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.
If (as some do) you exclude the sequels, then yes, it is magick. Due to his direct experience of the virtual reality, the real reality, and the signals that interconnected these two, he was in the position to realize that the real world follows very similar (if not identical) rules.
The literature of magick and neoplatonism strongly describe the world as based on energy not matter. Neo experiences an apotheosis, a god-becoming, which has been prophetically supported (in-universe) by the legend of "the One".
Thus, the real world is also a construct, virtual and can be manipulated psychically as well as physically.
I thought of it like this: Even the 'real world', Zion is part of the Matrix. It's all just one big program. Think of Zion as an alternate Matrix for the humans who didn't mentally accept the first Matrix. That's why the Architect tells Neo he is the sum of a remainder of an equation. Neo is nothing more than a program like the Oracle or the Keymaker. So what he is programmed to do, is reset the system, and choose 27 'humans' to repopulate Zion, thus starting over. The difference is all with Smith. He becomes a virus, so instead of resetting the Matrix, Neo destroys Smith to usher and area of 'peace', still inside the Matrix, unbeknownst to Morphius and everyone.
But if you really want your mind blown; The whole entire Matrix program was something HUMANS designed for MACHINES as a fail safe when they created artificial intelligence and it began to get out of hand.
Because after 2:02:00 @ Matrix Reloaded, Neo did not ever returned to the Real World, but instead went to a simulated replica of the real world.
When Neo walked outside from the architect room, the architect had made the following changes in "The Matrix"
1) While the architect was talking to Neo, he created a close replica of the "Real World". I shall call this the "Cloned World Program", and I will explain later the purpouse of creating this program and why it needed to be created at that exactly point of time.
2) He modified the telephone lines in order to stop releasing people from the to "Dream World Program". Instead, the telephone lines now send the people from the "Dream World Program" to the "Cloned World Program".
In the movie "Matrix Reloaded" at the near end (2:02:00) there is no explation on how did Neo and Trinity came back from the "Dream World Program". But is very likely that they did not returned to "Real World" but instead were routed to the "Cloned World Program" without knowing it.
At 2:04:00, the hovercraft ship that Morpheo used to command, exploded under the attack of the machines. The "Cloned World Program" did not need to replicate the exact details of this ship anymore, so Neo could not tell it was not the same ship he was before.
At 2:04:43 Neo clearly says; "
". A possible explanation is that, because he did not went back to "The Real World", but instead was redirected to the "Cloned World Program", he in fact "FELT SOMETHING DIFFERENT". He did not had too much time to think about it because he was to busy trying to stop the machines and then suddenly faints.
At 2:05:10, Neo destroys the machines and suddenly faints.
Why did Neo fainted?
A possible explanation is that an "Unexpected Exception" ocurred when Neo used his powers in the "Clone World Program". The way that exceptions are handled is the following:
The Matrix doesn't really know how to handle this "Unexpected Exception" beyond that point in time. The only reason why Neo exited that world was because they forced the "Merovingian" (Matrix Revolutions) to do so.
So in conclusion, right after 2:02:00 @ Matrix Reloaded, Neo did not went back to the "Real World" anymore, and everything that happened after he left the "Architect Room" was inside the "Matrix Simulation". That explains why Agent Smith can now posses a human body, why can Neo stop "things" in the "Real World" (which it isn't real, its just a replica called "Cloned World Program").
How many World/Programs can you count in the Matrix Trilogy? So far, I had counted;
 Can the architect make changes inside the Matrix? Yes and we had seen this before. In Matrix 1999, we can see a scene where Neo saids outloud "Deja Vu". Then I quote:
So yes, the Matrix can be changed at will. Some could consider the massive monitors showing Neo at the architect room as multiple "Deja vu's" happening at the same time.
 Can the architect make other Worlds/Programs?
Yes. He created the first and second Matrix. He also created the Oracle and created the Subway Station World Program.
 Why did the "Clone World" needed to be created at that particular point of time?
Because that was the time when the architect could see Neo's possible future reaction. The architect wasn't just chatting with Neo, he was scanning his possible future reactions. In fact, Neo's possible future reactions where being showed in the monitors inside the architect's room. The architect needed to somehow design a "Clone World" that could fulfill his needs in order to keep Neo trapped.
Also notice that in the cloned world, the hovercraft ship doesn't last longer than 5 minutes before being blowed up. This was intentional so that Neo couldn't tell the different between the real hovercraft ship and the cloned one. Yet he managed to say outloud "Something is different" before fainting.
 Can the architect modify the telephone lines in order to stop releasing people from the Dream World, and send them to the Cloned World Program? Yes. There is no limitation on what the architect can do inside his simulation/world/program. He can manipulate everything. Read  and .
 Cloned World Program? Can he do that? Yes. Read  and .
 Instead of returning to the Real World, Neo was send to the "Cloned World Program?" Yes. Read  and .
 How can we be sure that Neo was at the "Cloned World Program" at 2:02:00 @ Matrix Reloaded? Because that was the point in time where the architect had the power and information he needed. The Architect needed to know what Neo expected from the Real World, so he made a "Cloned World Program" out of that expectations. It was also the point in time when the ship was destroyed, when Neo used his powers outside the "Dream World Program", and when Neo was transported to the "Subway Station Program" after he fainted.
Before that, the Architect could not know how the "Real World" looked like, nor Neo reactions, so he could not make the "Clone World Program" yet.
Also before that, Neo did not felt "Something Diferent" as he said outloud, nor he tried to use his powers outside the "Dream World".
And lastly, before that point in time, Agent Smith did not manifestated himself in a human body, only after 2:02:00.
 Unexpected Exception? Why? Because Neo was not suppouse to use his powers in the Real World. He wasn't also suppouse to use his powers in the "Cloned World Program". Yet, he manages to do so, so a "Unexpected Exception" inmediatly happends, making Neo faint and moving his mind into the "Subway Station World Program". Quoting Matrix Revolutions;
That could mean that he is there because he did something he wasn't suppouse to do.
 Neo loses conciousness and moves to another world? Yes. Renember that Neo suppously was in "The Real World" when he fainted. Yet, instead of waking up from his "faint" back to the Real World, his mind woke up in the "Train Station World Program". Why did that happened?
Couldn't Neo wake up right after he fainted back into the real world?
He was not connected to the Matrix when he fainted.
You could assume that in "Matrix Revolutions", Neo was plugged into the Matrix while he was fainted. But why would anybody do that?
Couldn't they (Trinity, Morpheous, anybody) wake him up before plugging him to the Matrix?
When Neo fainted, he wasn't harmed and/or electrocuted. He had just destroyed some flying/robot/machines and out of nothing he fainted.
Can anybody of you explain why does the "mind of Neo" needs to appear inside a Matrix Simulation (Subway Station World Program), if he was "Disconnected" from the Matrix and in the "Real World?"
The only plaussible explanation that I find is that he was not in the Real World and yada yada yada.
Trinity needs to drink the Red Pill so she can wake up, just as Neo did in Matrix 1999. Also, she should check on Zion, but I bet they are pretty much dead since Neo did not actually manage to save them. 
 Why do you think that Zion is dead? Quoting the Architect;
Assuming all that the Architect and the Oracle had said before is true, then
So you could either think that:
a) The Oracle was wrong in saying that Neo is no the choosing one
b) The Architect was wrong in saying that Zion would not survive if Neo did not choose the right door
c) After a gibirish chat with the Architect, Neo suddenly becomes a god-like supernatural creature freak that can destroy machines and see without his eyes in the Real World, sic. Outside the Matrix simulation.
d) The Architect cannot think in a solution to Trick Neo in order to be forever trapped. He was just being pretentious when he said that stuff about how he become efficent in handling choosen ones, on how Neo was the 7th guy that tried this before and yada yada. He was just bluffing to see if that could stop Neo. Perhaps it did not work but it was worth the try I guess.
e) Morpheos was right about Neo being the choosen one, but the Oracle and the Architect where wrong about it.
f) When neo said that "Something is different", it was because either the Architect gave Neo a WiFi connection to the Matrix for no particular reason, or Neo growed a "Special Horn" that gives him WiFi low latency connection to the Matrix. It is very important that this connection be low latency, or otherwise Neo could not had destroyed the machines on time. Also, the Matrix WiFi hotspot has no encryption/password or whatsoever, so any crazy lunatic can just join the network, surf the web, destroy machines. Guess that Artificial Intelligence isn't that smart after all when it comes to detect an anonymous connection.
Or maybe he felt that his hand was all charged up with superpowers for no particular reason.
Or the Architect (A computer program) gave Neo real world super powers, even thou he is inside a computer simulation.
Or superpowers is just some natural thing like menstruation. You suddenly feel something warm like you pissed yourself and realise you are all covered in blood.
Might as well fly like superman if you belive in the superpowers theory.
Or the exact opposite...
a) The Oracle was right. Neo was not the choosen one. He in fact did not saved Zion because he choosed to save trinity instead.
b) The Architect was right. Zion was destroyed beyond recognition just as he predicted it.
c) Neo travels to a "Cloned World Program" instead to the "Real World" where he could do all those "Magic Tricks" he couldn't done before.
d) The architect was right when he said:
Impliying that he alredy had designed the perfect strategy to handle Neo future actions.
e) Morpheos got it wrong. Neo was not the choosen one. Mistakes happen, ya know? He is not a perfect program as the Oracle or the Architect, he is just a human being. Oh, and he is also dead because Zion was obliterated beyond recognition.
f) When Neo said that "Something is different", it was because he somehow did not feel he returned back to the same place he was before. Kinda like a "Deja vu" in the first Matrix (1999).
Here is a picture of blue pilled f**ks
Did the Architect had power, knowledge, motive to make a close replica of the Real World, and route the Telephone Lines to that Cloned World? (Yes / No)
At some point in time, the matrix figure out that people were escaping the matrix using the telephone lines.
By learning this, the architect of the matrix moved the telephone trunk lines into another space, where the people would assume they were outside the matrix but it wasnt.
Thats why the Oracle said that Neo was not the one. What Neo did when he visited the architect was to unconsiously give out the details of where they live outside and the way that place needs to look like.
They never scape the Matrix, they just went to another place. Thw architect created a happy ending for them, so that they will calm down. It actually worked because the architect tricked everybody into believing so.
That is why Neo could stop the machines and do many random things that he wasnt able to do.
The architect was right, he found an "efficient" way to handle the "choosen ones". Just reroute the trunk lines into a cloned outside matrix and create a happy ending that they would believe in.