Invariant mass

You don't need to be Editor-In-Chief to add or edit content to WikiDoc. You can begin to add to or edit text on this WikiDoc page by clicking on the edit button at the top of this page. Next enter or edit the information that you would like to appear here. Once you are done editing, scroll down and click the Save page button at the bottom of the page.

"Proper mass" redirects here. For the liturgical mass proper, see Proper (liturgy).

The invariant mass, intrinsic mass, proper mass or just mass is a characteristic of the total energy and momentum of an object or a system of objects that is the same in all frames of reference. When the system as a whole is at rest, the invariant mass is equal to the total energy of the system divided by c², which is equal to the mass of the system as measured on a scale. If the system is one particle, the invariant mass may also be called the rest mass.

Since the center of mass of an isolated system moves in a straight line with a steady velocity, an observer can always move along with it. In this frame, the center of momentum frame, the total momentum is zero, the system as a whole may be thought of as being "at rest" (though in a disconnected system, parts may be moving away from each other), and the invariant mass of the system is equal to the total system energy divided by c². This total energy in the center of momentum frame, is the minimum energy which the system may be observed to have, when seen by various observers from various inertial frames.

Image:Rest mass 0 and 1.svg

Possible 4-momenta of particles. One has zero invariant mass, the other is massive

Particle physics

In particle physics, the invariant mass is a mathematical combination of a particle's energy E and its momentum p which is equal to the mass in the rest frame. This invariant mass is the same in all frames of reference (see Special Relativity).

$(mc^2)^2=E^2-||\mathbf{p}c||^2\,$

or in natural units where c = 1,

$m^2 = E^2 - ||\mathbf{p}||^2 \,$

This equation says that the invariant mass is the relativistic length of the four-vector (E, p), calculated using the relativistic version of the pythagorian theorem which has a different sign for the space and time dimensions. This length is preserved under any Lorentz boost or rotation in four dimensions, just like the ordinary length of a vector is preserved under rotations.

Since the invariant mass is determined from quantities which are conserved during a decay, the invariant mass calculated using the energy and momentum of the decay products of a single particle is equal to the mass of the particle that decayed. The mass of a system of particles can be calculated from the general formula:

$\left(Wc^2\right)^2= \left(\sum E\right)^2-||\sum \mathbf{p}c||^2$

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

$\sum \mathbf{p}$ is the vector sum of the momenta of the particles (includes both magnitude and direction of the momenta)

Example: two particle collision

In a two particle collision (or a two particle decay) the square of the invariant mass (in natural units) is

$M^2 \,$	$= (E_1+E_2)^2-\|\|\textbf{p}_1 + \textbf{p}_2\|\|^2 \,$
	$= m_1^2 + m_2^2 + 2\left(E_1 E_2 - \textbf{p}_1 \cdot \textbf{p}_2 \right) \,$

References

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

da:Hvilemasse de:Invariante Masse is:Hvíldarmassi it:Massa a riposo hu:Invariáns tömeg sl:Mirovna masa sv:Vilomassa uk:Маса спокою

Acknowledgement and Attribution Regarding Sources of Content

Some of the initial content on this page may be incorporated in part from copyleft sources in the public domain including wikis such as Wikipedia and AskDrWiki. Drug information for patients came from the The National Library of Medicine. Infectious disease information may have come from the Centers for Disease Control (CDC). Differential Diagnoses are drawn from clinicians as well as an amalgamation of 3 sources: 1.The Disease Database; 2. Kahan, Scott, Smith, Ellen G. In A Page: Signs and Symptoms. Malden, Massachusetts: Blackwell Publishing, 2004:3; 3. Sailer, Christian, Wasner, Susanne. Differential Diagnosis Pocket. Hermosa Beach, CA: Borm Bruckmeir Publishing LLC, 2002:7 .

Invariant mass

Particle physics

Example: two particle collision

See also

References

Acknowledgement and Attribution Regarding Sources of Content

Views

Personal tools

Search

Navigation

Help

Toolbox

In other languages