The No-Rush Theorem in Theory of Entropicity (ToE)

The No-Rush Theorem in Theory of Entropicity (ToE): Comparison

Please note this is a comparison between Version 12 by John Onimisi Obidi and Version 11 by Catherine Yang.

Here, we give a brief introduction to the No-Rush Theorem of the Theory of Entropicity (ToE), where we state that "Nature cannot be rushed," so that no interaction in nature can proceed instantaneously.

Theoretical Physics
Quantum Physics
Field Theory
Particle Physics

1. Introduction

No-Rush Theorem

The "No-Rush Theorem" in the Theory of Entropicity (ToE), as first formulated by John Onimisi Obidi,^{[1][2][3][4][5][6][7][8][9][10][11][12]} establishes a minimum interaction time for physical processes, stating that no physical interaction can occur instantaneously. establishesIn a minimum interaction time for physical processes, stating that no physical interaction can occur instantaneously. It is a core principle of ToE, which proposes that entropy is not just a ToE, entropy is not merely a passive measure of disorder but a funddynamic, fundamental field thamental, dynamic field driving drives and mediates all physical phenomenainteractions.

The No-Rush Theorem asserts that:

The No-Rush Theorem is a foundational principle of the Theory of Entropicity (ToE), first formulated by John Onimisi Obidi. In ToE, entropy is not merely a passive measure of disorder but a dynamic, fundamental field that drives and mediates all physical interactions. The No-Rush Theorem asserts that:

No physical interaction can occur instantaneously; every process requires a finite, nonzero duration.

2. Entropy as a Dynamic Field

Entropy as a Dynamic Field

Field Promotion

Traditionally, entropy $S$ is a global quantity defined for systems in or near equilibrium. ToE promotes entropy to a spacetime-dependent scalar field $S (x)$ .
Couplings and Dynamics

Gradients $∇μS\nabla_\mu S$ and time derivatives $S˙\dot S$ appear directly in the equations of motion for matter and geometry, sourcing forces and mediating interactions analogously to the electromagnetic potential or the gravitational metric.

3. Statement of the No-Rush Theorem

Finite Interaction Time

Because interactions proceed via the exchange or redistribution of entropy—through informational currents, microscopic reconfigurations, or entropic gradients—they cannot “turn on” in zero time.

Minimum Entropic Interval

There exists a lower bound $Δtmin⁡\Delta t_{\min}$ , determined by the intrinsic “stiffness” of the entropic field (often linked to a Fisher-information term in the action), below which no causal influence can propagate., determined by the intrinsic “stiffness” of the entropic field (often linked to a Fisher-information term in the action), below which no causal influence can propagate.

4. Physical Implications

4.1. Causality and Speed Limits

Provides an entropy-based origin for why no influence can travel faster than a maximum speed, complementing relativity’s light-cone structure.

4.2. Gravity and Inertia

Bodies respond not only to spacetime curvature but also to the finite “ramp-up” time of entropic forces, potentially modifying inertial behavior at very small scales.

4.3. Quantum Processes and the Arrow of Time

Embeds irreversibility at a fundamental level. Quantum transitions, measurements, and decoherence processes require a nonzero duration, reinforcing the unidirectional flow of time.

5.

Causality and Speed Limits

- Provides an entropy-based origin for why no influence can travel faster than a maximum speed, complementing relativity’s light-cone structure.

Gravity and Inertia
- Bodies respond not only to spacetime curvature but also to the finite “ramp-up” time of entropic forces, potentially modifying inertial behavior at very small scales.

Quantum Processes and the Arrow of Time
- Embeds irreversibility at a fundamental level. Quantum transitions, measurements, and decoherence processes require a nonzero duration, reinforcing the unidirectional flow of time.

Connections to Existing Concepts

6.

Decoherence in Open Quantum Systems

Quantum coherence

¹³

is lost over finite timescales as systems entangle with their environment—an entropy-driven process.

Entropic Forces

Similar to how entropy gradients drive polymer elasticity or Verlinde’s^[14] emergent gravity, the No-Rush Theorem ensures these gradients cannot act instantaneously.

Information-Theoretic Limits

The minimum interaction time aligns with the time needed to transfer or distinguish quanta of information, linking ToE to information-geometry and Fisher information.

Decoherence in Open Quantum Systems

Quantum coherence is lost over finite timescales as systems entangle with their environment—an entropy-driven process.

Entropic Forces

Similar to how entropy gradients drive polymer elasticity or Verlinde’s emergent gravity, the No-Rush Theorem ensures these gradients cannot act instantaneously.

Beyond Traditional Physics

Many idealized models—instantaneous collisions, ideal springs, certain gauge approximations—assume zero-time interactions. The No-Rush Theorem treats these as approximations valid only when

is negligibly small compared to experimental timescales.

Experimental Predictions

Subtle delays or frequency-dependent response times in high-precision tests of fundamental forces could reveal the finite interaction interval predicted by ToE.

Information-Theoretic Limits

The minimum interaction time aligns with the time needed to transfer or distinguish quanta of information, linking ToE to information-geometry and Fisher information.

Challenging Instantaneous Assumptions

Many idealized models—instantaneous collisions, ideal springs, certain gauge approximations—assume zero-time interactions. The No-Rush Theorem treats these as approximations valid only when

$Δtmin⁡\Delta t_{\min}$

$Δ$

$t$ $_{m}$ $_{i}_{n}$ is negligibly small compared to experimental timescales.

Experimental Predictions

Subtle delays or frequency-dependent response times in high-precision tests of fundamental forces could reveal the finite interaction interval predicted by ToE.

7.

Challenging Instantaneous Assumptions

Summary

The No-Rush Theorem elevates the principle “nothing happens instantly” into a precise, quantifiable dictum: the entropic field’s dynamics enforce a strict, nonzero lower bound on all interaction times, reshaping our understanding of causality, force mediation, and irreversibility across physics.

References

Obidi, John Onimisi. The Entropic Force-Field Hypothesis: A Unified Framework for Quantum Gravity. Cambridge University; 18 February 2025. https://doi.org/10.33774/coe-2025-fhhmf
Obidi, John Onimisi. Exploring the Entropic Force-Field Hypothesis (EFFH): New Insights and Investigations. Cambridge University; 20 February 2025. https://doi.org/10.33774/coe-2025-3zc2w
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
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
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
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
Obidi, John Onimisi. Attosecond Constraints on Quantum Entanglement Formation as Empirical Evidence for the Theory of Entropicity (ToE). Cambridge University; 25 March 2025. https://doi.org/10.33774/coe-2025-30swc
Obidi, John Onimisi. Review and Analysis of the Theory of Entropicity (ToE) in Light of the Attosecond Entanglement Formation Experiment: Toward a Unified Entropic Framework for Quantum Measurement, Non-Instantaneous Wave-Function Collapse, and Spacetime Emergence. Cambridge University; 29 March 2025. https://doi.org/10.33774/coe-2025-7lvwh
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
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
Obidi, John Onimisi. Master Equation of the Theory of Entropicity (ToE). Encyclopedia.pub; 2025. https://encyclopedia.pub/entry/58596.. Accessed 04 July 2025.
A Concise Introduction to the Evolving Theory of Entropicity (ToE). HandWiki; 2025. https://handwiki.org/wiki/Physics:A_Concise_Introduction_to_the_Evolving_Theory_of_Entropicity_(ToE). Accessed 09 July 2025.
Zurek WH. Decoherence, einselection, and the quantum origins of the classical. Rev Mod Phys. 2003;75(3):715–775. doi:10.1103/RevModPhys.75.715.
Verlinde, Erik P. On the origin of gravity and the laws of Newton. JHEP. 2011;04:029. https://arxiv.org/abs/1001.0785.