RELATIVISTIC MASS IS NOT A SCALAR QUANTITY
gopalan sudhakaran
PROFESSOR OF PHYSICS at I AM DOING RESEARCH ON MY OWN WAY AT "CHETHANA,H&C ROAD, WEST MUNDAKKAL,KOLLAM, INDIA,PIN-691001
Relativistic mass is not a scalar quantity.Consider the FOUR MOMENTUM VECTOR. P={[m(0)U]}.Here m(0) is the REST MASS.U is the FOUR VELOCITY VECTOR. BUT U=[d/dT](ct,x,y,z). dT is proper time differential . (ct,x,y,z) is POSITION FOUR VECTOR OF THE PARTICLE.WE WRITE d/dT=[d/dt][dt/dT]acting on (ct,x,y,z)=L(u)d/dt(ct,x,y,z).L(u)=Lorentz factor. dt is coordinate time differential.But d/dt (ct,x,y,z)=(c,dx/dt,dy/dt,dz/dt)=(c,u(x),u(y),u(z))=So the FOUR VELOCITY is given by L(u)(c,u(x),u(y),u(x)).HERE (u(x)L(u),u(y)L(u),u(x)L(u)) are the spatial components of FOUR VELOCITY VECTOR.[cL(u)]is the temporal component of the FOUR VELOCITY VECTOR.The NORM OF THE FOUR VELOCITY VECTOR is defined by =c.c=square of velocity of light.SO FOUR MOMENTUM VECTOR=m(c,u(x),u(y),u(x))=(mc,mu(x),mu(y),mu(x)). mc=E/c=the time component of FOUR MOMENTUM VECTOR. HERE m=RELATIVISTIC MASS=m=m(0)L(u) showing that ‘’m’’ is NOT AN ABSOLUTE SCALAR