It's a strange time to be visiting London, Berlin, and Paris. The ties that bound Europe together for decades in an unprecedented era of peace are coming loose.

Britain holds a referendum today on whether to "Brexit" - quit the European Union. If that happens, it may trigger similar referendums in other European countries. And even if the British islanders choose to stay, the very idea of a united Europe - a union of 28 countries that are America's closest allies and share Western values of democracy and rule of law - is losing steam.

Yet waiting in the wings are no energetic reformers who want to address the EU's genuine flaws, but rather fearmongers on the far right who fan ethnic nationalism and blame immigrants for every ill.

And the European parties of the center seem unable to counter the rise of radicalism on the right and the left. Sound familiar?

That's why Americans should pay attention to the Brexit vote and what's happening to the idea of Europe. In a world where China is rising and authoritarianism is touted as an alternative to democracy, where a revanchist Russia uses force to re-create past glories, the EU is a crucial counterweight. It is also a crucial ally in fighting international scourges such as terrorism.

So here's what you should be watching for, in Britain and on the continent, and what I will be looking for myself.

In Britain, the "Leave" campaign played on fears of immigration, with a far-right party campaign poster featuring a photo of an endless, winding horde of dark-skinned refugees. Never mind that the Brits have accepted almost none of the recent flood of Syrians, Iraqis, and Afghans; half their migrants arrive legally from other EU countries and do much of the country's scut work, and many of the rest are from former British colonies.

The Leave campaign presents the restoration of Glorious England with a moat as the solution to all. So watch to see whether this mirage leads to a Brexit that will have dire economic consequences, not just for England but for global markets. A Brexit will also undercut America's special relationship with a crucial democratic ally, since a Little England will have much less international clout as a loner.

Most importantly of all, watch to see whether British voters take to heart the symbolism of Jo Cox's murder.

Cox was a dynamic new Labor member of Parliament and former aid worker with refugees who had campaigned strongly for remaining in Europe. In her forceful maiden speech, she said of her multicultural district: "We are far more united and have far more in common with each other than the things that divide us."

Her alleged killer, who shot her on the street, reportedly shouted, "Britain first!" and proclaimed in court: "Death to traitors, freedom for Britain."

Cox's husband has expressed the hope that her murder will impel Britons to fight such hatred.

We'll see whether the shock of her death convinces undecided voters to back "Remain" or whether false nationalist promises win the day.

On the continent, I will be asking about the impact of the Brexit vote on Europe's future. Even if it fails, the vote has sounded a warning to the EU's bureaucrats in Brussels that voters no longer understand the meaning of a united Europe. The concept once stood for democratic values but now is tarred with the euro and refugee crises. Brussels stands warned.

I will head for Berlin because Germany is at the heart of the European experiment. The EU was designed to keep a post-World War II Germany firmly rooted in democratic Europe, but now other states gripe that Germany has become too powerful. They blame Chancellor Angela Merkel for her humanitarian decision to accept one million refugees, which critics say accelerated the flow to the whole continent.

The Germans are embarked on a massive experiment to see if they can integrate this huge refugee influx and prevent the emergence of new Muslim refugee ghettos. They are also debating whether imams trained in Germany can promote a new European strain of Islam.

Moreover, a dicey deal with Turkey to stop the refugee flow may well fail. I will be looking at these questions.

In France, I will also be examining whether the continental crisis has produced new ideas on assimilating long-standing immigrant communities from North Africa and preventing radicalized elements from turning to terror.

In both Germany and France, radical-right parties are on the move, with France's Marine Le Pen likely to become a top candidate for president again in 2017.

Until this year, America had not fallen prey to the populist lure at the national level, but a look across the Atlantic can show where this path could lead us. As William Butler Yeats so memorably warned in his 1919 poem "The Second Coming":

Things fall apart; the centre cannot hold; ...

The best lack all conviction, while the worst

Are full of passionate intensity.

In Europe, I'll be asking whether the center can be put back together again.