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The No-Rush Theorem in Theory of Entropicity (ToE): History
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Contributor: John Onimisi Obidi

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
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. It is a core principle of ToE, which proposes that entropy is not just a measure of disorder but a fundamental, dynamic field driving physical phenomena.
 
No-Rush Theorem

The No-Rush Theorem is a foundational principle of the Theory of Entropicity (ToE), first formulated by John Onimisi Obidi.[1][2][3][4][5][6][7][8][9][10][11][12] 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.

Entropy as a Dynamic Field

  • Field Promotion
    Traditionally, entropy SS is a global quantity defined for systems in or near equilibrium. ToE promotes entropy to a spacetime-dependent scalar field S(x)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.

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.

Physical Implications

  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.

  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.

  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.

Connections to Existing Concepts

  • 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.

  • 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.

Beyond Traditional Physics

  • 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} 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.

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.

This entry is adapted from: https://doi.org/10.33774/coe-2025-n4n45

References

  1. 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
  2. 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
  3. 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
  4. 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
  5. 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
  6. 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
  7. 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
  8. 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
  9. 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
  10. 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
  11. Obidi, John Onimisi. Master Equation of the Theory of Entropicity (ToE). Encyclopedia.pub; 2025. https://encyclopedia.pub/entry/58596.. Accessed 04 July 2025.
  12. 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.
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