Henry Montgomery has spent more than 50 years behind bars after his conviction for killing a sheriff's deputy in Baton Rouge, Louisiana. He was 17 at the time of his arrest.

On Tuesday, the U.S. Supreme Court considered whether Montgomery is eligible for a new day in court -- and potentially freedom -- based on a 2012 decision that it was unconstitutional to sentence teenagers to an automatic term of life imprisonment without the possibility of parole.

Specifically, Montgomery asked the justices to establish that that 2012 case, Miller v. Alabama, be extended retroactively to prisoners like him -- people who as juveniles were sentenced to die in prison long before that ruling became the law.

In his case, that would be 1969, when a Louisiana jury -- following an earlier trial and death sentence that were invalidated, in part, due to a climate of racial agitation against Montgomery -- found the teen guilty and decided he should spend the rest of his days in state prison.