At work, I see examples of this grammatical error ALL THE TIME. I don’t mind it too much when it’s verbal, but it drives me crazy when it’s written. And so…
If you can’t say, "the white one belongs to I," then you can’t say "the white one belongs to Emma and I," either. I think we can all agree that you can’t say the first example. Therefore, you can’t say the second either. It’s not really all that difficult. I believe we all learned it when we were about 6 years old.
But just to get grammatical on your asses, "I" is a subject, which performs the action of the verb, and "me" is an object, which receives the action.
ps. no, this is not actually directed at anyone here… unless you deserve it.