If you had a catapult that could launch humans from 0 to 0.5c then they would be squished into a blob of organic paste about two microns thick.
That is on earth with gravity present, in space there is no such problem. More realistic would be damaging electronics with a massive electromagnetic field, but that can be overcome using technology. For example another electromagnet for shielding. Besides, we are about 50 years away from anti-gravity. Remember the higgs bosson, that small particle - or a wave - gives mass. Because it is a wave it could somehow be used in the future. Somebody tell me, how was the coral castle moved in one night? Ok with pyramids, maybe aliens, maybe 1,000,000 slaves, it was so long ago no one knows, but coral castle is less than 100 years ago, he just moved in 1 (one) night, by himself. You would need a crane, a truck, and about a month to move that castle by yourself - perhaps you wouldn't even be able to move it by yourself, you'd need a dozen illegal alien workers to help you. But he just move it by himself in one night. Look at the tools he used, there is a photo, nothing special. I bet he excited the matter somehow, with some sort of wave, but that is just guessing, we don't know, but we are close to something.
Look, you put an electromagnetic catapult into lunar orbit, so that it is in the dark side of the moon, in the shadow of our sun, this way you don't have to use liquid nitrogen for super conductive magnets, just like in the LHC. That thing would be modular, about 20 meters in diameter and 100 meters in length. You would stick a robotic probe inside of it, point the whole thing into the right direction, and fire.
Just picture a grain of sand, if sun is 100 microns across just like the grain of sand, then Alpha Centuri is 18.6 miles away from it. Picture this massive scale! Dude, light travels from Sun to Alpha Centuri 4 years! It's far far away. If you fire a robotic probe at Alpha Centuri at 50% speed of light, it will get to its destination in 8 to 10 years. Chances that your probe will hit something along its away are so slim, if you doubt it, go back to the scale at the beginning of this paragraph.
Hitting something is space is not a real problem, because most of the space is empty.
Human squishing because of massive acceleration is not a problem either, because at first we will send robotic probes, then dogs and monkeys, then Gagarin's grand son.
Much more real problem is deceleration once the vehicle arrives to Alpha Centuri. Conventional deceleration with booster rockets would not work. Given this just means adding time to our travel, maybe year, maybe more for deceleration, perhaps with solar umbrellas.
