Breakdown of Dimensional Analysis in Physics

Debnarayan Jana

University of Calcutta

Dimensional analysis (DA) provides us a very simple heuristic method to solve the depen- dence on the variables without invoking much theoretical knowledge. Moreover, this technique is of great help to experiments because it even- tually serves as a guide to the key parameters which influence the phenomenon. However, there are situations in physics where there is a breakdown of this dimensional analysis. We indicate few examples from classical mechanics, electromagnetism and statistical mechanics. We briefly point out the reasons behind such breakdown of such successful tool in theoretical physics.