Most modern Christians assume that at the incarnation: 1) the Son of God left Heaven, 2) the Son of God limited his deity, and 3) the Son of God was physically separated from the Father. These assumptions should be clarified by Scripture and the Christian tradition can help that clarification.
God is Immutable
First, it is essential to remember that the Logos is true God and, therefore, timelessly God. God cannot change. God said, “For I, the Lord, do not change; therefore you, the sons of Jacob, have not come to an end” (Mal. 3:6). God’s unchangeable nature (immutability) extends to his mind. God said, “God is not man, that he should lie, or a son of man, that he should change his mind. Has he said, and will he not do it? Or has he spoken, and will he not fulfill it?” (Num. 23:19). If God is omniscient and distinct from his space-time creation, it would not make sense for him to “change his mind” since he knows everything perfectly and eternally.
Furthermore, a change in the divine mind would necessitate some weakness in the divine mind that led to the change. James 1:17 clearly teaches that there is no “variation” in God. Therefore, there can be no change or limitation of the divine nature. God remains infinite (omniscient, omnipresent, omnipotent, and etc.).
God is Omnipresent
Secondly, since the Logos is infinite, eternal, and immutable, he cannot “leave.” The divine nature did not cease to be omnipresent. The Lord was incarnate through the assumption of his human nature to his person. The Logos remained infinite because the Logos is God. The human nature was conceived, grew physically and spiritually and psychologically, died and rose again. So, the Son was on earth, but the Son was also omnipresent. Both these truths exist without contradiction because the two natures exist on different planes of existence. Furthermore, this must be true since the finite cannot contain the infinite. Since the Son is infinite and unchangeable, the Son also could not be separated from the Father. Only the human nature could experience any sort of separation from God.
Christ, True God and True Man, and the Extra-Calvinisticum
“Partitive exegesis” describes the practice of biblical writers when they speak of one nature but not the other. The New Testament will speak of the human nature as limited (growing, developing, hungering, sleeping, dying, etc.). The New Testament also speaks of the divine nature as true God without limitation and full of glory. Both sets of statements are true because both natures exist in the one person of Christ. At other times Christ is spoken of as one person without concern for distinguishing the natures. Acts 20:28, for example, spoke of how Christ “purchased the church with his own blood.” God doesn’t have blood. Humans have blood. Christ, since he has two distinct natures, is both God and human. Only Christ, then, could fulfill what Acts 20:28 requires.
The reality that the Logos remained infinite and omnipresent while the human nature remained finite and limited to one location is often called the extra-Calvinisticum. In the early Christological debates, Athanasius reasoned that:
For he was not enclosed in the body, nor was he in the body but not elsewhere. Nor while he moved that [body] was the universe left void of his activity and providence. But, what is most marvelous, being the Word, he was not contained by anyone, but rather himself contained everything. And, as being in all creation, he is in essence outside everything but inside everything by his own power, arranging everything, and unfolding his own providence in everything to all things, and giving life to each thing and to all things together, containing the universe and not being contained, but being wholly, in every respect, in his own Father alone. So also, being in the human body, and himself giving it life, he properly gives life to the universe also, and was both in everything and outside all.
They thrust upon us as something absurd the fact that if the Word of God became flesh, then he was confined within the narrow prison of an earthly body. This is mere impudence! For even if the Word in his immeasurable essence united with the nature of man into one person, we do not imagine that he was confied therein. Here is something marvelous: the Son of God descended from heaven in such a away that, without leaving heaven, he willed to be borne in the virgin’s womb, to go about the earth, and to hang upon the cross; yet he continuously filled the world even as he had done from the beginning!
Athanasius continued his argument to display how the Logos, though united to, was distinct from the human nature. He said, “he was not bound to the body, but rather was himself wielding it, so that he was both in it and in everything, and was outside everything, and at rest in the Father alone.” The dyothelite nature of the incarnation was emphasized here. The Logos was active and did divine actions while at the same time working through the human nature.
The extra-Calvinisticum highlights the true force of dyophysitism, namely that there are two true natures present in Christ. The Logos “was not bound to the body.” The Logos continued to be true God, and retained the true mind of God. Since the Logos remained true God, then he remained the caretaker of the universe as is demonstrated in Colossians 1:17-20. Paul said, “in him all things hold together” (Col 1:17). Even as he reconciled all things through himself on the cross (Col 1:20), he remained the sustainer of the universe in Heaven (Col 1:17). The Logos remained true God and as true God he also retained the true divine mind.
Even during the incarnation, the Logos remained true God. Creation is “experienced” only in virtue of the true humanity assumed by the Logos. Similar to how God is omnipresent and omniscient in virtue of his action of upholding the universe, the Logos was present in the true humanity which creatures saw and interacted with during the incarnate life. “Like all other men, the man Jesus is in His time, His lifetime, the time He needs like all other men to be able to live a human life. But in this time of His He lives as the One He is in virtue of His unity with God.”
Two Natures (Dyophysitism) and Our Salvation
God, therefore, did not change at the incarnation. The Son remained true God and became true man. Without loosing anything that he was, he added the human nature to himself. This incarnation was necessary for the salvation of mankind. Hebrews 2:17-18 says, “Therefore, in all things He had to be made like His brothers so that He might become a merciful and faithful high priest in things pertaining to God, to make propitiation for the sins of the people. For since He Himself was tempted in that which He has suffered, He is able to come to the aid of those who are tempted.”
 St Athanasius the Great of Alexandria, On the Incarnation, 17, ed. John Behr, trans. John Behr, vol. 44a, Popular Patristics Series (Yonkers, NY: St Vladimir’s Seminary Press, 2011), 85–87.
 Athanasius, On the Incarnation, 17.
 Barth, Church Dogmatics: The Doctrine of Creation, Part 2, vol. 3, 439.