In 5 Centimeters Per Second, a boy and a girl get separated, and then try to meet with each other.
In the ending, when they are grown up
The boy sees the girl as they are crossing the train tracks. They are interrupted by trains. The boy waits for the girl, but when the trains pass, she is gone.
Why is that?
I attribute this to what would best be called a "Fleeting moment and feeling". His desire to see the girl again caused him to envision her being there for a moment which is personified by the passing train (another symbol that life moves on). But when it passes, so does his desire and like the train, he decides to move forward with his life.
In an interview of Makoto Shinkai found here, he answers a question regarding the plant at the beginning of Episode 2. Personally, I believed that it was a throwback to Voices of a Distant Star, but it--in a way--answers your question indirectly. To quote:
Takaki, the male character, had dreams of this girl he liked who was very far away. In the image they’re both on a distant planet that is far away, so he’s dreaming that he’s with her even though she’s in a far away place.
When viewing Makoto Shinkai's works, distance always plays a large factor. He treats it with a vague touch. However, Makoto Shinkai always injects the notion that distance(space) and time are intertwined (VoaDS is a perfect example) and that there are events that span them.
At the ending of 5 Centimeters per Second, the girl was obviously a vision, as the distance between them cannot be closed physically anymore and the time lost cannot be reclaimed. The act of forgetting his lost love is a slow process for Takaki (the male protagonist), which is what the title is actually alluding to. The movie is not only one about distance and time, but of the events and the memories associated with them.
Now, the way I relate them all together:
Cherry blossoms are almost only beautiful when they are on trees (when the relationship is intact), and are almost equally as beautiful when they're falling (because memories are almost equally as beautiful as the real thing). However, while memories themselves live on, the reality they used to be gradually differ from how the memories are, much like how falling blossoms slowly become a fragment of the beauty of where they used to be.
The title tells us that each time lost is more distance apart physically and emotionally, and that at the final moment where the cherry blossom cannot cover any distance anymore per unit of time is the moment where the memory is--not actually lost--but stays just that: a memory. In a nutshell, the vision by the railroad is the final moment of their cherry blossom, Takaki's living dream of the girl in the faraway place, before it finally stops moving and reminding him of the relationship that once was.
Just saw this twice and watched the ending carefully and listened to the song, since the last 5 or so minutes of the movie mirrors the lyrics of the song.
Basically here is the lyrics:
I'm always searching for you, searching for your figure.
In the City, at dawn. At Sakuragi-Cho.
Even though I know you can't be there.
If my wish were to come true, I would be at your side.
There would be nothing I couldn't do.
I would risk everything to embrace you.
I'm always searching for you, always searching for even a fragment of you.
At the shop I'm going to, in the corner of a newspaper.
Even though I know you can't be there.
If miracles do happen, I want to show you right now the new dawn, who I'll be from now on,
And the words, "I love you" that I never said.
I always end up looking somewhere for your smile.
At the railroad crossing, waiting for the express to pass. Even though I know you can't be there.
So if you really read it through the lyrics and the fragment of clips and images.
The boy never saw the girl again but was just seeing a hope that maybe he did see her.
If you think about it, they never contact each other for a long time, so the girl didn't even know where the boy could be.
So the boy simply smiled since he didn't see her and finally came to terms with it.
If he did see her there though, he would do everything and tell her everything he never said or did before when they were still together.
This may be a little late but Akari was at the railway crossing. The manga shows a picture of of a girl from behind then a close up of her left hand with a ring on it. After the trains are gone so is she, Takaki smiles and walks off. The next picture is of Akari but the young Akari standing on the other side, she smiles and waves good bye to Takaki who is already further down the road.
The ending scene can be taken both ways, maybe she was there, or maybe not. For me, I believe she really was there. This may be subtle, but as they passed by each other, both of them (even the girl) seemed to notice each other. However, when they look back, as the gods of love like to interfere, a train appeared.
As the train is passing by, Akari went ahead. I think it symbolizes that she had already moved on for a long time. However, the main character clearly still had lingering feelings for her, as seen in episode 2 and 3. He did not only look back, but he also waited for the train to pass. He even turned around and took his hands out of his pocket. However, when the train passed by, the woman was nowhere to be found. He took it as a sign to finally moved on, and as he was smiling, he turned away. If I remember correctly, he was sad in episode 2, and even more depressed in episode 3: he even tried to slept with other woman, and he even quit his job to forget the girl.
We don't know for sure who first stopped writing letter, but I think it was the boy. This can be seen in the scenes where they exchanged letters, though I don't think it means that the boy stopped liking her — as seen in the ending, he truly loves her. Maybe it was due to some other reason, like change of address, undelivered letter, or something we would never know. But we can see that even though they don't receive letters from each other, they still looked at the mailbox - both of them. Even when the girl was walking with another guy, she still looked at the mailbox.
Anyways, no matter how anyone views it. The movie was a masterpiece.
By the way, I remember reading an interview with the writer/director of the movie where he said that the theme for 5cm/sec was "reality" - it isn't always a happy ending in real life, most of the time love fails. (Sorry, but I don't have a source for this).
The song if translated say that he sees a figment of his imagination and This is show as he is riding his scooter and he sees Akari. But at the railway he sees her for real and I believe that, that is what they promised each other all those years ago; they promised each other to see the cherry blossoms fall and as it just so happens the cherry blossoms where falling which to takaki was the only way to finally detach.even in the manga he sees a ring which can only be there if she was real. Also after that when the younger version of Akari waves back I believe it was what he saw when she wasn't there otherwise he would have ran after her.
As Tohno (male character) contacted Akari through email and mail stuffs, they hadn't felt the true meaning of love. So the title "5 Centimeters Per Second" tells that their love was growing apart with time. So Akari gave up on their relationship and found a new guy. But Tohno's life got ruined by her beauty and he still loves her and this kinda relates to the ending song.
I believe that he really saw Akari because (after checking the movie over 3 times but i might of missed something) he had not seen Akari in years so how could he possibly know what she looked like all that time later without even seeing a picture of her. So he must of recognized her as he stopped and turned around but since she had gotten over their relationship over time she didn't wait to see if it was Tohno so she kept walking. Also they had promised each other to see the cherry blossoms fall again and as they walk by each other you can see the blossoms falling so it was a way of concluding their relationship and Tohno moving on with his life.
This may be too late to change your ending view, but in the manga you can see that in the ending the girl shouts from the other side of the train when passing. Also, there is another chapter (volume 2, chapter 11) after that, it is Kanae's story part. The anime only ended on volume 2, chapter 10 of the manga.
