ASHINGTON, March 21 — It has taken 50 years since Congress added "under God" to the Pledge of Allegiance for the validity of that cold war amendment to reach the Supreme Court, with arguments scheduled for Wednesday. But before the justices can decide whether those two words render the pledge unconstitutional, they have to answer a factual question that is inextricably entwined with the legal one: what exactly does it mean to pledge allegiance to "one nation under God"?

According to Michael A. Newdow, the California atheist who sued to stop the recitation of the pledge in his daughter's elementary school classroom, to recite the pledge with "under God" is to take "one side in the quintessential religious question `Does God exist?' " a statement of "sectarian religious dogma" that the government should not sponsor in a public school setting.

According to the Bush administration, which is defending the pledge, its recitation is no more a religious act than pocketing a coin imprinted with "In God We Trust." The administration's brief says both are simply patriotic acknowledgments of "the nation's religious history" and of the "undeniable historical fact that the nation was founded by individuals who believed in God," an empirical statement that poses no threat to the separation of church and state.

According to the Christian Legal Society, a group of lawyers, judges and professors, the pledge has a distinctly religious cast, and properly so. The group's brief says that the words "under God" support the concept of limited government, serving as a reminder that "government is not the highest authority in human affairs" because "inalienable rights come from God."

According to another group of religious individuals, 32 Christian and Jewish clergy members who take the opposite side in the case, reciting the pledge with "under God" invites a troubling kind of civic blasphemy. If children are supposed to utter the phrase without meaning it as an affirmation of personal faith, the group's brief asserts, "then every day, government asks millions of schoolchildren to take the name of the Lord in vain."

According to a form letter signed by President Bush and sent to those who wrote the White House about the federal appeals court decision in June 2002 that declared the pledge unconstitutional, reciting the pledge is a way of proclaiming "our reliance on God" and of "humbly seeking the wisdom and blessing of divine providence."

This letter, clearly in some conflict with the current official view, concluded by expressing the wish that "the almighty continue to watch over the United States of America." Americans United for Separation of Church and State and other organizations that oppose the administration's position included the letter in an appendix to their joint brief.

The striking range of views on just what "under God" signifies represents only the beginning, not the end, of the justices' task as they take up the case, Elk Grove Unified School District v. Newdow, No. 02-1624.

For example, if reciting the pledge is a religious act, is it a voluntary or coerced one, and is that distinction even relevant? In 1992, the court prohibited prayer led by the clergy at public high school commencement ceremonies on the ground that the graduating students were effectively coerced into participating. But a landmark Supreme Court decision from 1943 held that schoolchildren could not be required to recite the pledge. One of Dr. Newdow's points is that even if the pledge is nominally voluntary, daily classroom recitation inevitably labels children who do not take part as outsiders.

If reciting the pledge is seen as a patriotic statement of homage to the founding fathers, does that make it less problematic or more? Prof. Douglas Laycock of the University of Texas law school, speaking here Friday at the Pew Forum on Religion and Public Life, said that seen in that light, the message of the pledge is that "if you're doubtful about the existence of God, you are of doubtful loyalty to the nation." Professor Laycock represents the 32 clergy members who oppose the pledge.

If "under God" is unconstitutional, what is the fate of numerous other examples of religious references scattered throughout civic life and long accepted as a benign form of "ceremonial deism"?

Jay A. Sekulow, speaking at the same forum, said that even the Supreme Court marshal's intonation of "God save the United States and this honorable court" would be suspect.

Mr. Sekulow, chief counsel of the American Center for Law and Justice, a legal organization affiliated with the Rev. Pat Robertson, filed a brief on behalf of several dozen members of Congress who back the pledge as it is written, as well as 250,000 people who signed a supporting petition.

Justice Antonin Scalia has recused himself, raising the prospect of a 4-to-4 tie. His recusal, announced in October when the court accepted the case, stemmed from a speech he gave last year that pointedly criticized the lower court's reasoning.

Aside from the terrorism-related cases that will be argued next month, there is probably no more heavily freighted issue on the court's current docket than this one. Politicians touch the pledge at their peril: few have forgotten the 1988 presidential campaign, when George Bush, then the vice president, scored easy points by denouncing the veto that his Democratic opponent, Gov. Michael S. Dukakis, had cast of a bill requiring Massachusetts teachers to lead their classes in the pledge.

The attorneys general of all states have signed a brief supporting the pledge, as have the National School Boards Association and the National Education Association, the teachers' union.

The visibility of the pledge as a political issue faded after 1988, only to flare up again nearly two years ago, when Dr. Newdow, who has law and medical degrees and who argued his own case, won a 2-to-1 decision from the United States Court of Appeals for the Ninth Circuit, in San Francisco, that the pledge was unconstitutional. The court later narrowed its ruling to bar only recitation in public school classrooms.

Dr. Newdow will argue his case before the justices. He will be opposed by Solicitor General Theodore B. Olson and Terence J. Cassidy, counsel for the Elk Grove district, near Sacramento, where Dr. Newdow's daughter attends school.

A preliminary question, which will be part of the arguments on Wednesday, is whether Dr. Newdow, who was never married to the girl's mother and is not the custodial parent, has standing to pursue the case. The mother, Sandra L. Banning, has filed a brief supporting the pledge and her daughter's recitation of it. A decision that Dr. Newdow lacks standing would wipe out the lower court's ruling, but not the emotion the case has generated or the potential that a different plaintiff might renew the debate in the next case.