Mass and relativity mass measures resistance to changing the velocity This idea is true in relativity (although we have to redefine momentum when v is close to the speed of light)

Mass and Energy Einstein’s internship was to ship a jack-in-the-box to every person on earth. He wondered: should he ship them open or closed? He found that when you close them, they are easier to pack, but a little harder to accelerate! In other words, they have more_______

Mass, energy and Einstein Einstein: when we increase any “internal” form of energy of a system (any energy that is not kinetic energy of the center of mass) we increase its mass! e.g. spring or electrostatic, chemical or nuclear potential energy, KE of vibration, rotation. It’s only noticeable with big energy changes as in nuclear physics. So mass is not conserved in general, because we can add or take away energy from an object or system!

P1. Which otherwise identical car is a tiny bit harder to accelerate? a hot railroad car a cool railroad car

Mass, energy and Einstein Rest energy of an object: Because mass can be turned into energy, and vice-versa, we assign an energy to an object with its center of mass not moving. Now we can require total energy be conserved! Mass units 1 eV/c2 = 1.602x10-19 J /(2.998 x108 m/s)2 = 1.783 x10-36 kg   Atomic mass unit (1/12 of carbon atom mass) 1 u = 1.6605×10−27 kg = 931.494 MeV/c²

Relativistic energy and momentum Each object with its center of mass moving at speed v vs an observer has its own g, and that observer sees a momentum for that particle of and a total energy of Each object has a “rest energy” of , so the kinetic energy is

Momentum, energy and mass The above you don’t need for HW, but it ties these two together: And we see for photons (m=0)

Speed limit in our universe It takes infinite energy (and momentum) for an object with mass to get to the speed of light.

P2. If a particle of mass m moves at v = 0 P2. If a particle of mass m moves at v = 0.95 c, what is the kinetic energy? ______ mc2 A. 0.53 B. 1.3 C. 2.0 D. 2.2 E. 3.2 P3. How much momentum does it have? ____ mc A. 0.5 B. 1.2 C. 1.9 D. 2.1 E. 3.0

P4. How much energy must you add to a particle of at v = 0 P4. How much energy must you add to a particle of at v = 0.95 to get the speed to 0.999c? ______ mc2 A. 2.5 B. 5.4 C. 11 D. 19 E. 22 P5. If I double the speed of a particle from 0.2c to 0.4c, the momentum ______ A. doubles B. increases less than double C. increases more than double.

Mr. Thompkins in Wonderland Read here

Conservation of momentum: classical won’t work An unstable nucleus at rest explodes into pieces with masses M, and 3M. The larger piece is seen traveling to the right at speed 0.9c. How fast (classically) is the small piece going?

Let’s use relativity! An unstable nucleus at rest explodes into pieces with masses 20 GeV/c2, and 60 GeV/c2 . The larger piece is seen traveling to the right at speed 0.9c. How fast is the small piece going?

What was the mass of the original nucleus?

Working with photons: no mass Pretty simple:

Electron-positron annihilation We can sometimes turn mass completely into E/M energy: The photons conserve mass/energy and momentum!

Positron emission tomography Unstable nucleus (tracer) emits positrons. Gamma rays are detected

Electron-positron annihilation Suppose the electron is as rest, and the positron has a total energy of three rest masses. What are the two energies of the photons?

Electron-positron annihilation Suppose the electron is as rest, and the positron has a total energy of three rest masses. What are the two energies of the photons? Which photon has the highest energy? upward downward can be the same

Twin paradox One twin goes to a far planet at a speed so g =3, turns around and then comes home after 20 yrs as she measures it. Her sister has aged by 60 yrs. But why? From each point of view, the other moved away and came back.

Twin paradox Resolution of paradox: What is it about one’s experience that is fundamentally different from the other’s? Something she would notice even with her eyes closed. Acceleration! The one who accelerates the most is younger when they get back together. It doesn’t “prevent ageing”, but acceleration is necessary to get back together, and it determines how the two time streams finally mesh when they meet.