And we cannot even approach half the speed of light:
A paper published in Natural Science brings some boring common sense to the speed-of-light-travel table. In order to travel huge distances in next to no time, people need to travel close to the speed of light. In so doing, travelers cover extremely large distances very quickly and, thanks to the quirks of relativity, would feel like it took mere minutes because of an effect known as time dilation, which squashes perceived time.
Trouble is, traveling close to the speed of light brings about other effects, too. In Natural Science, Edelstein and Edelstein point out that hydrogen in any craft cable of traveling at the speed of light would also prevent it from traveling at the speed of light. They explain:
Unfortunately, as spaceship velocities approach the speed of light, interstellar hydrogen H, although only present at a density of approximately 1.8 atoms/cm3, turns into intense radiation that would quickly kill passengers and destroy electronic instrumentation. In addition, the energy loss of ionizing radiation passing through the ship's hull represents an increasing heat load that necessitates large expenditures of energy to cool the ship.
In other words, travel close to the speed of light and you'll be bombarded with so much radiation that you kick the bucket. The knock-on effect is that even if it's possible to create a craft capable of traveling close the speed of light, it wouldn't be able to transport people.
Instead, there's a natural speed limit imposed by safe levels of radiation due to hydrogen, which means humans couldn't travel faster than half the speed of light unless they were willing to die almost immediately. - http://gizmodo.com/5957697/super-fast-space-travel-would-kill-you-in-minutes
As an object approaches the speed of light, its mass rises precipitously. If an object tries to travel 186,000 miles per second, its mass becomes infinite, and so does the energy required to move it. For this reason, no normal object can travel as fast or faster than the speed of light. - http://science.howstuffworks.com/science-vs-myth/what-if/what-if-faster-than-speed-of-light.htm
Ever since the 19th Century and early 20th Century discoveries of the nature of electromagnetic radiation and subatomic particle physics, the fact that particle and electromagnetic radiation in space is deadly to potential space travelers and even deadlier at speeds that are a significant fraction of the speed of light has been well known. So your concern represents a strawman argument insofar as it may pretend there had ever been a serious proposal for humans to attempt to accelerate a space craft to those high speeds. In reality, the only serous proposals seek to a means of transiting interstellar distances using relatively slow speed spacecraft over periods of generations or discover a means of transiting those interstellar distances within fractions of a year or number of years by utilizing the effects of quantum mechanics to bypass normal spacetime and its relativistic restrictions.