# Can we give particle with no mass, mass? [duplicate]

Is it possible to take a particle with no mass and give it mass. For example light? Or increase mass?

• Does pair production count? – Jon Custer Jul 14 '16 at 14:19
• Possible duplicate: physics.stackexchange.com/q/17939/2451 – Qmechanic Jul 14 '16 at 14:20
• Particle mass results from interaction with the Higgs field. Unless you can find a way of turning this interaction on or off, the answer must be no. – Lewis Miller Jul 14 '16 at 14:24
• This is definitely a duplicate. – heather Jul 14 '16 at 14:34

Give it a try. The four momentum of a massive particle is $P~=~(E,~\vec p)$ and the invariant momentum interval is $$P^2~=~E^2~-~|\vec p|^2c^2.$$ Since E = $\gamma mc^2$ and $\vec p~=~\gamma m\vec v$ then $P^2~=~m^2c^4$ using $\gamma^2~=~1/(1 - v^2/c^2)$. Now suppose that this particle is converted into a photons with zero mass. This means $P~=~(h\nu,~h\nu/c)$ and $$P^2~=~(h\nu)^2~-~(h\nu)^2~=~0.$$ This implies that $mc^2~=~0$, which means something is wrong.
In the case of the Higgs field, the masses of the $W^\pm,~Z$ particles is due to the absorption of the Goldstone boson that corresponds to the weakly interacting component. This is permissible. If we have two massless particles with the same energy, one with four momentum $P_1~=~(h\nu,~h\nu/c)$ and the other with $P_2~=~(h\nu,~-h\nu/c)$ then $P_1~+~P_2=~(2h\nu,~0)$. this can equal some $mc^2$. The absorption of the Higgs Goldstone bosons is similar to this.