Swearing on a Bible was supposed to increase pressure on the witness to tell the truth, because of their fear of God should they violate an oath taken on the Bible.
My opinion is that this is a non-christian concept. We are not to swear on anything, but simply to let our yea be yea and our nea be nea.
But in any case, surely having a non-christian swear on a bible serves no useful purpose. They don't respect the bible or the religion, why would they care? Even the "so help me God" would mean nothing to an Atheist.
The problem is, if a muslim WANTS to swear on a Quran, they should be able to do so. It would mean as much as an average christian swearing on a bible. It's just symbolic, and the symbol should have some meaning.
From the state perspective, we should find out for each witness what it is that they value most, and have them swear on it -- if we really want it to be meaningful. Of course, we couldn't do that.
Last thought -- is swearing on a Quran acceptable to muslims? Or is it a sacrilige? We certainly would have to take great care -- if a non-muslim chose to swear on a Quran, and put his hand on it, that would be "desecration" and maybe some terrorists might try to kill us. (HEAVY SARCASM ALERT, LIKE TERRORISTS NEED A REASON).
My opinion is that this is a non-christian concept. We are not to swear on anything, but simply to let our yea be yea and our nea be nea.
It has also been recognized since the beginning of this Republic that certain Christian sects (and also, Orthodox Jews) do not swear oaths of any kind, therefore the "affirmation" option was included. It was called the "Quaker oath."
I think that we should do away with "swearing in" altogether, and in cases of court testimony read the witness a disclaimer warning that lying on the witness stand will result in criminal procsecution for perjury.