President Trump's term of office finishes at noon on January 20. From then on he becomes just another American citizen and, although he will continue to be addressed as "President" Trump, that is merely a courtesy title with no constitutional or legal rights attached to it.

It is now clear that the Senate trial will not commence before President Trump leaves office, and the US Constitution makes no specific provision for impeaching an ex-president. A leading proponent of the argument that Trump's trial would be unconstitutional is a well-known former Appeals Court judge, J. Michael Luttig, who believes the constitution is clear on this point. "Once Trump's term ends on Jan. 20," he writes, "Congress loses its constitutional authority to continue impeachment proceedings against him - even if the House has already approved articles of impeachment."

The constitution lends some support to Luttig's position. It specifically says: "The president, vice-president and all civil officers of the United States, shall be removed from office on impeachment for, and conviction of, treason, bribery, or other high crimes and misdemeanours." Citizen Trump wouldn't fall into any of these categories. Furthermore, as Luttig has pointed out, this clause is a statement about the very purpose of impeachment - that is to remove a president from office. Citizen Trump would have no civil office to be removed from after January 20.

A contrary argument has been made by Lawrence H. Tribe, a distinguished law professor at Harvard University and one of America's leading authorities on constitutional law. He bases his position on the clause in article I of the constitution, which says: "Judgment in cases of impeachment shall not extend further than to removal from office, and disqualification to hold and enjoy any office of honor, trust or profit under the United States ..."

The comma in the middle of that sentence is critical. Tribe believes that removal from office and disqualification from holding any office in the future are two separate penalties and, although Trump wouldn't have an office to remove him from, preventing him from becoming president again is what the impeachment power is all about. "Its function is prospective rather than punitive," Tribe asserts. It is there "to prevent officers who have betrayed their oaths from committing further abuses and thereby inflicting future harm".

It is true that in previous impeachment cases the Senate has regarded these penalties as distinct. It takes a two-thirds vote of the Senate to convict a president on impeachment, and removal from office would be automatic. But a separate vote is taken on disqualification, and that is based on a simple majority. However, if the purpose of impeachment is disqualification from future office, then it has to be asked why these two penalties are treated separately, and why disqualification is subject to a lesser standard, and why some of those convicted on impeachment in the past have not been barred from future office?

As with all arguments turning on ambiguities and silences in the US constitution, they need to be considered in detail and at length. What can be said about this argument so far is that it seems to have made little impression on the members of Congress involved in the impeachment process, or the majority of journalists reporting it. They assume that the impeachment trial of Donald Trump will go ahead as if he were still president of the United States.

But there is one aspect of the impeachment process that could turn this academic debate about the constitutional power of impeachment into a practical reality. The clause in article 1, section 3 of the constitution relating to the Senate having the "sole power to try all Impeachments" also says, seemingly unambiguously, that "When the president of the United States is tried, the Chief Justice [of the US Supreme Court] shall preside."

So, the first test of Luttig's argument will be whether or not Chief Justice John Roberts shows up to preside over the Senate trial. When it takes place, the President of the United States will be Joe Biden, but he will not be on trial. On the face of it, there is no reason for Chief Justice Roberts to be there.

If Roberts does preside, it would be taken as a signal that the post-presidential impeachment trial of Donald Trump is legitimate and constitutional. It would also be a signal that the Supreme Court would probably not entertain any challenge by Trump to the constitutionality of the trial. Surely Roberts would recognise a conflict of interest if he presided over the trial and then had to sit in judgment when Trump's challenge reached the court?

If, however, Roberts doesn't show up, then this action could only be read as meaning that the "president" is not being tried and citizen Trump may have grounds for a constitutional challenge. In the past, the Supreme Court has refused to get involved in impeachment cases because the constitution gives the Senate the "sole power to try all impeachments". This challenge would not be about the scope of the "sole power", but rather about who is subject to the impeachment process.

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Judge Luttig believes that only the Supreme Court can answer the question of whether Congress can impeach and convict an ex-president. He also concludes that: "It is highly unlikely the Supreme Court would yield to Congress's view that it has the power to impeach a president who is no longer in office when the constitution itself is so clear that it does not."

Luttig was a conservative judge with impeccable Republican Party credentials, and was considered by George W. Bush for a seat on the Supreme Court. He is probably in a good position to anticipate the outcome if the impeachment trial of Donald Trump did reach the Supreme Court, with its strong conservative majority and three of its justices owing their place on the court to him.

If it all turns out as Luttig suggests, it would create a major constitutional crisis in the US that would overshadow the substance of the impeachment charges. In any case, even if the constitutionality of the trial was not questioned, Trump could still escape a conviction if the Senate failed to secure a two-thirds vote against him.

The impeachment of Donald Trump may turn out to have unanticipated consequences, and may not lead to the justice that many Americans might expect from their system of government. Chief Justice Roberts could well provide the first clue about where the complex impeachment process is headed. But the saving grace of the US constitution is that it recognizes a path to justice beyond the impeachment process. Whatever happens in the Senate, or possibly in the Supreme Court, Donald Trump will still be subject to normal criminal procedures in the ordinary courts, where complex constitutional interpretation is not likely to distract from a "trial, judgment and punishment, according to law".