Some of the science on Star Trek is present in every day life. For example, cellular phones clearly outstrip the communicators of the original series. Even the ship's computer is realistic given developments in voice recognition software.
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Other science developments from the set of Star Trek at the stage in which they are imaginable but still impossible.
With the current limitations of contemporary science, there are some clear impossibilities from the realm of Star Trek science. For example, physicists have not developed a means of beaming matter from one location to another. Physicists have also eliminated warp drive due to the inability to travel faster than the speed of light.