Natural units are a system of measurement used in physics where fundamental constants of nature are set to a value of $1$, the [[multiplicative identity]]. This simplifies many equations and highlights the underlying relationships between physical quantities. Here's a breakdown: **Key Constants Set to One** - **Speed of light (c):** c = 1 - **Reduced Planck Constant (ħ):** ħ = 1 - **Boltzmann Constant (k_B):** k_B = 1 (often used in thermodynamics and statistical mechanics) - **Gravitational Constant (G):** G = 1 (sometimes used in high-energy physics and cosmology) **Why Use Natural Units** - **Simplification:** Equations become much cleaner as many constants disappear. For example, the famous Einstein's mass-energy equivalence E = mc² simplifies to E = m. - **Essential Relationships:** Natural units highlight fundamental connections between seemingly disparate physical quantities. For instance, setting c = 1 emphasizes the unification of space and time in special relativity. - **Theoretical Calculations:** Many calculations in particle physics and quantum field theory are easier to perform and interpret using natural units. **Examples of Expression in Natural Units** - **Energy:** Expressed simply as mass (because E = m in natural units) - **Momentum:** Also expressed equivalent to mass, as momentum and energy are closely related in relativity. - **Time and Distance:** Both measured in the same units (often inverse mass), demonstrating the spacetime connection. **Converting Back to Standard Units** To recover results in standard units (like meters, seconds, kilograms), you need to re-insert the relevant constants with their appropriate dimensions. There are online converters helpful for this process. **Common Areas of Use** - **Particle Physics:** Very prevalent in theoretical calculations. - **Quantum Field Theory:** Natural units streamline the formalism. - **Cosmology:** Sometimes useful when dealing with fundamental scales. **Important Notes:** - **Context is Key:** Papers and books using natural units usually state it explicitly, as units can be ambiguous otherwise. - **Not Universal**: While convenient for theoretical work, natural units are less practical for experimental measurements or engineering applications where standard SI units are a must. - # References ```dataview Table title as Title, authors as Authors where contains(subject, "natural units") sort modified desc, authors, title ```