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Logarithmic Differentiation

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When a car’s weight and driving forces act on a tire, they impose an external load on the rubber material. This load is resisted internally by forces distributed throughout the tire structure, which are defined as stress. The resulting deformation of the rubber due to this stress is quantified as strain. The relationship between stress and strain governs how the tire deforms under load and is central to understanding its mechanical response during operation.Rubber exhibits a nonlinear...

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Tension

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Tension is a force along the length of a medium, in particular, a force carried by a flexible medium, such as a rope or cable. The word "tension" comes from Latin, meaning "to stretch". Not coincidentally, the flexible cords that carry muscle forces to other parts of the body are called tendons. Any flexible connector, such as a string, rope, chain, wire, or cable, can exert pull only parallel to its length; so, a force carried by a flexible connector is a tension with a direction parallel to...

Tension

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Tension is a force along the length of a medium, in particular, a force carried by a flexible medium, such as a rope or cable. The word "tension" comes from Latin, meaning "to stretch". Not coincidentally, the flexible cords that carry muscle forces to other parts of the body are called tendons. Any flexible connector, such as a string, rope, chain, wire, or cable, can exert pull only parallel to its length; so, a force carried by a flexible connector is a tension with a direction parallel to...

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Related Experiment Video

Updated: May 28, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

A Complex Tension Origin for Dilaton Gravity: Jordan Stiffness and Logarithmic Einstein Dynamics.

Michaël Vaillant¹, Tony C Scott²

¹Meta-Connexions, 234 Route de Seysses, 31100 Toulouse, France.

Entropy (Basel, Switzerland)

|May 26, 2026

Summary

This study identifies the dilaton with a stiffness mode, explaining the logarithmic scalar-tensor structure in dilatonic gravity. This provides a microphysical origin for scalar stiffness laws and offers testable predictions for gravity theories.

Keywords:

Einstein frame Everett–Hirschman entropy Jordan frame complex scalar field dilaton gravity logarithmic Schrödinger equation quantum gravity scalar-tensor theory

Related Experiment Videos

Last Updated: May 28, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Area of Science:

Theoretical Physics
Quantum Gravity
Cosmology

Background:

Dilatonic gravity theories require a microphysical explanation for their scalar sector.
Existing models lack a fundamental understanding of the dilaton's origin and behavior.
Scalar-tensor theories are crucial for understanding gravity's fundamental properties.

Purpose of the Study:

To provide a microphysical completion for the scalar sector of dilatonic gravity.
To identify the dilaton with a specific physical mode within a discrete relational network.
To derive the logarithmic scalar-tensor structure from fundamental principles.

Main Methods:

Identifying the dilaton with the coarse-grained stiffness mode of a complex tension field.
Applying controlled ordered-regime coarse-graining to a discrete relational network.
Utilizing a Weyl map to establish the relationship between tension and the canonical scalar.

Main Results:

The real projection of tension scales as Φ(Θ)=Φ0cosΘ, leading to a phase-dependent Planck mass.
An emergent logarithmic structure for the Einstein-frame canonical scalar, φ∝ln[Φ(Θ)/Φ0].
This structure aligns with vacuum models inspired by the Logarithmic Schrödinger Equation (LogSE).

Conclusions:

A controlled microphysical origin for a specific scalar stiffness law (Φ(Θ)∝cosΘ) is established.
The derived logarithmic canonical structure provides a foundation for specific scalar-tensor theories.
The framework offers potential for satisfying Solar-System constraints and suggests avenues for experimental and astrophysical tests.