Tell that to a black hole.
Hey, I know. That's what's so crazy. Photons have zero mass (citation), which makes sense because according to General Relativity, anything with mass would require infinite energy to get up to light speed.
Yet they can be captured by a black hole and are bent by items with gravity wells. Almost like space is moving into the black hole faster than a photon travels.
Hey, I wonder if I'm on to something.