Massless particle
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A massless particle is a particle whose invariant mass is zero. Currently, the only known massless particles are gauge bosons: the photon (carrier of electromagnetism) and the gluon (carrier of the strong force). However, gluons are never observed as free particles, since they are confined within hadrons.
Neutrinos were, until recently, thought to be massless; but, because neutrinos change flavour as they travel, they must have mass. (See below.)
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[edit] Special relativity
The behavior of massless particles is understood by virtue of special relativity. See Mass in special relativity.
[edit] Dynamics
Massless particles do not experience time. This is why flavour change is impossible for massless particles, and why neutrinos must be massive.
The way that massless particles feel forces is more complicated than that for massive particles. Photons are known to experience the same gravitational acceleration as other particles (which provides empirical evidence for the equivalence principle), because it is their relativistic mass that acts as the gravity charge. Acceleration and velocity are both vector quantities, and they must be perpendicular to conserve speed, the magnitude of velocity. Thus, forces acting on massless particles simply change their direction of motion, the angle change in radians being GM/rc2 with gravitational lensing, a result predicted by general relativity. Massless particles move in straight lines relative to spacetime, and gravitational lensing relies on spacetime curvature. Gluon-gluon interaction is a little different: they exert forces on each other but, because the acceleration is parallel to the line connecting them (albeit not at simultaneous moments), the acceleration will be zero unless the gluons move in a direction perpendicular to the line connecting them (so that velocity is perpendicular to acceleration).
[edit] Gravitons
General relativity implies that gravitation is quantized by the graviton, which is a massless tensor boson (i.e. it has spin 2), which general relativity can only describe when expressed as Einstein-Cartan theory.