Is it possible to break the time barrier if we break the light-speed barrier?

The problem with breaking light speed is mass. The faster you go the more you weigh. By approaching light speed your mass becomes unbearable. The idea you are having is more solvable by actually creating a worm hole. By ripping through the fabric of time space you may be able to travel great distances and or hit different points in time.

The way I see it, space and time are like fabric, and space is much less stable than time. If you broke the light-speed barrier, you would only break through space, and create a "warp zone" or wormhole or enter hyperspace. Perhaps if you went faster than the speed of darkness...

Yes. If people traveled faster than light then magic would exist and anything could be possible.
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this is reply to the answer below. Everyone use to think the human could not go faster than 55 mph. when the first auto mobiles were built. Se how fast we are going now. Were are achieving Mach Speeds (Faster than Sound) give Us time Im sure somebody will do Light speed so me day.

I don't think so. Sound and light travel at certain rates of speed. Time is something altogether different.
Time is a way of looking at things. it is a tool with which we manage the world to make sense of 'all this' it is always Now the past and the future are mental constructs  What happens to make it awhile ago ? What happens to make it after awhile? time is the very fabric of which our perception of the world is made of.
I don't see how physical speed can 'out run'. that. Notwithstanding there are ways to alter our perception of time, but you will always find yourself in the now.Although we ARE IN THE NOW OUR MINDS ARE IN THE PAST OR DREAMING OF THE FUTURE NEITHER WHICH IS REAL.
THERE IS ONLY RIGHT NOW.

hitting the light speed barrier would do nothing but baisicaly "stop time" for you. in order to say travel to other times you would have to go faster than that. i think it was in order to go back in time you have to catch up to that light, in order to go forward in time you have to reach that light before it gets here

The magic is called entanglement.

You could go back in time. Time has a reflective wave, and this wave is like the reflective wave of the mismatched load, where the energy is not fully absorbed into the load. This is a reversal of the (in this case) light, so you cab go back or forward in time at the speed of light.