Major powers

 Once you leave conventional physics the theory is that anything's possible. In fact quantum physics now confirms that the rules of physics only exist in our direct world, but the structure beneath it has no such rules, meaning beneath the physical surface none of the laws we assume are fixed exist.

Time and space move from being absolute to relative. Location becomes a variable rather than a fixed, and the speed of light disappears altogether, replaced with instant communication and transport. Objects can travel from a to b without occupying the space in between. Objects any distance apart can react to each other instantly. And the one quantum effect always observable here is the observation effect, proven by the double slit experiment. If you send particles through a slit half should and do arrive on either side equally. Until you observe it. This adds our own consciousness into the equation. It confirms the quantum level includes our awareness, meaning all these powers are within our own potential control. And because our foundations are quantum, not only does it mean that quantum effects should work at every level, but our own intentions can direct them.

Therefore although scientists can gradually create quantum effects in experiments, it suggests that we can carry out any of them naturally by using our observation to affect the creation and movement of matter. 

If you imagine the power in dreams, particularly with lucid dreams where you realise you are dreaming, so realise you can fly or walk through walls, reflects the potential for our minds in a quantum higher frequency world.

Here is a situation where precedent applies. You only need one example of an object falling upwards or walking through a wall to realise the laws of physics only apply to 3D. And if you manage to bring anything like this deliberately you also know we can exploit these powers naturally. The fact most people go through their entire lives never witnessing a single example has created the impression that none of it exists. But experiments show it does and currently deliberately possible through mechanical means. But just because something is very unusual and almost impossible to discover directly does not stop it being an equally valid law of nature hidden behind our familiar 3D reality. And if someone who could do it performed it in public officially then everyone would know, it would then break down many people's belief blockages, meaning they would find they could do it as well.

In fact these things happen far more than we realise, but because we can't prove it or repeat it we dismiss them, even if it happens frequently. Most people will tell you that things have moved in their houses while no one was there, or disappeared and reappeared at some time later. Sometimes many times over. Again, remove the blockages and the obvious explanation may be the only one. There are other examples with witnesses and no other explanation for what happened, the clearest I know being of a Japanese obstetrician who was called from her house to her hospital late at night to deliver a baby and drove the two hour journey in half an hour. Again, using precedent, if time was allowed to dilate once as she may have subconsciously made it happen to arrive when she was needed, it shows in this case if proven a single exception undoes all the existing rules entirely.