Chapter 5: Relativistic Collisions
Analyzing collisions at relativistic speeds requires four-momentum conservation. Energy and momentum are conserved together as a single four-vector, enabling us to calculate threshold energies and predict particle creation.
Four-Momentum Conservation
\( \sum_{\text{initial}} p^\mu_i = \sum_{\text{final}} p^\mu_f \)
Four equations: one for energy, three for momentum
The power of four-momentum: use invariants! \( (\sum p^\mu)(\sum p_\mu) \) is the same in all frames.
Threshold Energy
To create new particles, the collision must have enough energy. The minimum (threshold) energy is calculated using invariants.
Example: Creating a Pion
p + p → p + p + π⁰ requires Ethreshold = 280 MeV kinetic energy (much more than the pion's 135 MeV rest mass, because momentum must also be conserved).
Compton Scattering
Photon scatters off electron, losing energy (wavelength increases):
\( \Delta\lambda = \frac{h}{m_e c}(1 - \cos\theta) \)
λC = h/mec = 2.43 pm (Compton wavelength)