When Alex Wellerstein, a nuclear historian who has studied crises and breakthroughs dating to the earliest Cold War arms races, tried to imagine the possible outcomes of President Trump’s planned meeting with Kim Jong-un, the North Korean leader, he found himself, like many experts, at a loss.

“What’s the game plan? Is it negotiating on sanctions? Is it stalling to defuse tensions in that time-honored DPRK way?” he asked on Twitter, using North Korea’s formal initials. “I don’t know.”

The meeting will bring together two personalities whose tendencies have already proved destabilizing: Mr. Trump, whose unpredictability and defiance of norms has led him to take on high-stakes issues with which he has little experience, and Mr. Kim, whose youthful boldness and willingness to embrace risk give him the swagger, perhaps unearned, of a major nuclear power.

But the meeting will also exemplify a world that is less constrained by the usual guardrails of international norms or policy processes — a world in which virtually anything can happen.