I in them and you in me explains the meaning of one in the last part of verse 22. Again the matter of someone being “in” another person causes difficulty, and it may be best to translate “just as I am united with them, and you are united with me.” Die Bibel im heutigen Deutsch translates “I work in them and you work in me,” and New American Bible “I living in them, you living in me.” To show the relation of this statement to the preceding statement in verse 22, it may be useful to have an introductory expression such as “that means,” for example, “To be one means that I am in them and you in me” or “… I am living in them and you are living in me.”
So that they may be completely one indicates both the intended purpose and the goal of I in them and you in me. Completely one is rendered “perfectly one” by Moffatt, Revised Standard Version, and New English Bible. Jerusalem Bible has “completely one,” and Goodspeed translates “be perfectly unified.” New American Bible reads “that their unity may be complete,” and Die Bibel im heutigen Deutsch has “so may they come to a perfect unity.”
That the world may know that you sent me and that you love them as you love me may refer to the reason Jesus had for giving his disciples the same glory that he possessed (verse 22); or it may refer to the unity of the disciples mentioned in the previous clause. The second of these choices is preferable—the absolute unity of Jesus’ disciples is to challenge the world to acknowledge that the Father sent the Son, and that the Father loves the disciples in the same way that he loves the Son.
In verse 21 Jesus speaks of the world’s “believing” and here of the world’s “knowing.” There is no essential difference in the meaning of these terms in the present context. (See comments at 17.3.)
Them, in the clause that you love them, is taken by at least one commentator as a reference to the world. Elsewhere in his Gospel John does speak of God’s love for the world (3.16), but in the present context the focus is on the relationship between the Father and the Son and the believers. Thus it is better to take them as a reference to the disciples, rather than to the world. Here Jesus prays that the world may recognize not only that he comes from the Father, but that the Father loves the Christian believers in the same way that he loves the Son.
Quoted with permission from Newman, Barclay M. and Nida, Eugene A. A Handbook on the Gospel of John. (UBS Handbook Series). New York: UBS, 1980. For this and other handbooks for translators see here .