Relativistic Energy & Momentum
Energy and momentum form another invariant spacetime structure. Rest energy, kinetic energy, and momentum fit one relation that reduces to familiar Newtonian formulas only at low speed.
What replaces Newtonian momentum and kinetic energy near light speed?
The Lorentz factor enters both momentum and total energy. Their values depend on frame, but the combination does not: it returns the object's rest energy squared in every inertial frame.
For a massive object at rest, and the total energy is still .
Move along one energy-momentum hyperbola.
At low speed γ ≈ 1, so Newtonian momentum reappears. Near c, the relativistic correction grows rapidly.
Its low-speed expansion approaches ½mv², but the exact relativistic expression remains valid all the way toward c.
The current energy-momentum values reconstruct 89.88 PJ of rest energy, matching mc² despite the boost.
frame-dependent vector quantity
includes rest energy and kinetic energy
approaches ½mv² when v ≪ c
Classical energy and momentum are the low-speed limit of this structure.
The conservation ideas from Mechanics survive; the formulas change so that conservation remains compatible with Lorentz symmetry.