Does God's omnipresence extend to hell?

I'd agree with Caleb here. God exists even in hell. Theologically I am not sure how God is able to be omnipresent, just that it is one of God's attributes.

Scientifically, one theory that holds promise is String Theory which implies that all in the past, present and future may exist at once. And God may be able to exist not only everywhere but at all times! I realize I am possibly muddling things up by bringing science in here, but so be it :)

I think the premise is inaccurate. "Present with God" is used in the Bible to mean being in Heaven. This does not mean that those who are not regenerate are not also before God in some capacity. In fact, Mike Horton has said in a White Horse Inn broadcast this year that God saves us, essentially, from Himself. Hell is, in my reading, the presence of God apart from the effective work of Christ.

This is an interesting question, indeed. We speak of omnipresence from the perspective of the physical, yet the Bible reveals that God is outside of the physical universe--God is spirit. He created the physical universe, but exists apart from it. He certainly entered into it as well in the incarnation and the Spirit indwells the spirits of believers everywhere.

"God is spirit, and those who worship him must worship in spirit and truth.” John 4:24 ESV

The Bible clearly presents God as omnipresent, yet this is quite possibly in a spiritual sense rather than a physical one.

Hell is actually the place where people are specifically separated from God.

They will suffer the punishment of eternal destruction, away from[a] the presence of the Lord and from the glory of his might... 2 Thessalonians 1:9 ESV

So, how could God be omnipresent and at the same time be separated from those in hell? It seems that separation does not necessitate isolation. When we experience conflict with another person, we could be standing right next to them, but be completely separated from them relationally. Perhaps the same is true of hell and those who are there. The presence of God need not be absent for there to be separation.

Well, God's omnipresence is logical under the assumption that God created everything, which Christians hold to be true.

If God created everything, nothing can exist out of God will. Things only exist if God wants them to exist.

Anything that exists is automatically "eternal" (in God's reference-frame, as opposed to our human reference-frame) because, as pieces of God will, they cannot be made void (which would require God to forget about them in an absolute sense, which is impossible).

From what I understand, Hell is not a place but more a state of a soul where it consciously rejects God while knowing who He is and of God respecting the soul's will.

I'm sure you already encountered once in your life a person who was proven wrong and still held to his statement despite all evidences and matching refuting testimony. You know how painful it is to see (because you know that this person knows they are wrong) and that it ultimately comes from stubborn pride.

Now imagine the private judgment at the time of death, and a person consciously choosing to reject God's presence rather than humiliate himself and admit that he has been wrong and that others were right. Add to that the perfect knowledge that they are wrong. Add to that the knowledge that the choice has been made once for all and can not be undone. Add to that the knowledge that the are the source of their state because God would have forgiven them everything immediately if they had asked. Add to that the hate that they feel towards God and toward themselves because they know that it's their own fault. Now put them with fallen "friends" that made them become like that.

So I think God "omnipresence" even in hell is not impossible. I would make a difference between actual presence, and relational presence. You can have someone in the same room (or lift/elevator) but ignore it completely. You can have a boss in your company. The company would not run without him, but you may never see him or speak with him. It's relational presence that is important.

About God relational presence:

• On earth, God presence cannot be felt completely because our limited capabilities.
• On earth, someone can have more God presence if he truly wants it and God gives it.
• On earth, someone can do the opposite.
• In "heaven", God presence will be full, leading to infinite happiness.
• In "hell", God presence (relational) will be null, with opposite effect.

In reading your question, I don't think the issue at hand is God's omnipresence at all. Frankly it's not a terribly important doctrine in the first place and while I think one could make a case for it from Scipture, I think it's a little forced. Much more importantly, the Scripture states the reverse quite plainly, that all things are in and held together by God/Christ.

Colossians 1:16-17 (ESV)
¹⁶  For by him all things were created, in heaven and on earth, visible and invisible, whether thrones or dominions or rulers or authorities—all things were created through him and for him. ¹⁷  And he is before all things, and in him all things hold together.

This includes hell. The problem with your question is not the doctrine of omnipresence, but the doctrine of hell. You state:

After all, hell is by definition, that one place that God is not.

But where does that idea come from in the Bible? The problem with hell is that God is there! It is where God pours out his eternal judgement on all things evil. This is a part of his nature and God's wrath will be a very present reality of hell for all eternity. While we can't paint an exact picture of hell, we do have have some fairly vivid and specific descriptions of the way God is involved in punishment:

Revelation 14:9-11 (ESV)
⁹  And another angel, a third, followed them, saying with a loud voice, “If anyone worships the beast and its image and receives a mark on his forehead or on his hand, ¹⁰  he also will drink the wine of God's wrath, poured full strength into the cup of his anger, and he will be tormented with fire and sulfur in the presence of the holy angels and in the presence of the Lamb. ¹¹  And the smoke of their torment goes up forever and ever, and they have no rest, day or night, these worshipers of the beast and its image, and whoever receives the mark of its name.”

What is different about it there is that it is a place separated from his grace. Neither the general grace that rains on the just and the unjust alike on this earth nor his specific graces experienced by believers will be experienced there. Folks will be separated from those aspects of God. He is only holding back his hand for a time.