Photons have no "rest mass". They are essentially zero-mass. In fact, objects with zero mass must travel at light speed.
E=MC2 does not say you can't reach lightspeed.
The Lorentz equations are the operable ones. They predict that the mass of a body increases without limit as "C" is approached. In essence, the energy you are putting in to "push" the object to go faster just gets soaked up in its increasing mass, not in velocity.
Photons have no mass, but the do carry momentum.
The reasons that light is affected by gravity is that light always follows "space-time geodesics". Ordinarily, such geodesics are "straight lines". Near a large mass (like the Sun or a black hole) the geodesics of space-time are not "straight" but bent by the gravitation of the body. Therefore light departs from a "straight line" and travels in a curve. This is because--in effect--the warping caused by the mass causes a curved path to be the "shortest distance" for the light to travel.
--Boris
Ah, thank you! For both the science lesson AND the grammar correction! I have always mixed those two up...
Sorry, I overlooked this one... By "no rest mass," do you mean that they have no mass when "still"? If objects with zero rest mass must travel at light speed (and are therefore never "resting"), how do we know that they have no mass while at rest? Please tell me to shut up if I'm annoying you with these simplistic questions :-)