NationMaster - Encyclopedia: Invariant mass

The invariant mass or intrinsic mass or proper mass or just mass is a measurement or calculation of the mass of an object that is the same for all frames of reference. For any frame of reference, the invariant mass may be determined from a calculation involving an object's total energy and momentum. This article or section is in need of attention from an expert on the subject. ... In physics, invariants are usually quantities conserved (unchanged) by the symmetries of the physical system. ... In classical mechanics, momentum (pl. ...

The term rest mass is applied for the mass of a body that is isolated (free) and at rest relative to the observer. By the mass-energy equivalence, the rest mass is equal to the energy content of the isolated (free) body at rest, divided by c². This result is valid also for a composite body, when the body is viewed from an inertial reference frame in which the body's center of mass is at rest and its total linear momentum is zero, called the center of momentum frame. 15ft sculpture of Einsteins 1905 E = mcÂ² formula at the 2006 Walk of Ideas, Germany In physics, mass-energy equivalence is the concept that all mass has an energy equivalence, and all energy has a mass equivalence. ... A line showing the speed of light on a scale model of Earth and the Moon The speed of light in a vacuum is an important physical constant denoted by the letter c for constant or the Latin word celeritas meaning swiftness.[1] It is the speed of all electromagnetic... The center of mass frame (also called the center of momentum frame, CM frame, or COM frame) is defined as being the particular inertial frame in which the center of mass of a system of interest, is at rest (has zero velocity). ...

1 Particle physics
2 Example two particle collision
3 See also
4 References

Particle physics

In particle physics, the mass is often calculated as a mathematical combination of a particle's energy and its momentum to give a value for the mass of the particle that is the same for all observers. This invariant mass is the same for all frames of reference (see Special Relativity). A mass for a particle is m in the equation Thousands of particles explode from the collision point of two relativistic (100 GeV per ion) gold ions in the STAR detector of the Relativistic Heavy Ion Collider. ... In classical mechanics, momentum (pl. ... This article or section is in need of attention from an expert on the subject. ... The special theory of relativity was proposed in 1905 by Albert Einstein in his article On the Electrodynamics of Moving Bodies. Some three centuries earlier, Galileos principle of relativity had stated that all uniform motion was relative, and that there was no absolute and well-defined state of rest...

$left(mc^2right)^2=E^2-(mathbf{p}c)^2$

The invariant mass of a system of decay particles which originate from a single originating particle, is related to the mass of the original particle by a similar equation:

$left(Wc^2right)^2= left(sum Eright)^2-left(sum mathbf{p}cright)^2$

Where:

W

is the invariant mass of the system of particles, equal to the mass of the decay particle.

$sum E$ is the sum of the energies of the particles

$sum mathbf{p}c$ is the vector sum of the momenta of the particles (includes both magnitude and direction of the momenta) times the speed of light,

c

A simple way of deriving this relation is by using the momentum four-vector (in natural units): In classical mechanics, momentum (pl. ... In physics, natural units are physical units of measurement defined in terms of universal physical constants in such a manner that some chosen physical constants take on the numerical value of one when expressed in terms of a particular set of natural units. ...

$p_i^mu=left(E_i,mathbf{p}_iright)$

$p^mu=left(Sigma E_i,Sigma mathbf{p}_iright)$

$p^mu p_mu=eta_{munu}p^mu p^nu=(Sigma E_i)^2-(Sigma mathbf{p}_i)^2=W^2$ , since the norm of any four-vector is invariant.

Example two particle collision

In a two particle collision (or a two particle decay) the square of the mass (in natural units) is In physics, natural units are physical units of measurement defined in terms of universal physical constants in such a manner that some chosen physical constants take on the numerical value of one when expressed in terms of a particular set of natural units. ...

$M^2 ,$	$= (p_1 + p_2)^2 ,$
	$= p_1^2 + p_2^2 + 2p_1p_2 ,$
	$= m_1^2 + m_2^2 + 2left(E_1 E_2 - vec{p}_1 cdot vec{p}_2 right) ,$

References

Halzen, Francis; Martin, Alan (1984). Quarks & Leptons: An Introductory Course in Modern Particle Physics. John Wiley & Sons. ISBN 0-471-88741-2.

Categories: Relativity | Mass | Fundamental physics concepts

Results from FactBites:

What Is The Mass Of A Photon? (592 words)
	However, it is possible to assign a "relativistic mass" to a photon which depends upon its wavelength.
	The mass of an object, though, is a fundamental and invariant property, and one for which we do need a word.
	Technically, it is the invariant length of the particle's four-momentum.

Invariant mass - Wikipedia, the free encyclopedia (363 words)
	The invariant mass or intrinsic mass or proper mass or rest mass or just mass is a measurement or calculation of the mass of an object that is the same for all frames of reference.
	For any frame of reference, the invariant mass may be determined from a calculation involving an object's total energy and momentum.
	In particle physics, the mass is often calculated as a mathematical combination of a particle's energy and its momentum to give a value for the mass of the particle that is the same for all observers.

More results at FactBites »

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Encyclopedia > Invariant mass

Contents

Particle physics

Example two particle collision

See also

References