In Tenet, when someone got shot by an inverted bullet, shouldn't the person be hurt before getting shot and recover immediately after the inverted bullet shoots him? If not, then why was the wall recovered immediately after being shot, but humans are not?
I struggled with this as it seemed to be a temporal loophole but I think there is an answer - which lies at the end if you don't care for the details.
Examining the relevant scenes of the film, this is what seems to be happening.
Regular - We see regular Kat being dragged into the see-through room while a bullethole is on the separating glass. Inverse Sator catches the bullet with his gun from the glass and the bullet passes through Kat's body and into the chamber of his gun. So now Kat is inversely shot and will soon die as her current regular timeline moves foreward. After this, inverse Sator walks backwards through the turnstile as she is bleeding.
Inverse - We see Sator entering Kat's room right after he inversed his timeline - exactly as the regular timeline above just ended. He finds Kat already wounded on the chair. There is not bullet hole in the glass because the shooting has not happened yet in the inverted timeline (which we are now in), nevertheless Kat is wounded because this is the future of her regular timeline. He picks her up, pulls the trigger, the bullethole appears on the glass and Kat is HEALED. He takes her in the car and the car pursuit unfolds with Kat being perfectly healthy in the car as we see her. Remember, this is Kat's past we are moving through now, this is why she is not bleeding. For Kat, this is happening before she got shot in the glass room.
- Regular - The Protagonist stabs the inverse Protagonist in the arm.
- Inverse - The inverse Protagonist starts feeling pain in his arm as they move inversely through time towards the Freeport in Oslo. Right before entering the Freeport, the wound is open and bleeding - so as he moves inversely towards the stabbing, his wound get worse. Then he enters the Freeport, the fight with his regular self occurs, and when the regular Protagonist stabs his already bleeding arm, the wound heals! (we don't explicitly see that one, but when he gets out through the other side there is no more mention of the wound and furthermore it logically follows from what has happened until now)
So, the answer is yes, a person is hurt before getting inversely shot and recovers immediately after the inverted bullet shoots him. This is consistent with the bullet holes also.
It's a mindbender, but this seems to be the answer. When you shoot someone, either regularly or inversely, you injure him for his own future. He will keep bleeding as his his own timeline moves on to its future. But in your, opposite, timeline the things you will experience are what led that person there on the first place. He deterministically needs to arrive there for the shooting to happen.
I'll say that again as is it the key. When you shoot someone, either regularly or inversely, you injure them for their own future. Your future is their past, in which they were sill alive.
The following sets of people objects have the same relationship each other:
In Tallin Inverted Sator and his inverted gun <==> forward Kat
In Oslo Forward Protagonist and forward metal lockpick <==> Inverted Protagonist
Therefore what should happen is that whatever state you are in, everything inverted from your perspective should appear to move backwards. That's why when Inverted Sator inverse shoots forward Kat, she appears to heal (from his perspective) because she's inverted relative to him. By the same relationship, when the Forward Protagonist forward stabs his inverted counterpart, he should appear to heal the wound just like the forward Kat appears to instantly heal to the inverted Sator.
Instead, the reversed protagonist appears to have a wound on his own body which is moving backwards from his perspective meaning it appears to move in the normal forward direction to his forward counterpart. What would actually be consistent is the reversed protagonist enters the hallway fight without a wound, gets stabbed with a weapon inverted to him (just like Kat is shot with a gun inverted to her) and then starts to bleed while exiting the turnstile now in the forward direction. Then the original forward protagonist would see the wound move both backwards (on his inverted self) and forwards on the copy of him exiting the turnstile on the other side.
Unless there is some other wound mechanic at play I think the stab wound in Oslo is simply inconsistent with the logic of the movie prior to that point. One cannot argue that injuries caused by inverted objects cause inverted wounds, because then inverting Kat would instantly heal her after the duration of time leading to when she was shot. Kat is inverted not to reverse time and instantly heal her wound but rather for some other explanation of the inverse radiation being less severe and allowing her to heal normally if she is inverted. This is never fully explained and characters' own bodies will always still move forward in time from their own perspective. Things can only appear inverted if they actually are inverted relative to you. I believe the best explanation for this plot point is that Nolan wanted to trigger the curiosity of a character seeing something move in reverse and notice it themselves vs seeing it on another inverted person that is farther away. It is hard to even notice that Sator heals Kat by shooting her while moving backwards but it would have been nice if he made those scenes more clear.