ENERGY MASS PRINCIPLE

1. MASS-ENERGY EQUIVALENCE PRINCIPLE AND ITS INTRIGUING APPLICATIONS E=MC2

2. Difference of Mass in Newtonian and Einstenian Mechanics Newton: • Mass is perceived as inertia i.e. resistance to motion. • Mass=m=m0 (Invariant) • F=ma, speed increase without limit! Einstein: • Mass is relativistic i.e. it depends on the motion of body. • Mass=m=m0/[1-(v/c)2]1/2

3. Energy in Newton and Einstenian Mechanics • Newton: energy of a mass m can be calculated by simply from work done definition, i.e.

4. Way to E=mc2 • Einstein: mass is not invariant. So, Since, m=m0/[1-(v/c)2]1/2 , by taking squares Taking differentials,

5. On simplifying, L.H.S is the integrand of our 1st equation, now we have expression for relativistic kinetic energy as, Now we are seeing some familiar terms! We can rewrite above eq. as

6. Put E=mc2 , rearranging last eq. gives Where m0c2 is called “Rest Energy” of particle. For K=0 , E=m0c2 For limit u<<c, we should expect Newtonian kinetic energy. Binomial expansion of kinetic energy eq. gives, E=m0c2

7. How powerful this E=mc2 NEW YORK city in America uses about 1011KW-Hr energy per year.

8. Variation of energy with velocity

9. The variation, as functions of the speed v of a body, of its relativistic energy Ε, its relativistic kinetic energy Κ and its classical kinetic energy Kcl=1/2 m0v2, expressed in units of its rest energy m0c2 , where m0 is the rest mass of the body

10. ENERGY-MASS Principle for MASSLESS PARTICLES Photon rest mass=m0=0. For photons, v=c , (from E= m0 c2 /[1-(v/c)2]1/2), E=0/0 (not interesting!). Dead end??? Luckily we have Quantum Mechanics: Since, E=hf And, f=c/Λ Then, E=hc/Λ, where h/Λ=p=momentum of Photon. E=pc

11. From E=pc and E=m0c2 , after some steps we have, E2=(pc)2+(m0c2)2 This is the most general relation for Energy. So for photons, though m0=0, but they surely have energy and that is E=pc

12. THANK YOU!