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The sitting president has accused his predecessor of an act that could have gotten the past president impeached. That's not your ordinary exercise of free speech. If the accusation were true, and President Barack Obama ordered a warrantless wiretap of Donald Trump during the campaign, the scandal would be of Watergate-level proportions.

But if the allegation is not true and is unsupported by evidence, that too should be a scandal on a major scale. This is the kind of accusation that, taken as part of a broader course of conduct, could get the current president impeached. We shouldn't care that the allegation was made early on a Saturday morning on Twitter. That's when Trump wrote: "How low has President Obama gone to tapp [sic] my phones during the very sacred election process. This is Nixon/Watergate. Bad (or sick) guy!"

The basic premise of the First Amendment is that truth should defeat her opposite number. "Let her and Falsehood grapple," wrote the poet and politician John Milton, "who ever knew Truth put to the worse in a free and open encounter?"

But this rather optimistic adage accounts only for speech and debate between citizens. It doesn't apply to accusations made by the government. Those are something altogether different.

In a rule-of-law society, government allegations of criminal activity must be followed by proof and prosecution. If not, the government is ruling by innuendo.

Shadowy dictatorships can do that because there is no need for proof. Democracies can't.

Thus, an accusation by a president isn't like an accusation leveled by one private citizen against another. It's about more than factual truth or carelessness.

The government's special responsibility has two bases. One is that you can't sue the government for false and defamatory speech. If I accused Obama of wiretapping my phone, he could sue me for libel. If my statement was knowingly false, I'd have to pay up. On the other hand, if the president makes the same statement, he can't be sued in his official capacity. And a private libel suit mostly likely wouldn't go anywhere against a sitting president — for good reason, because the president shouldn't be encumbered by lawsuits while in office.

The second reason the government has to be careful about making unprovable allegations is that its bully pulpit is greater than any other. True, as an ex-president, Obama can defend himself publicly and has plenty of access to the news media. But even he doesn't have the audience that Trump now has. And essentially any other citizen would have far less capacity to mount a defense than Obama.

For these reasons, it's a mistake to say simply that Trump's accusation against Obama is protected by the First Amendment.

False and defamatory speech isn't protected by the First Amendment.

And an allegation of potentially criminal misconduct made without evidence is itself a form of serious misconduct by the government official who makes it.

When candidate Trump said Hillary Clinton was a criminal who belonged in prison, he was exposing himself to a libel suit. And the suit might not have succeeded, because Trump could have said he was making a political argument rather than an allegation of fact.

But when President Trump accuses Obama of an act that would have been impeachable and possibly criminal, that's something much more serious than libel. If it isn't true or provable, it's misconduct by the highest official of the executive branch.

How is such misconduct by an official to be addressed? There's a common-law tort of malicious prosecution, but that probably doesn't apply when the government official has no intention to prosecute.

The answer is that the constitutional remedy for presidential misconduct is impeachment.

That would have been the correct remedy if Obama had "ordered" a wiretap of the Republican presidential candidate's phones. The president has no such legal authority. Only a court can order a domestic wiretap, and that only after a showing of probable cause by the Department of Justice and the Federal Bureau of Investigation.

Breaking the law by tapping Trump's phones would have been an abuse of executive power that implicated the democratic process itself. Impeachment is the remedy for such a serious abuse of the executive office.

That includes abuse of office in the form of serious accusations against political opponents if they turn out to be false and made without evidence. These, too, deform the democratic process.

The Constitution speaks of impeachment for "high crimes and misdemeanors." A lot of ink has been spilled over these words, which date back at least to impeachment proceedings in the 14th century. This isn't the place for a detailed analysis.

Suffice it to say that what makes crimes "high" is that they pertain to the exercise of government office. That's exactly what accusations by the executive are: actions that take on their distinctive meaning because they are made by government officials.

What's more, government acts that distort and undercut the democratic process are especially serious and worthy of impeachment. The Watergate break-in to the Democratic National Committee headquarters was part of an effort to steal the 1972 election. A wiretap of Trump's campaign would've had political implications.

And accusing the past Democratic president of an impeachable offense is every bit as harmful to democracy, assuming it isn't true. Obama is the best-known and most popular Democrat in the country. The effect of attacking him isn't just to weaken him personally, but to weaken the political opposition to Trump's administration.

Given how great the executive's power is, accusations by the president can't be treated asymmetrically. If the alleged action would be impeachable if true, so must be the allegation if false. Anything else would give the president the power to distort democracy by calling his opponents criminals without ever having to prove it.

Noah Feldman is a Bloomberg View columnist. He is a professor of constitutional and international law at Harvard University and was a clerk to U.S. Supreme Court Justice David Souter. His books include "Cool War: The Future of Global Competition" and "Divided by God: America's Church-State Problem — and What We Should Do About It." nfeldman7@bloomberg.net.