# Planck units

Many people are familiar with the idea that in special relativity, we can set the speed of light equal to one. This is simply a choice of units -- it means that if we measure time in seconds, we should measure distance in light seconds. (After all, the speed of light *is* one light second per second.)

In quantum gravity, there are three dimensional constants that can all be set to one: the speed of light c, Newton's constant G, and Planck's constant ℏ. The resulting units are called "Planck units." The Planck length (length 1 in Planck units) is

\[L_p = 1.6 \times 10^{-35}\; \rm{m}\]

the Planck time is

\[T_p = 5.4 \times 10^{-44} \; \rm{s}\]

the Planck mass is

\[M_p = 2.24 \times 10^{-8} \; \rm{kg}\]

For quantum gravity, these are "natural units," units set by the theory itself. It is generally believed that they also set the scale at which quantum gravitational effects become important -- that is, we might not have to worry about quantum gravity too much if we are looking at physics at length scales much larger than \(L_p\) or energies much smaller than \(M_pc^2 = 10^{19}\; \rm{GeV}\).

### Contributors

- Steve Carlip (Physics, UC Davis)