well humans aren\'t very far yet in this field. Right now at the most advanced tech we have that could be in use is Ion Engines. The Mini-Magnetospheric Plasma Propulsion is still in development. And as for Gravitational Engines, scientists right now don\'t really no where to begin, it\'s still all pen and paper.
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I got the rest of this info from a different website, this is not my own info, but I thought I\'d share it.
One of the reasons that prevent any object with a mass going at or faster than the speed of light is that the mass is not constant - it increases with velocity and it goes to infinity at the speed of light. So that eventually you need infinite amounts of energy to accelerate infinite mass past the speed of light mark. (and as far as I know we have yet to find an infinite source of energy.
We really do not know what would happen to time when an object passes the speed of light. The only thing we have to rely on is the Special Theory of Relativity (Einstein 1905) and according to it time in a moving reference frame (say your space ship) goes slower as compared to a stationary frame (say Earth) the faster you go. In fact the equation that governs this so called time dilation is given below:

So you see when you start off - at zero speed (0% of speed of light) your time is just regular i.e. the time slowing factor (xt) is equal to 1. As you speed up your time runs slower by the factor shown on the y-axis. As you are approaching 100% of the speed of light your time slows more and more until it is infinitely slowed down. (You should realize that everything slows down including your heart beats, your thoughts, etc.) So for an example if your ship goes at 98% of the speed of light and you take a one year journey, when you return to Earth five years have gone by.

This region of speeds below 100% of the speed of light is the region of our regular time or Real Time.
Now say somehow you were able to go faster than the speed of light (i.e. the v in the above equation is now greater than c the speed of light). The equation will then give us a square root of a negative number on the right hand side (which is an imaginary number.) Well I can factor out the imaginary unit number (i or the square root of minus one) and plot the result on the same graph. This region I call Imaginary Time since it is some weird time with an imaginary unit attached to it (so I don\'t really know what this time means.)
However you see that time in this imaginary region will speed up from infinity to the regular time speed of 1 and continue speeding up. At 140% or higher speed of light, time slowdown factor is less than one, i.e. time will go faster than in the stationary frame! So for an example if your ship goes at 200% of the speed of light and you take a one year journey, when you return to Earth only about 7 months have gone by. However I need to stress again that this is just a crazy thought experiment which produces some weird imaginary time and has no physical meaning.
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My own thoughts:
So what I believe is that maybe we can go pass the speed of light but only if the rules are bent, not broken.