What are natural units?

Question

I need to make a presentation on natural units. My professor asked me to visualize a world where $c$ and $\hbar$ are actually equal to unity. Like, what are the consequences? I also want to know the philosophical meaning behind natural units.

Answer 1

You already live in a world where natural units apply. The speed of light is exactly $1$ light-year/year, or equivalently $1$ light-second/second.

Or approximately $1$ foot/nanosecond. This is useful for designing computer circuits. It helps you figure out how far a signal can propagate in one clock cycle.

You can choose units where $\hbar$ is also exactly $1$.

This allows you to simplify equations. For example, $E=m$. Or for a beam of light, $d = t$.

This helps clarify some concepts. In space-time, space and time are on equal footing. $d = t$ makes this clearer than $d = ct$.

We live in a world dominated by gravity. Horizontal distance is an entirely different thing than altitude. They are unrelated concepts. They have different names and units. We use kilometers for horizontal distances, $x$, and meters for altitude, $h$.

If you want to calculate a slope, s, you need a special constant, $K$, that I just made up. $K = 0.001$ km/m. $K$ is a fundamental property of the universe.

$$s = Kh/x$$

But if you use natural units and measure everything in meters, equations get simpler. You start to see relationships that were obscured.