"What Einstein already figured out is that as you approach the speed of light, in your reference, time slows down" -- this is not quite correct. Time is as measured by an observer and the clocks in his co-moving reference frame ( let's stay with Special Relativity to avoid the complications of curved space-time). When the observer looks at any processes in a reference frame moving in relation to his, he sees those other clocks as running slow, BUT another observer in the other reference frame sees the original observer's clocks as running slow, too. Nobody sees their own clocks as running slow. The apparent paradox is resolved by remembering that the two observers don't measure the same distances either. The good example is the muons generated by cosmic rays in the upper atmosphere which are seen at the earth's surface, even though their rest frame half lives are too short for them to survive all the way to the surface. As observed by us at the surface the muon half-lives have been lengthened, their time has "slowed down", but as seen by the muon, it's half life is always the same, but because of the relative speed between it and the earth, it observes that the distance from creation to the surface is relativistically shortened so it has plenty of time before decay to travel that short distance. I don't want to speculate much about the photon traveling at the speed of light -- but to abuse the math -- they don't age as observed by anyone else, but any distance they go is relativistically shortened to zero from their reference -- I'm uneasy about that explanation.