Invariant Mass

The invariant mass, rest mass, intrinsic mass, proper mass, or (in the case of bound systems or objects observed in their center of momentum frame) simply 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 related by Lorentz transformations. In the center of momentum frame, the invariant mass of a system is simply the total energy divided by the speed of light squared. In other reference frames, the energy of the system increases, but system momentum is subtracted from this, so that the invariant mass remains unchanged.

If objects within a system are in relative motion, then the invariant mass of the whole system will differ from the sum of the objects' rest masses. This also equals to the total energy of the system divided by c2. See mass–energy equivalence for a discussion of definitions of mass. Since the mass of systems must be measured with a weight or mass scale in a reference frame in which the system has zero momentum (the center of momentum frame), such a scale always measures the system's invariant mass. For example, a scale would measure the kinetic energy of the molecules in a bottle of gas to be part of invariant mass of the bottle, and thus also its rest mass. The same is true for massless particles in such system, which add invariant mass and also rest mass to systems, according to their energy.

For an isolated massive system, the center of mass of the system moves in a straight line with a steady sub-luminal velocity (with a velocity depending on the reference frame used to view it). Thus, an observer can always be placed to move along with it. In this frame, which is the center of momentum frame, the total momentum is zero, and the system as a whole may be thought of as being "at rest" if it is a bound system (like a bottle of gas). In this frame, which always exists, the invariant mass of the system is equal to the total system energy (in the zero-momentum frame) 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.

Note that for reasons above, such a rest frame does not exist for single photons, or rays of light moving in one direction. When two or more photons move in different directions, however, a center of mass frame (or "rest frame" if the system is bound) exists. Thus, the mass of a system of several photons moving in different directions is positive, which means that an invariant mass exists for this system even though it does not exist for each photon.

Because the invariant mass includes the mass of any kinetic and potential energies which remain in the center of momentum frame, the invariant mass of a system is usually greater than sum of rest masses of its separate constituents. For example, rest mass and invariant mass are zero for individual photons even though they may add mass to the invariant mass of systems. For this reason, invariant mass is in general not an additive quantity (although there are a few rare situations where it may be, as is the case when massive particles in a system without potential or kinetic energy can be added to a total mass).

Systems whose four-momentum is a null vector (for example a single photon or many photons moving in exactly the same direction) have zero invariant mass, and are referred to as massless. Such systems have an invariant mass of zero. A physical object or particle moving faster than the speed of light would have space-like four-momenta (such as the theoretical tachyon), and these do not appear to exist.

Read more about Invariant Mass:  Invariant Mass Vs. Rest Mass, As Defined in Particle Physics, Example: Two-particle Collision, Rest Energy

Other articles related to "invariant mass, mass, invariant":

Invariant Mass - Rest Energy
... Einstein's famous conclusion about equivalence of energy and mass ... See background for mass-energy equivalence ... On the other hand, the concept of the equivalent Dirac invariant rest mass may be defined in terms of the self energy corresponding to the product of a geometric matter current and a generalized potential as ...
Relativistic Mass Distortion - Conservation Versus Invariance of Mass in Special Relativity
... in reactions between particles, but rest mass (in the sense of being a sum of particle rest masses) may not be conserved through an event in which rest masses of particles are converted to other types of energy, such ... In general, for isolated systems and single observers, relativistic mass is conserved (each observer sees it constant over time), but is not invariant (that is ... Invariant mass, however, is both conserved and invariant (all single observers see the same value, which does not change over time) ...
Center-of-momentum Frame - Properties - Special Relativity
... c is the speed of light) therefore gives the rest mass (positive invariant mass) of the system The invariant mass of the system is actually given by the relativistic ... Systems which have energy but zero invariant mass (such as photons moving in a single direction, or equivalently, plane electromagnetic waves) do not have COM ...
Relativistic Mass Distortion - The Mass of Composite Systems
... The rest mass of a composite system is not the sum of the rest masses of the parts, unless all the parts are at rest ... The total mass of a composite system includes the kinetic energy and field energy in the system ... magnitude) p of the total momentum vector, the invariant mass is given by In a mathematical system where c = 1, for systems of particles (whether ...
Relativistic Mass Distortion - Invariant Mass
... The invariant mass is the ratio of four-momentum to four-velocity and is also the ratio of four-acceleration to four-force when the rest mass is constant ...

Famous quotes containing the word mass:

    No doubt Jews are most obnoxious creatures. Any competent historian or psychoanalyst can bring a mass of incontrovertible evidence to prove that it would have been better for the world if the Jews had never existed. But I, as an Irishman, can, with patriotic relish, demonstrate the same of the English. Also of the Irish.... We all live in glass houses. Is it wise to throw stones at the Jews? Is it wise to throw stones at all?
    George Bernard Shaw (1856–1950)