W1.6 Making sense of the unfamiliar
The quantity (hG/c5)1/2 is of some physical significance. What can you say about it?
[The symbols h, G and c have their usual significance.]
Solution
RevealSolution
Even though you’re unlikely to have met this combination of fundamental constants before, there are two useful things you can say about it: you can figure out its units; and you can work out its magnitude.
Consider its units first of all.
The units of h are:
The units of G are:
The units of c are:
Thus the units of (hG/c5)1/2 are
So this quantity is a time. Let’s call it τp for short.
Substituting in the values of the fundamental constants we find-
So it is a very short time!
To within a factor of 2π, τp is what is known as the Planck time; it represents the age of the universe at which, thinking backwards towards its big-bang-birth, our current formulation of physics ceases to apply.