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Canonical static concept record

Energy–momentum four-vector

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Summary

The four-vector $p^\mu=(E/c,\mathbf p)$ satisfying the mass-shell relation for a free particle.

Record metadata

Canonical name: Energy–momentum four-vector
Concept ID: energy_momentum_four_vector
Content version: 2.3.0
Primary field: Physics
Fields: Physics
Primary domain: Relativity & gravitation
Domains: Relativity & gravitation
Alternate terminology: No alternate terminology is currently authored for this record.
Concept type: Relativistic quantity

Concept sources

Wikipedia — Four-momentum — Four-momentum · encyclopedic reference · source ID wp-physics-energy_momentum_four_vector
Cambridge — Dynamics and Relativity — Dynamics and Relativity · University of Cambridge lecture notes · source ID tong-relativity
PDG — Review of Particle Physics 2026 — Review of Particle Physics 2026 · Particle Data Group reference · source ID pdg-rpp

Incoming relations (arrows to this concept)

Each relation below ends at this concept.

Energy Energy–momentum four-vector

Permalink to relation

This is an authored directed relation from the source endpoint to the target endpoint.

Relation ID: energy_to_fourmomentum
Relation type: Theory component theory-component
Direction: source → target
Endpoint roles: source: Contributes to; target: Contains theory component
Authored annotation: time component

Authored explanation

Energy is the time component, up to units, of relativistic four-momentum.

How to interpret this relation type

The source supplies a substantive formal ingredient, dynamical sector, law, field content, or mechanism of the target theoretical framework.

Relation sources

Wikipedia — Energy — Energy · encyclopedic reference · source ID wp-physics-energy
nLab — energy — energy · mathematical physics reference · source ID nlab-physics-energy
Cambridge — Classical Dynamics — Classical Dynamics · University of Cambridge lecture notes · source ID cambridge-classical-dynamics
Cambridge — Dynamics and Relativity — Dynamics and Relativity · University of Cambridge lecture notes · source ID tong-relativity
Wikipedia — Four-momentum — Four-momentum · encyclopedic reference · source ID wp-physics-energy_momentum_four_vector
PDG — Review of Particle Physics 2026 — Review of Particle Physics 2026 · Particle Data Group reference · source ID pdg-rpp

Four-vector Energy–momentum four-vector

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This is an authored directed relation from the source endpoint to the target endpoint.

Relation ID: fourvector_to_momentum
Relation type: Framework specialization framework-specialization
Direction: source → target
Endpoint roles: source: Specializes to; target: Special case or refinement of
Authored annotation: four-momentum

Authored explanation

Energy and three-momentum form a four-vector.

How to interpret this relation type

A more specific theory, model, entity class, or regime is obtained by restricting or extending the scope of a broader framework.

Relation sources

Wikipedia — Four-momentum — Four-momentum · encyclopedic reference · source ID wp-physics-energy_momentum_four_vector
Cambridge — Dynamics and Relativity — Dynamics and Relativity · University of Cambridge lecture notes · source ID tong-relativity
Wikipedia — Four-vector — Four-vector · encyclopedic reference · source ID wp-physics-four_vector
nLab — Minkowski spacetime — Minkowski spacetime · mathematical physics reference · source ID nlab-physics-minkowski_spacetime

Linear momentum Energy–momentum four-vector

Permalink to relation

This is an authored directed relation from the source endpoint to the target endpoint.

Relation ID: momentum_to_fourmomentum
Relation type: Theory component theory-component
Direction: source → target
Endpoint roles: source: Contributes to; target: Contains theory component
Authored annotation: spatial components

Authored explanation

Linear momentum supplies the spatial components of relativistic four-momentum.

How to interpret this relation type

The source supplies a substantive formal ingredient, dynamical sector, law, field content, or mechanism of the target theoretical framework.

Relation sources

Wikipedia — Momentum — Momentum · encyclopedic reference · source ID wp-physics-linear_momentum
nLab — momentum — momentum · mathematical physics reference · source ID nlab-physics-linear_momentum
Cambridge — Classical Dynamics — Classical Dynamics · University of Cambridge lecture notes · source ID cambridge-classical-dynamics
Cambridge — Dynamics and Relativity — Dynamics and Relativity · University of Cambridge lecture notes · source ID tong-relativity
Wikipedia — Four-momentum — Four-momentum · encyclopedic reference · source ID wp-physics-energy_momentum_four_vector
PDG — Review of Particle Physics 2026 — Review of Particle Physics 2026 · Particle Data Group reference · source ID pdg-rpp

Outgoing relations (arrows from this concept)

Each relation below starts at this concept.