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Planck units

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  • 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 \(M_pc^2 = 10^{19}\; \rm{GeV}\).