Chapter 37Special Relativity

(Momentum and Energy)

Relativistic Momentum

Relativistic EnergyAn 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.

Rest EnergyThe relativistic energy given earlier E=γmc2 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 E0 instead of E to emphasize it is the energy at rest although it is actually just a special case of E.

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

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.

Common unit: eV/c for Momentum

Energy of a speedy proton 1

Find the rest energy of a proton in electron volts.

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?

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

Relativistic Kinetic energy

The KE is the difference between the total energy and the rest energy. Another way is to write it as:

E =E0 +KE

Newtonian limit of KE

Please remember that the above result is only true at very low speed.

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?

Energy Summary

Momentum and Energy

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

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?

Velocity From p and E

Doppler Effect

General Relativity

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

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.

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

Expansion of Universe

The cosmological constant

“The greatest blunder of my life.”Einstein

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