Time dilation and mass increase happens only near large mass, such as Earth or the Sun. An accelerating vessel moving away into deep space will no longer experience these effects. Faster than light travel is possible.

Read about why information processing is fundamental in Nature now.

To dumb it down, you can think of mass having a “slowdown” effect on fundamental operation of physical matter. That is why there’s time dilation and mass increase. However, once out of solar system, a spaceship can accelerate way past the speed of light.

Since gravity emerges the same way as time dilation, it turns out a space debris can be “pulled” out of the way of a speeding spaceship.

It’s time to re-examine Einstein’s relativity in a more practical way. We have means to prove it wrong: send a space probe out to deep space on a trajectory that takes it as far away as possible from any mass. Accelerate the probe, and confirm that time dilation dissipates with distance.

Done!

Not really that hard, is it?