The Physics
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Opus in profectus

# Mass-Energy

## Summary

• The special theory of relativity is a founded on two postulates (assumed truths).
1. The laws of physics are invariant in all inertial reference frames.
• An invariant property is one that does not change under any circumstances.
• An inertial reference frame is one where the observer is not accelerating.
2. The speed of light in a vacuum is the same for all sources and observers
• The speed of light is not affected by the motion of the source or the observer.
• This results in two new equations for the energy and momentum of a moving object.
• Relativistic energy  E = mc2 √(1 − v2/c2)
or using the Lorentz gamma notation…

E = γmc2

For objects at rest (v = 0, γ = 1) this reduces to the mass-energy equivalence.

E = mc2

• Relativistic momentum  p = mv √(1 − v2/c2)
or using the Lorentz gamma notation…

p = γmv

At low speeds (v → 0, γ → 1) this reduces to the classical equation for momentum.

p = mv

• These two equations can be combined mathematically to yield a relativistic energy-momentum relation.
• In general, for massive particles in motion, the equation is written as…

E2 = p2c2 + m2c4

• For massive particles at rest, the equation reduces to the mass-energy equivalence

E = mc2

• For massless particles (e.g. photons) moving at the speed of light, the equation reduces to…

E = pc