Technically, Time itself does not exist, it is merely an illusion created by humans to keep track of things, it is but an organizer so that we can look into the past and see what has happened and what has resulted from it. So, no the past doesn't exist for, to exist is to be here right now, at the moment, and the past is the exact opposite of such a definition. Only physical objects can "exist" persay but feelings exist within ourselves so, an emotion exists as long as someone is always feeling it somewhere in the world.