So if there is no known way that the laws of physics can currently support what we see on the screen, it is the responsibility of the writers to come up with some relatively convincing way for us to suspend our disbelief. In this case, you can't just say we have some new technology that just works because it is not a matter of technology. Simulating gravity is squarely a physics problem, and most of the time there is no attempt to explain it to audiences.
To make matters even worse, if a space ship undergoes any acceleration, it must still be felt inside the ship. Given the speeds that we are supposed to believe are being reached in short periods of time in order to travel huge distances, the number of g's involved would immediately kill you in the real world. Most film and TV shows will have the crew knocked around a bit from time to time, but it usually reflects very small changes in acceleration. It was always amusing to see the Enterprise crew sway from side to side while the ship was supposed be changing its speed by a factor of c (speed of light) every few seconds or so.
Oh well. I guess after this long we have to let it slide, as long as people sit up and notice when a writer actually makes a successful attempt to handle the problem.