-- SPOILER AHEAD --

The problem is, they live in a different time. Their worlds are set 3 years apart.

Mitshua even goes to Tokyo to meet Taki in person. But he doesn't know who she is.

Because the whole body-switching will take place for him in 3 years.

They are both 'out of sync' and cannot communicate directly.

Only via the diary-app on their phones or by written messages in books, on their body, etc.

Somehow it's not something you question while watching the movie.

There is sufficient communication between the two.

Well that's quite a twist. Sounds pretty good.

@DoubleUK said:

-- SPOILER AHEAD --

The problem is, they live in a different time. Their worlds are set 3 years apart.

Great answer! If Taki tried to call Mitsuha he'd get a dead line because she is dead in his time. I think he does try that one time and can't reach her. If Mitsuha tried calling Taki, she's end up calling a Taki 3 years before he started experiencing the switches and would assume someone is playing a prank on him. They don't show her trying to call but like you said she does try meeting in person and see's a very young version of Taki on the train.