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Relativistic Mechanics

Relativistic Mechanics. Momentum and energy. Momentum. p = g mv Momentum is conserved in all interactions. Total Energy. E = g mc 2 Total energy is conserved in all interactions. Rest Energy. E = g mc 2 If v = 0 then g = 1, E = mc 2 Rest energy is mc 2

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Relativistic Mechanics

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  1. Relativistic Mechanics Momentum and energy

  2. Momentum p = gmv Momentum is conserved in all interactions.

  3. Total Energy E = gmc2 Total energy is conserved in all interactions.

  4. Rest Energy • E = gmc2 • If v = 0 then g = 1, E = mc2 • Rest energy is mc2 • Kinetic energy is (g–1)mc2

  5. Mass is Energy • Or, E = K + mc2 • Particle masses often given as energies • More correctly, as rest energy/c2 • Customary unit: eV = electron·Volt • 1 elementary charge pushed through 1 V • Just like 1 J = (1 C)(1 V) • e = 1.60×10–19 C, so 1 eV = 1.60×10–19 J

  6. Particle Masses • Electron 511 keV/c2 • Proton 983.3 MeV/c2 • Neutron 939.6 MeV/c2

  7. Correspondence At small b: Momentum gmvmv Energy gmc2 = (1–b2)–1/2mc2 Binomal approximation (1+x)n 1+nxfor small x So (1–b2)–1/2 1 + (–1/2)(–b2) = 1 + b2/2 gmc2mc2 + 1/2 mv2 Is this true? Let’s check:

  8. Convenient Formula E2 = (mc2)2 + (pc)2 • Derivation: show R side = (gmc2)2

  9. A massless photon • p = h/l • E = hf = hc/l • h = 6.62610–36 J·s (Planck constant) • gmc2 incalculable: g = and m =0 • But E2 = (mc2)2 + (pc)2 works: • E2 = 0 + (hc/l)2 = (hf)2 • E = hf

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