# Why can't massless particle exceed speed of light?

Why massless particle can't exceed speed of light?

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It's just what it means for a particle to be massless. For a general motion of a particle in the vacuum, the rest mass $m_0$ satisfies $$m_0^2 c^4 = E^2-p^2 c^2$$ If the left hand side is zero, it follows that $$E=|p|c$$ which means that the energy-momentum vector is null (light-like). In general, the speed may be calculated from the direction of the energy-momentum vector as $v=pc^2/E$ and it equals $v=c$ if the formula above is satisfied. Massless particles are not only unable to move faster than light; they're unable to move slower than light, too. The massless particles must move exactly by the speed of light.

The general absence of any signals that move faster than light is required by the special theory of relativity; a signal or particle that would be moving faster than light would be equivalent (from a viewpoint of a different inertial system) to a signal or particle that moves backwards in time, which would lead to logical contradictions (killing grandfather before he met your grandmother etc.).

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I think your answer is only correct under classical thinking... the more modern answer IMHO would be that ' They must move at the velocity of least resistance which is localized to the quantum fluctuations in their system with respect to uncertain energy introduction from higher dimensions. ' –  Jay May 20 '12 at 15:20
Dear Jay, there is nothing classical about the argument, about energy, about momentum, or the rest mass. All these are standard quantum mechanical observables and my answer was the up-to-date quantum particle-physics answer. Higher dimensions may affect details of particle physics or not but they do not affect this elementary question. –  Luboš Motl Mar 11 '13 at 16:24

To be absolutely simple.... A particle has got a certain mass and acquires a certain dimension in space.. We CAN'T define a Particle with mass=0.

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Aritro you are new here , but you have to realize that there are many physicists here who know that you can have a particle with zero mass, the most known one is called a photon and demonstrates the so called wave/particle duality. Elementary particles are dimensionless anyway, as far as we have been able to measure. –  anna v Jan 4 '13 at 19:13

## protected by Qmechanic♦Jan 4 '13 at 22:08

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