I've just watched an episode by MinutePhysics called "Real World Telekinesis". In it, Neil Turok (I wonder if that is his actual name; I remember playing a game called "Turok: Dinosaur Hunter" on Nintendo 64) explains that before Faraday and Maxwell, there was a real problem describing things such as magnets affecting each other or the sun warming the earth without resolving to telekinetic explanations. He then explains that when Faraday and Maxwell introduced the concept of fields, and that changes in this field traveled at the speed of light, thereby dissolving the problem that these phenomena would comprise "spooky action at a distance" explanations.
However, this got me thinking. What would it have taken for these phenomena to actually be telekenetic? Would it be if the electromagnetic wave traveled to all points in space instantly (and was not bounded of the speed of light)? Would it be if only certain points were affected, but not intermediate points? I guess no one, before Faraday and Maxwell, believed that if the Moon got in between the earth and the sun, it wouldn't be heated up.
So, in physics, what would a definition of something telekinetic look like?