It seems that the principle is timeless. That is, the head-covering (hair) for women is a timeless principle in all ages and in all places, since angels have co-existed with man since man was created. In fact, angels preexisted man.
The Hebrew Bible (Job 38:7) indicates that the "sons of God" rejoiced at the creation of the world. These "sons" were angels (please click here), and therefore they preexisted man on the earth. If we recognize that the serpent in the Garden of Eden was Satan (Rev 12:9 and Rev 20:2), then angels were aware and observed Adam and the woman (Eve) in the Garden of Eden; in fact, cherubim were posted to guard the Garden of Eden so that no one could return there after Adam's disobedience (Gen 3:24). According to the Christian New Testament, angels today observe the behavior of men on earth (1 Cor 4:9; Eph 3:10; 1 Tim 3:16; and 1 Pet 1:12).
Thus angels have been aware of the creative order; that is, the man (male) was created before the woman (1 Cor 11:8-9). Before the introduction of sin into the world, the man (male) was the representative of God's authority on earth. The Lord God "crowned" him with God's authority of rulership on the earth (Ps 8:5-6). These verses in the Psalms indicate that the "head" of the man is therefore "crowned" with the glory of authority. (Incidentally and very interestingly, these same verses indicate that man was created lower than the angels --please compare Hebrews 2:7-8-- that is, the angels precede man in the creative order.) Then woman was created after the man as his "help meet" (Gen 2:18, KJV). Thus her head was not "crowned" with authority, but with the glory of the beauty of her hair (1 Cor 11:15).
God's glory is his authority (1 Chr 29:11). Man (or the male) reflects that glory as the authority of God on the earth. His head is therefore not to be "covered" with the glory of beautiful hair in the fashion of a woman (1 Cor 11:14). Although woman is "one flesh" with man (Gen 2:23), her glory on the other hand is her beauty, and therefore her head is covered with hair (or a wig, which is the alternative head-covering for a woman). She is not the glory of God (authority), but the glory of man (beauty). Otherwise a woman without hair is shamed. If a woman insists on bucking the creative order (and she happens to have long hair), then she might as well as shave her head (1 Cor 11:5), because bucking the creative order is shameful. Likewise as just mentioned, a male with long hair is shameful (to which Paul invokes "nature" as testimony in 1 Cor 11:14).
In other words, the angels have recognized the creative order between God and man, since they existed before man. (Thus man was created lower than the angels, which the angels also recognize.) Therefore the biblical principle of the created order (man, then woman) is not restricted to any cultural or era of time... but is timeless to the present day. That is, the angels also recognize God's creative order between man and the woman in creation, and the place of man, who is created lower than the angels. Man and woman are "one flesh," but the one who reflects the authority of God is man, and the one who reflects the glory of man is the woman (and not vice-versa).
Thus the principle of the "creative orders" of God are as timeless as the angels -- thus Paul mentions "because of the angels."
For an amplified discussion of the "created orders," please click here.