Dominus vobiscum (note that strictly speaking the priest should have his eyes downcast)
The Council of Hippo, way back in 393, ruled that no lector could be permitted to say
Dominus vobiscum, for the excellent reason that the people could not properly reply to him
Et cum spiritu tuo – since only the ordained in what came to be called major orders (bishops, priests and deacons, but not subdeacons, who have been enumerated among the major orders only since the 13th century) "have the Spirit" given them by their ordination, as St John Chrysostom says (for thereby priests and pontiffs are empowered to offer the Holy Sacrifice); lesser ministers, not having been sealed with the indelible sacramental character imprinted by the Holy Ghost, cannot be said to have the Holy Spirit in the unique fashion of those in holy orders.
(Unfortunately, this vital distinction has been veiled by the current impoverished English version used in the modern liturgy these past forty years and more – but thankfully, the new translation about to be introduced next year will at last remedy this, so we will reply to our priests, "And with your spirit".)
What the significance of this salutation? It is a deprecatory blessing, a jussive subjunctive, a commanded blessing authoritatively stated by the priest, who is ordained to bless: "The Lord be with you" is not a mere wish, but a strong prayer made in the name of the Church, a sacramental working not merely ex opere operantis, but ex opere Ecclesiæ, which will be effective if not impeded by sin. It is as it were a prophetic conditional declaration: for all prophecy is conditional (as with Jonah's "Yet forty days and Nineveh will be destroyed" – the Ninevites did penance, and the threatened judgement was averted; in reverse, a prophecy of good will be frustrated by evil deeds).
The term "salutation" is suggestive: for to salute someone is to wish them good health (salus), or, in supernatural terms as should become Christians, to heartily desire and pray for that person's eternal salvation.
It is even more evident that this applies in the case of the Pax Domini sit semper vobiscum, which Luther – of all people – quite perspicaciously regarded as a prayer of blessing to prepare the people for making their communion, something in his age largely forgotten, but which is borne out by parallel, even more explicit pre-communion benedictions in related liturgies such as the Ambrosian and Mozarabic, to say nothing of the episcopal benedictions imparted at that point of the Mass, as survivals of the old Gallican rite or as embellishments of the phrase, during mediæval and later times.
"The Lord be with you", then, is a powerful prayer, not merely a conventional half-understood turn of phrase to be mumbled and ignored: the priest, standing in the place of Christ, blesses his flock, that the Risen Lord be with His people the Church, and His faithful then call down the same blessing upon their priest. We recall the promise of Our Saviour, victorious over sin and death: Ecce Ego vobiscum omnibus diebus, "Behold, I shall be with you all days..." – "For when two or three are gathered in My name, there am I in the midst of them."
The priest says Dominus vobiscum eight times during the traditional Mass (seven, at High Mass, since then the Deacon says this at the Gospel, instead of the priest), four times facing the altar, and four times turning to face the people, extending his hands in blessing. (He turns also a fifth time when saying Orate fratres, and a sixth when imparting the concluding benediction.)
Jungmann explains that each time this salutation is issued, it marks an important stage in the celebration of the Mass: the summons to pray and to hearken at the Collect, the Gospel, the Offertory, the Preface, the Postcommunion, the dismissal (and, secondarily, since at High Mass this is not sung aloud, at the priest ascending the altar and at the Last Gospel).
As regards the Gospel and the dismissal, in both cases it precedes the deacon's part – indeed, it is thought that originally, as at the dismissal, Dominus vobiscum was sung by the priest, not the deacon, at the Gospel. As regards the Collect, the Preface and the Postcommunion, it heralds the main sacerdotal prayers. The Orate fratres likewise precedes the Secret, and the Pax Domini the reception of the Sacrament. Why is it not sung at the Lord's Prayer, though Oremus is? Because this is a continuation of the great prayer begun at the Preface and continued through the Canon.
Jungmann also notes that the Dominus vobiscum in a sense prefigures the Per Dominum nostrum Jesum Christum of the orations, and likewise the Et cum spiritu tuo the Amen. We can only pray in Christ, and through Christ; and the good Christian people respond to the priest's greeting, as with a hearty "So be it" they express their agreement with the prayer.
I am indebted for what follows to St Peter Damian, most of whose Letter 28, to Leo the hermit, I've just read: it is a treatise on the use of "The Lord be with you", answering the query of certain solitaries, who wondered whether they should greet the stones and boards of their cells, or reply themselves to their own greeting...
That Doctor of the Church and Cardinal replied to such questions, "No, the priest is not alone. When he says Mass or prays, he has before him the whole Church mysteriously present and she it is whom he salutes by saying Dominus vobiscum. And since he represents the Church, she answers him through his own mouth, Et cum spiritu tuo." (St Peter Damian, Dom. vob., c. 6, 10, etc.)
If a priest says a private Mass with only one server present, or only one member of the faithful, nonetheless he still says Dominus vobiscum, not tecum. Similarly, if the priest be by himself, he himself gives the response, even saying Et cum spiritu tuo, being forbidden by the tradition of the Church from modifying these hallowed Scriptural words, thus prevented from perverse misused rationality tricking him into saying Et cum spiritu meo!
One might as well be entirely ridiculous and say, "Let me pray", instead of the universal "Let us pray", which is used even if one is alone; likewise, as all the collects of the Office and Mass are couched in the plural, to be recited identically whether alone or with others, it would be insane madness to presume to change them into the singular. The Psalms, likewise, indifferently use singular or plural, even within the same psalm – as St Peter Damian put it, "our solitude is communal and our community is [one, or] singular".
So, too, even if the priest be entirely alone, is he not, as St Augustine wrote, both a priest for the Christian people, and also himself a Christian? for he is at once by ordination a man set apart to act in the person of Christ the Head as priest and mediator, and by baptism a member of Christ's Body the Church. Therefore, qua sacerdos, in persona Christi he says Dominus vobiscum, and qua Christianus, in persona Ecclesiæ replies to his own greeting with Et cum spiritu tuo. For in himself he is the local instantiation of the entire Church, one member acting in the name of all – just as all Christians together form one Body: in pluribus una, in singulis tota. For we all have received one Spirit to drink, as the Apostle recalls, and this Spirit dwells wholly in each as well as in all.
The priest all alone is still in a real, sacramental, mystical unity with the whole Church, with whom he shares and to whom he is joined by the unity of faith and charity. Furthermore, even at the altar by himself, he sees by faith what his eyes cannot: the faithful throughout the world (yea, and those departed, the saints and the holy souls, and also the angels), truly, spiritually present at his solitary Mass: for every Mass is an action of Christ and His Church.
Mgr Klaus Gamber was once asked who it was he greeted each day at his Mass all alone (for, unwilling to use the modern Liturgy, he was condemned by the illiberal liberalism of those times to offer the Sacrifice behind closed doors, he being thought an embarrassment best sequestered). He replied that it was all the forgotten, despised Christians whom he saluted in spirit.
In any case, it is an established principle of liturgy that one can supply the words of another – as at baptism, when the parents and godparents speak on behalf of the speechless infant.
Thus, even at the traditional rite of Mass when alone (I am constrained to mention that the Ordinary Form has a contrary rule), the priest still says Dominus vobiscum, and, for utterly the same reason, Pax Domini sit semper vobiscum; similarly, he blesses those unseen, but to whom he is present in Christ.