In the Matrix, why did Neo have magic powers in the real world? For example,
(1) Those scenes where he blows up those robots purportedly with his mind.
(2) That one where he has no eyes but can see.
The main explanation I've seen, and that seems to be pretty official, was that the plug thing Neo has in the back of his head worked as a wireless device. Well, as you will read below, this isn't actually specified like this, but since the source speaks of the "brain becoming a wireless connection", it seems the safest thing to assume.
In any case, no magic is involved.
In the IMDB FAQ page for Matrix Reloaded, we see the question: Neo is able to have extraordinary powers inside The Matrix because he is The One, designated by the machines for equilibrium. What explanation does the movie give for Neo having his powers in the real world?
And the answer is (emphasis mine).
If you want to force an explanation,the idea is that Neo is like an virus inside matrix same as one virus would be on your computer,but when Neo is unplugged/your pc powered off it can't pose any threat.
But if the virus was so good,and your hardware(motherboard BIOS) poorly built/programmed...the virus could theoretically take control of your motherboard,and next time you boot up your PC it could overclock its voltage until it burns out.
This could partially explain how he would destroy the robots,and seeing the machines would be just your windows recognizing your new USB keyboard however windows won't run on powered off pc so they can't recognize anything but on the other hand Neo,unlikely the windows had an advantage of existing in both worlds(software/hardware).
He couldn't just beat up the robots like he did in matrix since there was much more effort needed,he had to implement the whole new hardware part to his strategy,which would also explain why he didn't do it more often.