the arrow of time. The discussion also explores the potential complementarity between the two approaches — whether F-HUB’s information-Higgs paradigm can be viewed as a subset or emergent limit within ToE’s entropic field dynamics, and how both contribute to the broader quest for a unified theory of nature.

By placing these two modern entropic theories side by side, this paper seeks not only to highlight their differences but to illuminate their shared ambition: to move physics beyond static geometry and probabilistic abstraction toward a living, self-organizing universe driven by the flow of entropy and information. In that sense, both ToE and F-HUB belong to the same intellectual lineage that began with Boltzmann, extended through Shannon, and now finds new life in the synthesis of entropy, information, and cosmological structure. Their comparison offers a glimpse of how future physics may finally unite the thermodynamic, quantum, and relativistic descriptions of reality under a single entropic principle.

 Foundational Premises

Mathematical Architecture

F-HUB

• Uses a single “master equation”:
  $S = (H' \cdot M^2 \cdot k_B \cdot \alpha) / c^3$
  which ties mass $M$, the Higgs field contribution $H'$, and entropy $S$.

• It is dimensionally consistent but phenomenological, not a field equation.

• Does not yield Euler–Lagrange dynamics or spacetime tensors; rather, it gives algebraic proportionalities.

• Verification is numerical (Python, symbolic solvers) — not variational.

ToE

• Begins from the Obidi Action and its path-integral form (Vuli-Ndlela Integral),
  combining a classical term, gravitational entropy term, and irreversibility term.

• Produces full field equations, geodesics, and the Master Entropic Equation (MEE).

• Predicts observable phenomena (light bending, perihelion precession, entanglement delays) directly from these equations.

• Entropy is treated as a tensorial field $S(x)$ obeying a differential field equation, not merely an algebraic relation.

Summary: F-HUB provides a scalar correlation; ToE constructs a continuous field theory with explicit dynamical evolution.

Concept of Entropy

Relation to Other Theories

Mathematical and Physical Scope

Conceptual Differences

1. Origin of Mass:

• F-HUB → Higgs × Information interaction.
• ToE → Frozen Entropy; mass is constrained entropic flux.

2. Nature of Gravity:

• F-HUB → Informational optimization effect.
• ToE → Entropy flow curvature; gravitational potential is an entropy potential.

3. Role of Light:

• F-HUB keeps light fundamental.
• ToE redefines light as the signal speed of entropy propagation — the Pyros limit.

4. Temporal Dynamics:

• F-HUB: time as structural evolution.
• ToE: time as entropic irreversibility, giving dilation and causality.

5. Epistemic Status:

• F-HUB remains within informational metaphysics.
• ToE is a physical field theory intended to subsume relativity and quantum mechanics.

Strengths and Weaknesses

Synthesis and Comparative Assessment

Both theories share the intuition that spacetime, mass, and gravity are emergent — not fundamental — and both root their explanation in entropy and information.
However, their ontological hierarchies differ:

• F-HUB: Information → Entropy → Mass → Gravity → Spacetime.

• ToE: Entropy → Information → Mass → Motion → Spacetime.

In effect, ToE reverses the causal order: entropy is not produced by information—it produces it.
Thus, ToE can be viewed as a deeper physical layer beneath F-HUB’s informational emergence model.

Final Evaluation

Conclusion

F-HUB and ToE both dismantle the assumption that spacetime and gravity are fundamental.
F-HUB views them as outcomes of quantum information structuring through the Higgs field.
ToE goes further — entropy itself becomes the field from which information, Higgs structure, and all motion arise.
Hence, ToE can be interpreted as the next-generation generalization of F-HUB, where information is a manifestation of entropy, not its foundation.

References

1. Medium: Comparative Analysis Between John Onimisi Obidi’s Theory of Entropicity (ToE) and Waldemar Marek Feldt’s FELDT-HIGGS Universal Bridge (F-HUB) Theory
2. LinkedIn: Comparative Analysis Between John Onimisi Obidi’s Theory of Entropicity (ToE) and Waldemar Marek Feldt’s FELDT-HIGGS Universal Bridge (F-HUB) Theory: From Information Fields to Entropic Dynamics: Evaluating Competing Foundations for a Post-Einsteinian Physics in Our Understanding of Nature and Reality 
3. Theory of Entropicity (ToE) Resource Website: Comparative Analysis Between John Onimisi Obidi’s Theory of Entropicity (ToE) and Waldemar Marek Feldt’s FELDT-HIGGS Universal Bridge (F-HUB) Theory
4. The FELDT-HIGGS Universal Bridge (F-HUB) — Part One: The Birth of Spacetime — An Informational Framework for Mass, Gravity, and Entropy. DOI: 10.5281/zenodo.14884924
5. Obidi, J. O. (2025). The Theory of Entropicity (ToE) Derives Einstein’s Relativistic Speed of Light (c) as a Function of the Entropic Field: ToE Applies Logical Entropic Concepts and Principles to Derive Einstein’s Second Postulate. Cambridge University. doi:10.33774/coe-2025-f5qw8
6. Obidi, J. O. (2025). The Theory of Entropicity (ToE) Derives and Explains Mass Increase, Time Dilation and Length Contraction in Einstein’s Theory of Relativity (ToR): ToE Applies Logical Entropic Concepts and Principles to Verify Einstein’s Relativity. Cambridge Open Engage. https://doi.org/10.33774/coe-2025-6wrkm
7. Obidi, John Onimisi. 2025. On the Conceptual and Mathematical Foundations of the Theory of Entropicity (ToE): An Alternative Path toward Quantum Gravity and the Unification of Physics. Cambridge University. Published October 17, 2025. https://doi.org/10.33774/coe-2025-1dsrv
8. Obidi, John Onimisi. 2025. A Simple Explanation of the Unifying Mathematical Architecture of the Theory of Entropicity (ToE): Crucial Elements of ToE as a Field Theory. Cambridge University. Published October 20, 2025. https://doi.org/10.33774/coe-2025-bpvf3