Both the fundamental constants $\hbar$ and $c$ have dimensions. In particular, $[\hbar]=ML^2T^{-1}$ and $[c]=LT^{-1}$. But in natural units, we make them dimensionless constants of equal magnitude. How is this possible? This means length is measured in the same units as time which is measured in the units of inverse mass! Am I measuring the distance between two points in seconds??? Can we do that? I cannot make myself comfortable with it :-( Also why is it not possible to make $\hbar=c=G=1$ simultaneously?
Answer
Can we measure distance in seconds? Definitely. When you set $c=1$, “one second of distance” is simply the distance that light travels in vacuum in one second. And “one meter of time” is the amount of time it takes for light to go one meter in vacuum.
It is possible to set $\hbar=c=G=1$ simultaneously. This is what produces Planck units.
Natural units are not just a nice simplification. They allow the physics of an equation to “shine through” more clearly. For example,
$$E^2-\mathbf{p}^2=m^2$$
says “Mass is the invariant length of the energy-momentum four vector” more clearly than
$$E^2-\mathbf{p}^2 c^2=m^2 c^4$$
does, with its extraneous factors of $c$.
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