John's portrayal of Jesus' agony in Gethsemane shows Jesus praying: "Now I am no more in the world, but these are in the world" (Jn. 17:11). He is returning to the Father in exaltation, so he is no longer in the world. He no longer will interact with others in the way that he has previously. He will not teach or preach to the multitudes. He will heal no more the lame, halt, or blind. His remaining work is to undergo the agony of his pain in the Garden of Gethsemane and on the cross, to die, to preach the gospel in hell, and to be resurrected, returning to the Father to sit in glory at his right hand. But his disciples remain in the world for which he will now suffer, and he is concerned about them being in that world.
Jesus' concern shows itself when he prays for his followers; he prays that they may have the same unity that he and the Father have: "[I pray] that they all may be one; as thou, Father, art in me and I in thee, that they also may be one in us" (Jn. 17:21). Presumably that unity is a protection against the problem of remaining in the world while a follower of Jesus. What kind of unity does Jesus have in mind? What is the unity of the Godhead?
The next sentence of the prayer is the beginning of an answer: "Keep through thine own name those whom thou hast given me" (Jn. 17:11). George R. Beasley-Murray's argument that the Greek en here means "in loyalty to thee" rather than "through" is persuasive.* In that case, the clause means "Keep those whom you have given me loyal to your name."
To be one as followers of Jesus is to be one in the name of the Father. It is to be able to genuinely call him "Holy Father," as Jesus does (Jn. 17:11). It is to be loyal to him as Jesus is—as a son, a child. Ultimately what makes us one as Christians, then, is not doctrine (though I don't want to make light of doctrine or its importance), but our status as children of our Holy Father, as those who have joined the holy family of the Father and the Son.
Mormons take the claim that we are God's children quite seriously. For us it is not merely a metaphor. We have a children's hymn, "I am a Child of God" (Children's Songs, #2). The first verse says:
I am a child of God,
And he has sent me here,
Has given me an earthly home
With parents kind and dear.
This reflects our belief in human pre-existence: prior to mortal life, all those who have lived on the earth or who will live on it were with the Father in a spiritual existence (Abraham 3:22-26). But that is not what the New Testament understands when it speaks of being a child of God, which is not to say that the belief is not true, only that it is not what the New Testament is speaking of.
In the New Testament, not everyone is a child of God. Rather, his children are those who have returned to the Father as adoptees through the indwelling of the Holy Spirit (cf. Rom. 8:14-15). Though we begin as children of God, through sin we give up that birthright—our place in his celestial family—and we can only reenter by being adopted back into it.
Jesus' prayer in the Garden explains what that adoption means: in John 17:5-6 and 26, he shows us that the disciples have been made one by receiving the revelation he has given them. Presumably that is his self-revelation as love, for he prays "that they may be perfect [whole] in one [i.e., unified]; and that the world may know that thou hast sent me, and hast loved them, as thou lovest me" (Jn. 17:23). Jesus' revelation of himself is a revelation of the Father, a revelation of their mutual love (1 Jn. 4:16). And the unity of the disciples is the unity created in the loving imitation of that divine love.
Our adoption into the family of God occurs when we receive the revelation of the Father through his Son, Jesus the Messiah. We receive a revelation of the infinite love ultimately demonstrated in the Garden, on the cross, and in the resurrection. To be a child of God in the New Testament sense is to be one who has seen God's love on the cross, accepted it, and committed himself or herself to imitate it, to become fully in the image of God, remaining loyal to the name of the Father in love.