this could have happened in a virtual genjutsu world that was cast on kakashi
... in the genjutsu obito shows kakashi that he has no heart thus convincing him that ...
The day kakashi let RIN die his heart plunged into depths of an ocean called pain and can never ever be recovered ( in the world which they presently live ) and the only way to heal the pain in his heart is THE INFINITE TSUKUYOMI ; a vitual world where obito,rin and kakashi can live happily for ever
~ by showing that he has no heart i feel obito was implying that it has been lost in pain and is no more inside him ~
plz feel free to comment , critisize and share your opinion on my assumption