[clueless (OP)]

(…) So, travelling at close to the speed of light would theoretically allow time travel into the future, as time slows down for the speeding object in order to "protect" the cosmic speed limit of the speed of light. A corollary of all this is that, if it were possible to exceed the speed of light, then it would also be possible to go back in time, which raises the possibility of time-travel paradoxes (where a person goes back in time and interferes in their own past or kills their own grandparents, etc), although some scientists believe that some as yet undiscovered law of physics may intervene to prevent such paradoxes. Actually, special relativity does not specifically forbid the existence of particles that travel faster than light, and there is a hypothetical sub-atomic particle called a tachyon, which would indeed spend its entire life travelling faster than the speed of light, but it is currently still hypothetical.

In physics, spacetime is any mathematical model that combines space and time into a single interwoven continuum. Hence, and behold, our space time continuum. If time machine is accelerating so it reaches the cosmic speed limit of the speed of light, I, clueless, project my gut feeling, which is plausibly an unexpected idea and quite original too. So what does my gut feeling likewise quite possibly flawed logic tell me? Well, since this universe apparently has four dimensions, my opinion is that space cannot exist w/o time, hence space time continuum. So when this time machine reaches the speed of light, time slows down and stops, thus time and three-dimensional space will cancel each other out and time machine will vanish, for w/o the passage of time, time machine cannot neither exist in our universe nor compromise spacetime, having certain laws of physics in mind. Ergo traveling into the future is possible. However, traveling into the past is impossible, which makes tachyons but a fairytale. I guess the question here is, can time slow down so it comes to a halt and then somehow transform into anti-time in order to travel back into the past. Since there is apparently the cosmic speed limit of the speed of light, it is reasonable to assume there is the cosmic time limit of the speed of time, which renders traveling into the past… impossible.
 
Have a nice day. If you can. 

[yor_on]

You can do it this way to. Equalize 'c' to a clock, then the clock has only one direction, locally invariant and frame dependent :)

[clueless (OP)]

Do not speak to me about a clock… A clock is gracious only to Elves, who lack our honor! We but Dwarves came to Elves once, starving, homeless, but they turned their back. They turned their backs to the suffering of my people, and the infernal time that destroyed us. No wonder we and mortal Men doomed to die want to travel back in time to Erebor and Dale, for that is our salvation, all those merry moments we once lived, before Cronus the Terrible flew from the North, and his timeless wings turned our cities into ash.

[yor_on]

Hmm, a little too much warcraft perhaps?
Still, the game of choice :)