Apologizing and Forgiving

I have been thinking. I think that the whole act forgiving someone or apologizing to someone has a basic flaw. Just like light is made up of photons, packets of energy, time is made up of moments or seconds (more or less). 

Now, when person A does something to person B at time T1, something for which A will have to apologize to B at time T2, neither of A nor B will remain the person they were at T1. Their passports will have the same name and same will remain their respective fingerprints but these "identities" alone don't make a person. A person can only be aptly defined at a particular time, at a particular moment as he's constantly evolving, with every passing moment. 

Now, at T2, A and B can only recall from their memory the timeline of T1. This recalling might indeed stir same emotions, but like a wind is not a storm, this stir won't be able to cause theirs veins to pop, heart beats to pound, and their eyes to water like they did earlier at T1.

In order for me to validate this act of apologizing and forgiving, the act of hurting from A to B should be simultaneously done with the act of forgiving, which we can all agree that simply sounds absurd. 

I guess in the end, as we forgive someone at T2, all we are doing is letting go of all the anger; forgiving ourselves for holding that anger back for so long. May be that's why when A hears the words "I forgive you" and feels relieved, B doesn't concern himself to explain that he's actually letting go. B is no more concerned about it. A simply accepts the forgiveness because he's concerned about that. On a different timeline, with different subjects, A just might find himself at B's place and understand what had happened back at T2.

And time over time, this whole series of hurting, apologizing and forgiving has become so frequent, now neither all the As nor all the Bs realise what exactly is going on at T2.