The wormhole aliens existed outside linear time and at any one point in time there was only one Sisko.
Up to a point I agree with what you are saying. For all intents and purposes they are the same person in the same way that regenerated Spock was the same person. However, the reality is that they just APPEAR to be the same person because they have been reconstructed with the same DNA and the same memories. Technically, they are still copies.
Pauln6:
If the original Sisko died multiple times because of his constant use of the transporter and had been replaced with similar copies, then...
1. Why hasn't he or any other Starfleet officers discover any truth behind any physical or mental differences between the before and after versions of people during transport?
2. Why didn't the Wormhole Aliens look at Sisko as an impostor when he used the transporter so many times?
3. Why did the Wormhole Aliens decide to take him after he died in the Fire Caves and not when he died in the transporter for the first time (while he was replaced by a duplicate)?
In fact, in Sacrifice of Angels: The prophets had stopped him from ending his life when he decided to go up against a fleet of Dominion ships that were coming thru the wormhole. Why did they stop him then and not during any supposed transporter deaths?
I mean, seriously, if the transporter really was a doppelganger maker: would the Prophets be all that happy at the idea of their Emissary being killed and replaced by copies of himself over and over again?
If the transporter opened up a subspace corridor that they could step through, it would be the same person. However, their matter is destroyed and converted to energy. A living carbon life form cannot survive that!
That is why it is science fiction. There are many things within Star Trek that don't make sense and or will never happen (obviously). The transporter bends the normal rules of science as we know it and it de-materializes living and non living matter into energy for transport and then re-materializes it magically. It is a conversion of matter to energy and then back again. Just because it doesn't seem possible to you or me by normal science we use today, doesn't mean that is not how the device actually works within the show. Also, like I said before, you can die and you can still come back and be the same person, too. Death is not the defining factor of something being different or being a copy. However, death in the transporter could happen in .00000003rd of a second for all we know. It could be so fast and so instantaneous that it really wouldn't significantly be a definitive moment that would be a real death upon a person's life because it happens so quickly. However, there is evidence within Star Trek that your mind is perfectly preserved and living on as transporter energy during the transporter process within that fraction of a second (or seconds). Remember the DS9 episode titled "Our Man Bashir" where the memories of some of the command crew had been integrated into Doctor Bashir's spy program? How does the transporter store memories or the minds of people if they are no longer flesh and blood anymore?
Well, the answer is simple, the episode tells us very clearly that the mind lives on during the energy portion part of the transporter process. Any speculation beyond that is just that. Pure speculation with no real basis in fact within the official Star Trek universe.
In addition: I just watched the TNG episode "Second Chances" and it clearly tells us that Riker #2 is actually identical to Riker #1. It was further said that both Rikers are real and not some type of second rate copy or clone.
If your interested: Here are the scenes from the episode that confirm this...
http://www.tubechop.com/watch/67813
http://www.tubechop.com/watch/67815
Sources:
http://memory-alpha.org/wiki/Our_Man_Bashir_(episode)
http://memory-alpha.org/wiki/Second_Chances
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