You can edit either φ0 or λ (the scaling parameter).
Changing one automatically re‐derives the other via
λ = √[(ħ·c)/G] / φ₀.
All other derived constants update immediately.
| Symbol | Description | Value |
|---|---|---|
| ħ (hbar) | Reduced Planck constant | J·s |
| c | Speed of light | m/s |
| G | Gravitational constant | m³·kg⁻¹·s⁻² |
| e | Elementary charge | C |
| me | Electron mass | kg |
| ε0 | Vacuum permittivity | F/m |
| φ0 | Scalar field amplitude | |
| λ | Scaling parameter |
| Constant | Equation | Computed (sci) |
Full Value (non-sci) |
Measured | Deviation (%) |
|---|
\( G = \frac{\hbar \cdot c}{\lambda^2 \cdot \phi_0^2} \)
with derived Planck mass: \( m_P = \lambda \cdot \phi_0 \)
\( G = \frac{\hbar \cdot c}{\lambda^2 \cdot \phi_0^2} \)
with derived Planck mass: \( m_P = \lambda \cdot \phi_0 \)
(and \( \phi_0 = \frac{m_P}{\lambda} \) gives \( \phi_0 \approx 2.18\times10^{-18} \))
Adjust the inputs below. All constants used in the calculation are tunable.
\( \phi_0 = \frac{m_P}{\lambda} = \frac{2.18\times10^{-8}}{1.0\times10^{10}} = 2.18\times10^{-18} \)
\( \lambda = \frac{m_P}{\phi_0} = \frac{2.18\times10^{-8}}{2.18\times10^{-18}} = 9.98364277087673\times10^9 \)
Derived Planck Mass (mₚ):
Calculated G:
Deviation from measured value:
This calculator elegantly demonstrates how the gravitational constant \(G\) can be derived purely deterministically – without any tuning parameters. All the values, including the scaling parameter \(\lambda\) and the scalar field amplitude \(\phi_0\), are computed directly from fixed equations.
In our model, the relation \[ \phi_0 = \frac{m_P}{\lambda} \] (with \(m_P\) representing the Planck mass) automatically yields \[ G = \frac{\hbar \cdot c}{\lambda^2 \cdot \phi_0^2}\,. \]
With \(m_P \approx 2.18\times10^{-8}\) kg and \(\lambda \approx 1.0\times10^{10}\), the scalar field amplitude is fixed to \(\phi_0 \approx 2.18\times10^{-18}\). This deterministic approach shows that the fundamental constants are not arbitrarily adjustable but instead emerge naturally from the intrinsic structure of the scalar field.