We have discovered the very useful concept of a relativistic invariant, quantities that have the same value in different reference frames. Specifically

1
We have discovered the very useful concept of a
relativistic invariant, quantities that have the
same value in different reference frames.
Specifically
Invariant Spacetime Interval Ds2 Dx2 Dy2
Dz2 c2 Dt2
Other invariants can also be constructed
Energy-Momentum Invariant E2 - p2c2 E'2 -
p'2c2 m2c4
Note what this says about a massless particle,
like a photon E2 p2c2, or E pc, just like
Maxwell.
2
Summary Relativistic Mechanics
Velocity

• Lorentz Transformation
• Coordinates

Energy-Momentum Invariant
3
Accelerators Adding KE to Charged Particles
LEP Electron Accelerator Maximum Energy KE ? 1011
eV (100 GeV)
Proton Accelerator Maximum Energy KE ? 1012 eV (1
TeV)
Question
How would a Tevatron proton, a LEP positron, and
a 2-eV photon finish in a race down the 2-mile
SLAC linear accelerator?
4
Preliminary the masses
5
Next energies, momenta, speeds, and race results
Over the 2-mile course the ? wins by 130 nm over
the proton and by 32 nm over the electron!
6
Example Using the Energy-Momentum Invariant

• Designing the Bevatron What is the minimum
  energy of a proton beam to produce antiprotons
  in collisions with stationary target protons?
• Energy and momentum are conserved and invariant
  quantities have the same value in all reference
  frames.
• Demand E2-p2c2m2c4 in the lab frame before the
  collision equals the same quantity in the
  center-of-mass frame after.

7
Emc2 and the Energetics of Nuclear Power

• Nuclei are built of protons and neutrons.
• The mass energy of the whole is less than the sum
  of the mass energies of the parts.
• Difference is Binding Energy ?E

Nucleus of mass number A and atomic number Z.
Lure of nuclear power B.E.s 106 ? those of
electrons in atoms.
8
Nuclear Fusion and Fission

• The measure of stability is binding energy per
  nucleon total binding energy divided by the
  number of protons and neutrons.
• Determines whether energy is gained or lost by
  adding/removing a nucleon.
• The most stable nuclei are the middleweights,
  like iron.

• Energy is liberated by fusion of small nuclei
  into bigger ones (stars and major players on the
  weapons scene), or fission of big nuclei into
  middleweights (Xcel Energy and nuclear weapons
  wannabes).