Repeated particle-accelerator tests support the speed-of-light limit, and relativity works for particles moving close to that limit.

“the it's it's just horrible and then like farther out in the solar system is even worse we're not leaving the solar system because the speed of light is just too slow and we're not getting past it we know that we can't go faster than the speed of light we have really good science and really good experimental evidence to that effect um you know we've tested the speed of light limit over and over again in particle accelerators that's a lot of you know particle accelerators get”

“particles up to almost the speed of light we know that our theories of you know relativity work in that domain we know that you cannot get a spaceship going that fast and we know that if you got a spaceship going anywhere near that fast it would have enormous problems with radiation and shielding”