question_answer 31)

A great physicist of this century (P.A.M. Dirac) loved playing with numerical values of Fundamental constants of nature. This led him to an interesting observation. Dirac found that from the basic constants of atomic physics (c, e, mass of electron, mass of proton) and the gravitational constant G, he could arrive at a number with the dimension of time. Further, it was a very large number, its magnitude being close to the present estimate on the age of the universe (w 15 billion years). From the table of fundamental constants in this book, try to see if you too can construct this number (or any other interesting number you can think of). If its coincidence with the age of the universe were significant, what would this imply for the constancy of fundamental constant ?  

Answer:

Using basic constants such as speed of light (c), charge on electron (e), mass of electron , mass of proton (m ) and gravitational constant (G), we can construct the quantity, Now                  Clearly, the quantity t has the dimensions of time. Put      and        = 0.667 billion years. This time is slightly less than the age of the universe ( 15 billion years). It implies that the values of the basic constants of physics should change with time because the age of the universe increases with time.