Time travel

Currently, he is not actually changing anything in the past.

In real life, the most accepted theory of time travel in physics is this:

“Everything that should happen already happened.”

It means that, if there are changes in time because of time travel, all of it already happened. In other words, time still flowed linearly. It means that there is only one timeline. Absolutely nothing changed because of time travel, it already happened that way its supposed to happen. There is no grandfather paradox or any paradoxes. It just is.

This is what the current time travel by the ML is so far about. Everything that should happen already happened. (aside: It has nothing to do with predestination.) Him holding the FL's hand at a mall, already happened. Nothing changed there. He didn't save her, he's supposed to be there because it already happened.

Now, this is problematic because it leads to one very crucial limitation of his time travel ability: he needs to do the things that already happened at the right time and at the right moment.

If he fails, then that's when things are actually going to change.

There are only two ways he can actually change the past:

1. Not traveling at the right moment (origin time) and at the right time (target time) when the FL saw him.
2. Being at a time (target time) when he was not originally there.

No. 1 would be very hard to avoid at his current state because he doesn't have any control (yet). When the FL saw him travel, it was his version that has no control over his powers (yet), so those time travels happen the way it already happened for everyone.

In addition, he can only do No. 1 if he already have prior information, like information from the FL.

• a. Future ML told the FL his origin time.
• b. Then FL told the present ML that information.
• c. Present ML travels back into that target time, changing his origin time.

Then we can say he changed the past. Not only the past, but also his future. “His future” is also important, as was stressed multiple times in E04.

No. 2 is within his reach, but as his father explained, it will depend on how much he wants to save her. He can test this in the Spa/Sauna incident.

It was already established that the ML never saved her from her fall at the Spa. So we know for a fact he never did and he was never there as a time traveler.

However, if he can make himself appear there and save her from her fall, thus, preventing the hospital scene, then we can truly say he actually changed the past.

Both No. 1 and No. 2 fulfills what E04 hinted at: “Her past is his future” and “His future is her past”.

There's one more thing. Who actually saved the FL during the school fire incident?

E04 hinted at two possible things:

1. The FL told him a lie.
2. Or, the FL unknowingly told him the truth.

Here's the kicker, both No. 1 and No. 2 can be true.

How?

• The FL told him a lie. No one saved her. It happened the way the ML saw it happened, and the way the FL remembers it.
• However, when the FL lied about it, that gave the ML a thought, or an idea. Maybe in the near future, he figured out that the door is not about his fireman friend, but about her. (Well, it's obvious for us the audience.)
• The ML will probably figure out that if he can save the FL, then his friend won't die.
• I am suspecting that the person trapped inside, that the other student told his friend, was the FL. So, his friend's death is connected to the FL. He cannot save his friend directly, he has to save the FL so that other student wouldn't tell his friend there's someone else inside.
• So, No. 1 is true, the FL told him a lie. But, No. 2 is also true, because the FL changed his future, which effectively changed her past.

Remember what they both said?

• ML: Your past is my future.
• FL: Your future is my past.

The FL's past, the “lie” that he saved her from the fire, is what will change his future. At the same time, once his future changes, the FL's past will also change.

What will change with the FL's past? She more likely won't end up with the Sauna loan shark / adopted mother.

Finally, there's a problem. If the FL's past changes, they probably wouldn't meet after that.

Also, the ML's past will change as well, and his wife's death wouldn't happen because the ML wouldn't be obsessed with something which led to him abandoning his family (unintentionally because of his uncontrolled travels).

Which brings us to the final question: How can they avoid a grandfather paradox? Because if the FL can change his future which leads to him changing the FL's past which indirectly affects his own past as well, then there's going to be a grandfather paradox, because those changes never happened.

Here is what I think. Every moment that has happened will happen as it did, for like you said, the ML hasn't yet done some of the things in the past but he cannot change them. Each time where the FL was 'saved' by his future self, she already experienced it he just hasn't done it. He never saved her from something that would change the outcome. We never saw new things when he time traveled, just got more clearance to what we already knew happened.