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Rest mass (invariant mass) in physics

Rest mass is the invariant mass of a particle or system measured in its rest frame. It is a Lorentz‑invariant property distinct from outdated 'relativistic mass' and central to mass–energy relations.

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Overview

Rest mass, often called invariant mass, is the mass of a particle or isolated system measured in the frame where the system as a whole is at rest. It is a scalar quantity that does not change with the observer's uniform motion and therefore differs conceptually from the older idea of "relativistic mass." For introductory context see further reading.

Key characteristics

  • Frame independence: rest mass is invariant under Lorentz transformations and has the same value in every inertial frame.
  • Relation to energy and momentum: energy E, momentum p and rest mass m are linked by E² = (pc)² + (mc²)², so mass and energy are closely related.
  • Massless particles: some particles (for example, photons) have zero rest mass yet carry energy and momentum.
  • System mass: the invariant mass of a composite system can differ from the sum of component rest masses because kinetic and binding energy contribute to the total.

Historical development

The concept of rest mass gained precision with special relativity and Einstein's mass–energy equivalence. Early 20th‑century literature sometimes used a velocity‑dependent "relativistic mass," but modern practice favors the invariant rest mass as the fundamental property. For a concise historical note see background and a technical perspective at additional source.

Uses and examples

Rest mass is central in particle physics and cosmology. It labels elementary particles (electrons, protons) and appears in decay and collision kinematics: the invariant mass of decay products identifies parent particles. A notable example: two photons traveling in opposite directions can form a system with nonzero invariant mass even though each photon individually has zero rest mass. Practical references are available at related material.

Distinctions and notable facts

Important distinctions: rest (invariant) mass vs relativistic mass; rest mass is intrinsic to a particle, whereas energy and momentum depend on frame. Binding energy alters the mass of bound systems (for example, atomic nuclei have mass slightly less than the sum of their constituents because binding energy reduces total mass). In general relativity mass appears in the stress–energy tensor, which sources spacetime curvature; here energy, pressure and momentum all contribute to gravitational effects.

Formula

When using natural units in particle physics, energy and mass have the same unit. The center-of-mass energy is then generally the square root of the total quadrature momentum:

\sqrt{s} = \sqrt{ \left( \sum_{i=1}^n{P_i} \right) ^2} ,

where by the square is meant the scalar product of the Minkowskimetric:

\sqrt{s} = \sqrt{ \left( \sum_{i=1}^n{P_{\mu, i}} \right) \cdot \left( \sum_{i=1}^n{P_i^\mu} \right) }.

Here is

  • nis the number of particles
  • P_{i}their quad pulses.

Properties

  • The center-of-mass energy is invariant under Lorentz transformations; hence the name invariant mass. This follows from the fact that the sum of four-vectors is a four-vector and the square of a four-vector is a Lorentz scalar, i.e. a scalar which remains invariant under Lorentz transformations. Correspondingly, the root of a Lorentz scalar is also a scalar.
  • The center-of-mass energy of all particles before a collision is equal to their center-of-mass energy after the collision (conservation quantity).

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AlegsaOnline.com Rest mass (invariant mass) in physics

URL: https://en.alegsaonline.com/art/82318

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