Does an object's mass increase as it speeds up?

Modern usage keeps mass as the invariant rest mass and attributes the growth of inertia at high speed to the rising relativistic energy and momentum; the older 'relativistic mass' language describes the same physics but is now generally avoided.

How can a photon have momentum if it has no mass?

The invariant relation E^2 = (pc)^2 + (mc^2)^2 reduces for a massless particle to E = pc, so a photon carries momentum proportional to its energy, which is what makes radiation pressure and Compton scattering possible.

Relativistic Energy and Momentum

In special relativity energy and momentum combine into a single four-vector whose invariant length is the rest mass, giving the famous relation E = mc^2 and a conserved quantity for all high-speed processes.

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Definition

Relativistic energy and momentum are the time and space components of the energy-momentum four-vector p = (E/c, p), whose conserved total governs particle dynamics and whose invariant magnitude equals the rest mass times c.

Scope

This topic covers the relativistic definitions of momentum and energy, the energy-momentum four-vector, the invariant relation E^2 = (pc)^2 + (mc^2)^2, rest energy and mass-energy equivalence, the behavior of massless particles such as photons, and the conservation of four-momentum in collisions, decays, and reactions.

Core questions

How must momentum and energy be redefined so that conservation laws hold in every inertial frame?
What does E = mc^2 mean for a body at rest, and how does energy add to mass?
How can massless particles like photons carry momentum and energy?

Key concepts

Relativistic momentum
Rest energy and rest mass
Energy-momentum four-vector
Invariant E^2 = (pc)^2 + (mc^2)^2
Massless particles
Conservation of four-momentum

Key theories

Energy-momentum four-vector: Energy and momentum are the components of a single four-vector that transforms by the Lorentz transformation, so that total four-momentum is conserved in all frames and its invariant magnitude is the rest mass.
Mass-energy equivalence: A body at rest possesses rest energy E = mc^2, and any change in its internal energy changes its mass correspondingly, so that mass is a form of energy and the two are interconvertible in nuclear and particle processes.

Clinical relevance

Mass-energy equivalence underlies the energy release of nuclear fission and fusion, the creation and annihilation of particle-antiparticle pairs in colliders and in PET imaging, and the binding-energy accounting that explains why stars shine and why some nuclei are stable.

History

Einstein's short 1905 follow-up paper deduced that a body emitting energy loses mass, giving mass-energy equivalence; the relation was sharpened by Planck and others and decisively confirmed by nuclear physics in the 1930s, where measured binding energies matched mass defects.

Key figures

Albert Einstein
Max Planck
Gilbert N. Lewis

Seminal works

einstein1905b
rindler2006

Frequently asked questions

Does an object's mass increase as it speeds up?: Modern usage keeps mass as the invariant rest mass and attributes the growth of inertia at high speed to the rising relativistic energy and momentum; the older 'relativistic mass' language describes the same physics but is now generally avoided.
How can a photon have momentum if it has no mass?: The invariant relation E^2 = (pc)^2 + (mc^2)^2 reduces for a massless particle to E = pc, so a photon carries momentum proportional to its energy, which is what makes radiation pressure and Compton scattering possible.