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.

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