Natural Units

Natural Units

Particle physicists use a system of natural units where the speed of light $c$ and the reduced Planck constant $\hbar$ are both set to 1. This eliminates factors of $c$ and $\hbar$ from every equation and keeps numbers at a human scale.

Key Conversion Constants

The bridge between natural units and SI is the product $\hbar c$:

$\hbar c = 197.3269804 \text{ MeV·fm}$

where 1 fm (femtometre) $= 10^{-15}$ m is the typical scale of a nucleus.

Energy

The electron-volt (eV) and its multiples are the natural currency of particle physics:

$1 \text{ MeV} = 10^6 \text{ eV} = 1.602 \times 10^{-13} \text{ J}$ $1 \text{ GeV} = 10^3 \text{ MeV} = 1.602 \times 10^{-10} \text{ J}$

Mass

Using $E = mc^2$, mass is quoted in GeV/$c^2$. To convert to kg:

$m_{\text{kg}} = m_{\text{GeV}} \cdot \frac{1.602 \times 10^{-10}}{c^2}$

The proton has mass $m_p \approx 0.938272$ GeV/$c^2 \approx 1.673 \times 10^{-27}$ kg.

Your Task

Implement three unit-conversion helpers. All physical constants must be defined inside each function body.

• MeV_to_joules(E_MeV) — converts MeV to Joules using $1\text{ MeV} = 1.602 \times 10^{-13}$ J
• GeV_to_kg(m_GeV) — converts GeV/$c^2$ to kg using $c = 299792458$ m/s
• hbar_c_MeV_fm() — returns the constant $\hbar c = 197.3269804$ MeV·fm