The topic of psychokinesis, or “telekinesis”, being used in science is a blurry one. While the null hypothesis states that it doesn’t exist and it’s impossible, with no other existent “magical” forms having been found yet, it’s impossible to say it most certainly doesn’t exist. However, I wouldn’t get your hopes up too high.
In an online survey conducted by psychologist Richard Wiseman which surveyed 400 magicians worldwide, the question “Do you believe that psychokinesis exists (i.e., that some people can, by paranormal means, apply a noticeable force to an object or alter its physical characteristics)?” was met with a mostly negative response. In fact, 83.5% of the magicians surveyed said NO, while only 9% said YES. The other 7.5% were UNCERTAIN. While this in itself is not evidence by any means, it gives a good sample of what those who practice the art of deception have to weigh in on the subject.
While many believe that because we supposedly only use 10% of our brains, meaning there’s nearly infinite possibilities for what we may be able to do if we were to access the other 90%, this is in fact a myth, as we have been shown to use 100% of our brains through the use of imaging (including PET scans). As a matter of fact, according to the same article, if our brain waves were able to have some sort of impact on the physical realm, it would be rendered useless, as the waves would only travel a few millimeters away from our heads.
On the contrary, a longitudinal study cited in this article highlights the potential of our mind’s power through the use of Random Event Generators (REG). While the results may have appeared promising, though subtle, we run into the same problem that we did with the studies on preemptive prayer. As such, with the lack of additional studies to back this work up, as well as the lack of a mechanical explanation for it, it’s very possible that this study suffers from a false positive.
The problem is, without a mechanic that can undeniably explain it, save for some more wild theories on quantum mechanics, it’s hard to make progress on the possibility. But at the same time, we run into the opposite end of the spectrum: The fact that it can’t be proven that a mechanic doesn’t exist out there. Until we have definitive evidence that things like quantum superposition exists beyond just theories, you probably shouldn’t expect to see any breakthroughs in telekinesis that aren’t surrounded by a LOT of superstition and caution.