He had a very strong imagination. He sat on a bus, and realized that IF he were to move at light speed, away form a clock. The clock would appear fixed in time. He said that this is because you are going the same speed as the light, so the light that is coming to you is the past. And outside he said because you are going so fast, it would seem to everyone from the outside of the bus, that the people inside the bus were going slower than them in routines, like drinking coffee, or reading a paper. While still flying at light speed.
So he was in belief that light speed, breaks the time barrier.
It sounds like you are confusing special and general relativity. The thought experiment about chasing a beam of light has nothing to do with time dilation but the apparent change of time by an outside observer.
The thought experiment for GR and the Equivalence Principle was quite different:
Imagine youre standing in a room in a spaceship, with no windows. You cant look out, and you cant see what kind of situation or environment the room is in. The rocket engines fire, and you begin to accelerate. Now the question you have to answer is, Is the force you feel the force of gravity or the force of the rockets thrust?
Einsteins answer to the question was that there is no experiment you can make that will differentiate the two causes of the force you feel. In other words, they feel exactly the same. And, indeed, when you get in an elevator and the elevator starts to go up, you feel your weight increase, and the pressure of your feet on the floor increases, just as the elevator starts to move. This feeling dissipates when the elevator achieves constant motion. This fact is so well known, now, that the force of acceleration the pilot feels when a fighter jet pulls out of a steep dive is called g-force, where 1 g is one gravity, 32 ft/sec/sec, the force we feel due to the earths gravity.
Einstein thought, if you cant discriminate the force of gravity and the force of acceleration experimentally, then there really is no difference. The two concepts are just different ways of describing the same thing. In other words, gravity is not an external force reaching out to you like rays propagating from the earths core, its actually the inertia of your own body being deflected from its normal path, just like the car turning induces a centrifugal force and throws you to the side.
