The legal issue is connected to a larger question: how to deal with the frequent claim that online speech is a special form of playacting, in which a threat is as unreal as an attack on an avatar in World of Warcraft. Gilberto Valle — known as the Cannibal Cop for fetish chat-room messages in which he talked of capturing, cooking and eating specific women — persuaded a judge to overturn his conviction by saying he was just expressing a dark fantasy. In the ongoing ‘'GamerGate'’ campaign, a faction of video-game enthusiasts tweeted death threats to women who had criticized misogyny in video-game culture. When a few of the women felt scared and left their homes, some gamers scoffed, dismissing the threats as ephemeral.

If it’s possible to shrug off anonymous online threats, it’s much harder to do that when a threat is made by someone you know intimately. In these cases, dread felt by targets is rational and may leave them struggling to sleep, eat or work. To escape, they may uproot themselves and their families. This kind of disruption fits with the Supreme Court’s rationale for allowing laws that ban threats. ‘'We usually think of freedom of speech as enhancing liberty, but this is speech that takes away someone else’s liberty,'’ said Danielle Citron, a law professor at the University of Maryland.

For years, activists have lobbied for laws that punish stalking, given that burden of fear. Elonis’s threats, they say, should be treated like stalking because it was reasonable for Tara to feel threatened by them. Cindy Southworth, a vice president of the National Network to End Domestic Violence, points out that when a relationship goes bad, threats become both a tool of manipulation and a reliable predictor of physical assault. ‘'Every abuser says, ‘I didn’t mean for her to think I would kill her,' '’ Southworth said.

But advocates for civil liberties want to give more breathing room to free speech and don’t think the question of whether a statement online qualifies as a threat should be ‘'in the eye or ear of the beholder,'’ the A.C.L.U. and other groups put in a brief they filed in the Elonis case. ‘'Words are slippery things, and one person’s opprobrium may be another’s threat.'’ In a case that worries free-speech activists, a teenager named Justin Carter got into a Facebook exchange and wrote, ‘'I think I’ma SHOOT UP A KINDERGARTEN.'’ After someone in Canada alerted the police, he spent months in a Texas jail for that comment and is still facing charges. ‘'I wasn’t trying to scare anyone, I was trying to be witty and sarcastic,'’ he wrote to the judge. ‘'I failed, and I was arrested.'’

To prevent people from being locked up over a misunderstanding, the A.C.L.U., like Elonis, wants a higher bar for conviction. ‘'The age-old principle is that we don’t criminalize speech without that clear intent,'’ said Lee Rowland, an A.C.L.U. staff attorney.

The truth is that even when intent to do harm seems obvious, online threats are rarely prosecuted. Citron looked at the federal law that is the basis for the Elonis case and found that it has been enforced fewer than 50 times, online and off, over the past eight years. Stalking laws, domestic-violence advocates say, aren’t enforced much, either.

If the Supreme Court requires evidence of a speaker’s intent to harm in true-threats cases, it could give the police and prosecutors one more reason not to bring them. Maybe that’s simply the unavoidable consequence of a broad interpretation of the First Amendment. Let’s be clear, though, that such an approach to free speech doesn’t come free. The choice in this case between points of view — Anthony’s or Tara’s — mirrors another choice, between types of personal liberty. His or hers.