Does the concept of an afterlife even make sense? It is true many religions teach or assume an afterlife for people. In some cases it is reincarnation, and others it is heaven or hell or something in between. But what does it mean for someone to leave this life and enter an afterlife? Put another way, how do we know it is the same person in the after-life? If I die, and someone called Daniel enters heaven, is that me, or is it just someone like me with my name?
One can ask: what makes me me? How do I know I'm the same person as that person that looked just like me and inhabited my house yesterday? Well, there is a physical continuity between me and that person, and I have the same memories has he had, and my personality is the same. Perhaps none of these are perfect answers as they are all subject to gradual change, but let's suppose they contain a majority of what defines me.
Now clearly death is the end of our bodies. So physical continuity between us and whatever comes afterwards definitely breaks down. Then at best, from an correspondence perspective, an exact copy of one could be made, including a copy of the states of all one's neurons so that one's memories and personality are the same. Now I doubt most people would really want this, especially those suffering from diseases such as Alzheimer's, but assuming an improved body just complicates the correspondence, and I'll pass over that for now. Assuming then that an exact replica of me is made, including the state of my brain and my memories. Is that me?
Well if this is possible, there is no need for me to die for a replica to be made. A replica could be made now and placed in an appropriate world. Is that me? I would not think so, and I would not care for that replica any more than I would any other person. Another possibility is that after I die, not one but two replicas are made of me. One is put in heaven and one in hell. What should I think about that? Which one is me or are both me? I can't say that I care too much about the fate of my replica or replicas and would not consider them me. So it seems there is a crucial correspondence problem between me and whatever being is supposed to be me after I die. If an exact copy of me now is not going to be me, then an exact copy of me after I die is not going to be me, nor is any other improved copy.
Some might reply: it is one's soul (or spirit) that defines a person, and the transference of the soul is what constitutes a correspondence of a person. That is, it is me if my soul gets transferred to that body. But what is the soul? What part does it play in one's person? Presumably it is a non-physical thing, as if it were physical thing it would join the body in the grave. But can a non-physical thing influence the physical world? If it does then physics as we know it breaks down at that point. So I think we can safely reject that, and so conclude that whatever the souls is, it has no effect on the body or world. So it seems the most the soul can be is a label for a person; after one dies the soul or label gets attached to some other body. But this seems strange -- why should I care about some other body just because it gets my label? Moreover, if bodies can be replicated, maybe souls can too. Then perhaps multiple bodies will get my label after I die.
To conclude: I have a direct connection to my past and future in this world, and I understand how my current actions affect the future state of myself in this world. However, even if there is an afterlife, I see no connection between me and whatever creature or creatures follow me in the after-life. It is the same as someone making a clone of me -- all very well, but I have no attachment to that clone. In addition, transferring or copying my soul into that clone doesn't build any direct connection to it.