Does the Star Trek transporter problem apply to the concept of souls as well?

For those who need a quick run down of the problem, it's a question of identity. The oversimplified version asks, if you step into the transporter, are dismantled particle by particle and then reassembled perfectly in a different location so that what comes out is the same as you in every way anyone can ever... show more For those who need a quick run down of the problem, it's a question of identity. The oversimplified version asks, if you step into the transporter, are dismantled particle by particle and then reassembled perfectly in a different location so that what comes out is the same as you in every way anyone can ever perceive, is it really you or did you die when you were disassembled?

Now, I'm not really interested in answering the problem itself here, but I'm curious if the same question would apply to a soul. Your physical body is destroyed. But, this soul that identifies as you persists. Weirder still, let's say you had Alzheimer's. I'm told that the soul version of you would not have any of the effects of the disease. So, this soul would have all your memories, all the cognitive faculties you once had, and in essence, be very different from the version of you that had died. Doesn't that raise questions of it's identity even more than the transporter problem would?
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