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FULL QUESTION: When I observe the theories written about the posibility of 'time travel' one question comes into my head, it is proofed that, if a massive body (doesn't matter how small its mass is) moves with the speed of light its mass becomes infinte, then why photons (light particles)  made such a long journey in the universe? do they are acted up on by an infinite force?

ANSWER : Because light has a dual nature, photons are not actually particles in space, they show particle nature only when interacting with other matter on an atomic level.

"massive" bodies cannot truly achieve the speed of light.

The logic is, if you go far away, and then return, you will have effectively traveled a little into the future (according to relativity), depending on how far you traveled.

Since you need to go very far to make a noticeable difference, it seems you need the speed of light.

That's untrue, you can use wormholes (shortcuts of the universe), to go quite far and return without using any incredible speed.