2. Relativistic Momentum

3. Relativistic Energy An object of mass m moving at velocity v has a total energy given by: Recall that γ≥1 and c is a very very big number, this means that in general E is a huge number.

4. Rest Energy The relativistic energy given earlier E=γmc 2 has a strange implication: When an object is at rest ( v =0 ), this gives γ =1. However the energy is still non-zero. This means an object with mass always carries non- zero amount of “intrinsic” energy even when not in motion. This energy is call the rest energy. Einstein’s most famous equation. We sometimes write E 0 instead of E to emphasize it is the energy at rest although it is actually just a special case of E.

5. An exploding chicken Calculate the total energy released if a 1kg chicken is converted into energy completely.

6. Common unit: eV for Energy J is the SI unit for energy, however in particle physics (where relativity is used most frequently) we often use another more convenient unit, the electron volts ( eV ), because the energy in particle physics is often very small.

7. Common unit: eV/c for Momentum

8. Energy of a speedy proton 1 Find the rest energy of a proton in electron volts.

9. Energy of a speedy proton 2 The total energy of a proton is three times its rest energy. What is the speed of the proton?

10. Electron mass in MeV Given the mass of the electron is 0.511MeV, find its mass in kg.

11. Relativistic Kinetic energy The KE is the difference between the total energy and the rest energy. Another way is to write it as: E =E 0 +KE

12. Newtonian limit of KE Please remember that the above result is only true at very low speed.

13. Energy of a speedy proton 3 The total energy of a proton is three times its rest energy. What is the KE of the proton?

14. Energy Summary

15. Momentum and Energy This equation is often useful in computing either energy or momentum of an object when the velocity is not given explicitly.

16. Energy of a speedy proton 4 The total energy of a proton is three times its rest energy. What is the momentum of the proton?

17. Velocity From p and E

18. Doppler Effect

19. General Relativity

20. Testing General Relativity  General relativity predicts that a light ray passing near the Sun should be deflected in the curved space-time created by the Sun’s mass  The prediction was confirmed by astronomers during a total solar eclipse

21. Precession of Mercury Newtonian theory (after taking into account things such as the gravitational forces from the other planets, the non- spherical shape of the sun…) differs from observation by 43 arc second (43’’ = 0.012°) per century. This tiny difference is perfectly explained in the general theory of relativity.

22. Black Holes  If the concentration of mass becomes very great, a black hole may form  In a black hole, the curvature of space-time is so great that, within a certain distance from its center, all light and matter become trapped

23. Expansion of Universe The cosmological constant “The greatest blunder of my life.” Einstein

24. Experimental Tests of Relativity Muon decay Clocks flying around the world Clocks on a tower GPS The bending of starlight Gravitational radiation of binary stars Particle accelerators Compton effect … and many many more

25. Units 1eV = 1.6×10 -19 J