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Where did atoms originally form?

I am studying the Big Bang and trying to make sense of it. Is there research or ideas on how atoms initially formed? Has there been experiments done starting with basic subatomic particles to create a Hydrogen atom, for example? I know we can take existing atoms and smash them together to form higher-order atoms. The question is: Is there an existing level of research addressing (new) Atomic Synthesis?

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Closing Statement from Gary Post

I have asked this question or a form of it on TED and across multiple sites. I have yet to hear a good answer that does not involve deux ex machina (a ghost in the machine) type answer. For example, I read about references to Chaos Theory and plasma and etc. I'm beginning to think some of the Intelligent Design proponents have a better handle on this than mainstream science. At some point, the line between we don't know and the far-reaching fantastical musings screams for the questioner to just have faith that it was a naturally occurring process. Atomic synthesis might happen once or twice by chance, but how could something like this happen in exactly the same way in such a repeated, perfect fashion? It defies logic and believabilty.

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    Oct 22 2013: None that I'm aware of: when it comes to this matter we have too little knowledge and too many opinions. I've read a few papers about this subjects over the years, but all sound no different from priests talking about God: basically they assume too many concepts to prove their point, sounding just like any religious person.

    Allow me to give you something to think about. Did you ever stopped to notice that we can have the infinite enclosed in a finite limit? Think: how many decimals do we have between 1 and 2? Infinite. Therefore, how many sub-atomic particles might exist? The answer is: infinite. So, how can we make any reasonable theory when the simplest of the elements has in it such a huge level of complexity?

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