Symmetry Principles and Conservation Laws in Atomic and ...

GENERAL ARTICLEGalileo, contrary to common experience, that the velocityof an object is self-sustaining and remains invariantin the absence of its interaction with an external agency.This principle identi¯es an inertial frame of referencein which physical laws apply. This great discovery byGalileo was soon incorporated in Newton's scheme asthe First law of mechanics, the law of inertia. Newtonrecognised, following his invention of calculus, thatit is the change in velocity that seeks a cause. Newton'scalculus expressed the rate of change of velocityas acceleration which is interpreted as the `e®ect' of thephysical interaction that generated it. Newton's secondlaw expresses this `cause-e®ect' relationship as a linearresponse of the system to the physical interaction it experienced:¡! F = m ¡! a . The mass m of the object is theconstant of proportionality between the e®ect ( ¡! a ) andthe cause ( ¡! F ).1 This article is partly based onthe talk given by PCD at theKarnataka Science and TechnologyAcademy’s special lecturesat the Bangalore Universityon 23rd March, 2009.In the following section we will begin by considering howNewton's third law introduces a simple illustration ofthe relation between a symmetry and a conservation law.In the remainder of the article we will explore similar relationshipsthat impact much of the frontiers of physics,which are being investigated today; these studies usepowerful theoretical frameworks and sophisticated technology.2. Translational Invariance and Conservation ofMomentumWe consider a closed system of N point particles in homogeneousisotropic space. The force on the kth particleis the sum of forces on it due to all the other particles¡! F k =NX ¡! f kj : (1)j=1j6=kWe now consider `virtual' translational displacement ofthe entire N-particle system in the homogeneous space.Newton’s third lawintroduces asimple illustrationof the relationbetween asymmetry and aconservation law.RESONANCE September 2010833