It is believed that there is a period of time so short that the theory of gravity (or any of the known interactions) cannot make meaningful predictions. Interestingly, there exists an algebraical arrangement of three fundamental constants that gives units of time. The constants are G (Newton’s gravitational constant), h (Planck’s constant), and c (the speed of light).

(a) Use dimensional analysis to find this period of time (called the Planck time). Our current understanding suggests that for the first instant of the Big Bang, from t = 0 to the Plank time, the known laws of physics did not apply, and this epoch remains a mystery.

(b) The shortest time interval that can be currently measured is about 10^-18 s. How many Planck time intervals would occur during this minimum measurement time?