Our dreams can be no higher than our language. How often we take beautiful God-filled words and make them so banal and so far short of the wonderful pictures God has painted for us.
Even many secularists will exchange Christmas cards carrying the phrase "Peace on Earth, Good Will to Men" - the Christmas angelic proclamation to the shepherds. It should be enough of a clue that if secularists would use the word "peace" then something (the meat) of the depth of meaning God intended is missing. Yet, could there still be a hint or clue there?
Most people first think of the lack of war or an unconflicted state of mind as the meaning of "peace", yet we are confronted with perpetual war and almost constant conflict - unless we find internal escape from the world with the Buddhists or accept the unreality of reality with the Hindus. We are all painfully aware there is a problem, we only differ on where the real problem resides.
The unbelieving world sees the problem as a correctable, superficial human problem (obviously, with other people) that will yield to liberal doses of education, law, and "I'm OK, You're OK" psychotherapy. But God has defined the problem as a hereditary illness and brokenness within called rebellion against God that we all have willfully embraced. We have estranged ourselves from home, and, like the prodigal son in a far country, we all long for home and the missing relationship - even when we don't know where home is, we simply know there ought to be a home.
The external wars and conflicts are just extensions of the sickness and longings from within. For those willing to admit this source of the problem - me - God sent a Son to be born in a manger to make the only way to restore the wholeness between Father and us, His children.
And so the angels proclaimed at the birth of Jesus, "Wholeness and restored relationship with the Father is available to all who will acknowledge the Giver and accept the Gift." Now, there can be Peace even when there is no peace. In fact, without this internal "Peace on Earth", there is no hope of external "peace on earth" at all.
Savor the full beauty and wonder of that night long ago. See the Glorious picture of when our Peace came.
p.s. - Just viewed a video post by Greg Koukl (Stand to Reason) on this verse from Luke 2:14. He added one additional perspective - horizontal vs vertical. Secular application of "Peace" in this passage is horizontal, man to man, but the Biblical application is vertical, God to man. This is very similar to the common distortion of Mt 22:36-39 - "Love your neighbor as yourself." It appears the vertical relationship always precedes and informs the horizontal.