Why do photons travel at the speed of light without having mass?

[madmike159]

Einstein's theory of relativity means that the faster an object travels and the more mass it has the more it will curve space-time. This means something like a spaceship could never travel at the speed of light because it would take an infinite amount of energy to reach that speed. So obviously photons have no mass or else they wouldn’t travel at the speed of light and there would be no speed of light.

However we know from E=hf that photons have a certain amount of energy.

So it should have a mass = E/c^{2}

but that would mean that a photon couldn't travel at the speed of light. Does anyone know why they either don’t have mass or why they are excluded from this rule?

 

[ZapperZ]

Please read the FAQ in this section of PF.

Zz.

 

[HallsofIvy]

No, E= mc² refers to "rest" mass: mass measured in a reference frame where the velocity is 0. Since photons never "rest" it does not apply to them.