A couple of preliminary points to consider:
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Originally Posted by Christian
There are some slight problems with the Big Bang theory, which states that all matter in the universe exploded from a small point about twenty billion years ago.
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Big Bang theory does not state this. There are several theories going back to Lemaitre, but the central theory does not address the moment of creation. It is concerned with the subequent inflationary period and expansion of the universe. You also may be confusing the expansion of all matter that we can detect with the universe beyond it.
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Originally Posted by Christian
... the Second Law of Thermodynamics, which states that unless energy is introduced into a particular state, the energy of that state will always be less than the initial state. This is known as entropy.
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This applies to a conventional explosion. The Big Bang was apparently not an explosion.
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Originally Posted by Christian
Thus, in order to explode, any original matter (wherever it came from) would have had to create energy in some way. To form planets, suns and entire galaxies, which is entropy running backwards, it would in effect need to create vast amounts of energy from nowhere, as well as vast amounts of matter (which is also impossible).
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The Big Bang was not an explosion. It was also a series of interconnected processes by which energy and eventually matter were created. It is different from the middle dimentional physical processes common on earth, and initially exists outside the physical and dimentional processes you are trying to apply to it.
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Originally Posted by Christian
Where did that original cosmic egg come from? Where did its energy come from? Why did it suddenly explode? Where did it get sufficient matter for hundreds of thousands of galaxies from?
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Asking these questions does not mean that the tenents of the Big Bang theory are wrong. Also keep in mind the a theory is not a fact nor a belief, but can be modified, trusted via testing or observation, or dropped if replaced by improved data.
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Originally Posted by Christian
Also note: if the universe originated from a big bang, matter should be evenly spread out. It isn't. We note large densities of matter in some places, and virtually empty spaces between galaxies in others.
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This uneveness is a dynamic that allows for us to exist. The theory does not forbid uneveness. The uneveness is also homogeneous and isotropic on the largest cosmic scales.
Check out these questions from astronomer Ned Wright's website. You may find them helpful:
http://www.astro.ucla.edu/~wright/cosmology_faq.html