A simplistic approach to “The Uncertainty Principle”

Abstract

ABSTRACT Throughout the world, almost all of the courses in Physics commence with an  introduction to Newton’s Laws! These laws elegantly describe “our” macroscopic  world. These laws beautifully explained movement of planets, justified elliptical  orbits and helped us in understanding this vast universe including our Solar System. These laws seemed flawless initially but further discoveries challenged Newtonian  interpretation. Newton’s laws couldn’t explain the observations in the atomic arena  and in the cosmic arena. Let us see what has transpired in atomic world since  Newton through Uncertainty Principle deduced by Heisenberg. We must know  following two variables about a system at any point of reference in time in order to  study time and space evolution of the system: Position, Momentum. Newton stated  that these physical quantities could be nimbly determined in an experiment to a  great precision. However, things changed drastically with the advent of Quantum  Mechanics. The birth of Quantum Mechanics was marked by the energy  quantisation law given by Max Planck. This new law was the explanation for the  Ultraviolet Catastrophe related to the black body radiation. Later, a lot of scientists  built upon this subject in a collaborative effort. In this article, the main emphasis  would be on Heisenberg approach which is based on Linear Algebra and matrix  mechanics. Heisenberg stated that the position and momentum of a quantum  particle can’t be measured simultaneously with full accuracy. He challenged  Newton’s fundamentals with mathematical deductions. He named his new  discovery very aptly as “The Uncertainty Principle”. This article tries to deduce same mathematical results using a different approach.