Relativistic Momentum and Energy
Momentum and energy have to be redefined for conservation to hold in every frame, and the redefinition gives every mass a rest energy. Mass and energy become two readings of the same quantity.
What a learner can do afterwards
- Computes relativistic momentum, kinetic energy and total energy for a fast particle
- Relates energy, momentum and rest mass and applies the relation to a massless particle
- Explains rest energy and where it shows up in nuclear reactions
1 · Read
Fast momentum is classical momentum stretched by gamma: p equals gamma m u. At low speeds gamma sits near 1 and the old rule returns. Total energy is E equals gamma m c squared, which splits into rest energy m c squared plus kinetic energy.
At rest the energy is not zero: mass itself holds m c squared. That locked energy breaks out when mass converts, as in fission, fusion, and annihilation. In a fusion reactor hydrogen isotopes become helium, and a small lost mass returns as a large released energy.
Energy, momentum, and mass obey E squared equals p c squared plus m c squared squared. A photon has no mass, so the rule shrinks to E equals p c: it always moves at light speed and carries momentum E over c. In units with c set to 1, a photon of energy 4 carries momentum 4.
No massive thing can reach light speed, since its gamma, momentum, and energy would all have to turn infinite. Light speed is a limit, not a target.
Stretch momentum and energy by gamma, keep rest energy in mass, and let massless light obey E equals p c.
2 · Watch
Take it off screen
Where it sits
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.