Deconstructing c³.

Deconstructing c³.

Proposal for a New Natural Constant Governing Spacetime Coupling.

1. Motivation.

In many physical formulas, the speed of light c appears in powers, such as in the Planck length.

formula: ℓₚ = √(ħG / c³). This exponentiation is usually seen as a dimensional artifact, although c is a limiting velocity.

This theory proposes that c³ can be decomposed into c and a new constant X, which may carry independent physical meaning.

2. Mathematical Reformulation.

Proposal: Replace c³ with c · X, where X is a new constant with the unit m²/s².

New Planck length:

ℓₚ = √(ħG / (c · X))

This is dimensionally consistent:

ħG = m⁵/s³, c·X = m³/s³ ⇒ ℓₚ = √(m²) = m

3. Interpretation of X.

X may be interpreted as a spacetime coupling constant – representing a structural density or area-inertia coupling.

4. Planck Scale Comparison.

The new constant X can also be applied to other Planck quantities:

• Planck length: ℓₚ = √(ħG / (cX))
• • Planck time: tₚ = √(ħG / (cX²))
• • Planck energy: Eₚ = √(ħcX² / G)

5. Conclusion.

Introducing the constant X offers a new perspective on the structure of fundamental constants.

It decouples the limiting speed c from its structural context and invites reinterpretation in quantum gravity frameworks.