I have a very good reason for saying this, not just that I've practiced telekinesis until skilled enough to record this video (but am not good enough at it to do it any time I want):
"Psi wheel in a clear closed box 2"
http://www.youtube.com/watch?v=pKJGb4RNRB4The reason is it only works when you observe the psi wheel (or other target object) in a state of mind that will not change depending on if it moves or not. You must have no reaction to what happens, only observe. That is a necessary but not sufficient condition. In that state of mind, your subconscious mind starts feeling deep slow waves, which you subconsciously explore into by making small adjustments to your thoughts. Its like learning to ride a bicycle, don't say it can't be done just because you fail to balance on it many times.
There is a theory of time travel called Consistent Histories. It says its possible to go back in time as long as you don't affect things, that whatever small things you do affect move slightly to line up with the loop and incoming and outgoing events consistently. I extend that to include mobius time loops and any kind of self consistent shape, not just single loops, so if you kill your grandfather and that causes you to not exist and not kill your grandfather so you do exist again to kill him, that would probably not work since killing your grandfather has other effects that would not line up the second time around, but it is possible that if your grandfather had little effect on the world it could be pushed, with enough physical force on the time network (not time line), to have a mobius where you kill your grandfather and that causes you to not kill your grandfather on the other side of the loop, and that causes you to have a consistent history with the first side where you do kill your grandfather, closing the mobius, and still allowing other events to enter and leave at various points in the time network.
Since a necessary but not sufficient condition of telekinesis is to have a state of mind that is not affected by the future a second ahead, if the target object moves or not, and since the expanded version of consistent histories theory (which I think is true for other reasons in thermodynamics based timeless physics) says the same thing, I say telekinesis is a form of short term consistent histories time travel.
That would also explain its connection to precognition, like when I used to hear my microwave beep a few seconds before it really beeped, so I would already be there opening the door when it beeped, and a more common experience of many people, knowing who is calling before picking up the phone, sometimes. There was some research on people playing baseball. It said they react to the movements of the ball faster than their neurons should be able to. I think this is how brains normally work, something about the Time Symmetry of physics, and to say there is not enough time for that to happen between neural activations (as Max Tegmark, a professional physicist, writes) is to ignore the very theory its about, that information flows backward and forward in time.