The deep reason for why and how photons have no mass is something that Physicists have been trying to figure out since Einstein. Truely understanding photons would revolutionize modern science. What we do know is; to make all the physics equations that we have work right, we have to assume photons have zero mass.
For an interesting read about what happens when things with mass get close to the speed of light I suggest : [Relativistic Baseball (xkcd.com)](https://what-if.xkcd.com/1/)
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