I am traveling to Moscow this weekend, at a time when Russian media are speculating about World War III and U.S. media are debating whether we are embroiled in a new Cold War.

The crisis du jour is the U.S. missile strike on Syrian military sites to punish the Assad regime for another banned chemical-weapons attack on civilians. Russian military personnel are present at key Syrian bases; Russia's chief of military staff, Valery Gerasimov, had warned the United States in March against endangering Russian personnel, but it seems the U.S. attack avoided doing so.

Yet this very limited attack — only targeting three sites connected with chemical weapons — will not shift a Syria balance in which Russia has little incentive to rein in Bashar al-Assad or the Iranians who are building bases in Syria that threaten Israel.

Nor does the attack indicate that President Trump will approach his dealings with Vladimir Putin more seriously. On Wednesday, Trump, in his feckless way, taunted the Kremlin by tweeting: "Get Ready Russia because [the missiles] will be coming `nice, new and smart!' " By telegraphing the attack, the president gave the Syrian regime time to move key armaments to sites manned by Russian forces.

Trump's tough stance on chemical weapons is sharply at odds with his refusal to confront Putin over cyber-espionage. It remains to be seen whether the U.S. missile strike will inspire the Russian leader to retaliate indirectly, with more cyber-sabotage.

One way or another, the Syria crisis will heavily color my trip.

I will be looking at how the fraught U.S.-Russia relationship appears from the Russian side: how Russians currently view Trump (in whom the Kremlin had invested big hopes); how new U.S. economic sanctions targeting Putin cronies affect the Russian economy; and at the why and how of Russian cyber-trolling.  I will also be talking with Russian experts about the foreign aspirations of Tsar Vladimir — whose closely held goals have inspired a new science of Putinology that rivals the Kremlinology of Cold War days, when outsiders tried to divine the secretive doings of the Politburo.

To inject a bit of optimism into my visit, I also hope to talk with young Russians who still believe they can build a more democratic country from the ground up.

Before departure, I spoke with the former U.S. Ambassador to Moscow Michael McFaul, whose new book, From Cold War to Hot Peace: The Inside Story of Russia and America, looks at the complexities of the current U.S.-Russian relationship.

McFaul told me he uses the phrase hot peace because he wants to echo certain dimensions of the Cold War that are back but also to make clear that this is "not the old Cold War but rather a Cold War 2.0."

For starters, Russia does not have the heft of the old Soviet Union, with a current GDP roughly the size of Italy's and an economy that is stagnating, despite rich energy resources. Low oil prices and Putin's failure to modernize the economy are a further drawback.

Of course, Russia has a substantial nuclear arsenal, which it is modernizing. But, says McFaul, the danger is not the numbers of nukes per se, but the fraying rules of the nuclear game.

While we are safer than in the Cuban Missile Crisis period,  "we are not necessarily better off than during the late Cold War [in the 1980s], when there were rules of the game about how states interacted that made it safer. Back then, things like annexation didn't happen." McFaul is referring to Moscow's annexation of a portion of neighboring Ukraine in 2014.

Moreover, when Washington and Moscow were engaged in arms control negotiations, "we slowed down and decreased the number of nuclear weapons." At present, McFaul says, "there is a new qualitative arms race on the offensive and defensive side" with no negotiations in sight. Both Putin and Trump are bragging about new nuclear capabilities.

Moreover, despite treaty limits on Russian conventional forces in Europe, "the Russian defense ministry has made faster, better weapons and has a formidable conventional force in the European theater."  This force has been making its presence well-known with massive military exercises on the borders of European states.

Perhaps the most disturbing part of Cold War 2.0 is the new Russian doctrine of hybrid warfare, as espoused by Gen. Gerasimov. He advocates "nonmilitary means of achieving political and strategical goals." Under that heading comes cyberwarfare, wider disinformation wars, and interference with Western political campaigns. And also an ideological struggle, of which Americans are too unaware.

"We in the West are asleep to this dimension of hot peace," the former ambassador argues. "We say communism is dead and liberal democracy triumphed. But Putinism exists and has become an anchor for conservative authoritarians around the world who stand against the 'decadent, immoral, liberal West.' "

This kind of  "shirt-off, strongman, anti-liberal authoritarianism was initially aimed at Russians, but now Putin is exporting it, finding allies in Europe," funding and promoting far-right parties from Hungary to France and elsewhere.

And, of course, as McFaul notes, the strongman ideology of Putinism has followers in the United States, including Trump's former chief strategist, Steve Bannon. And, wittingly or unwittingly, Donald Trump.

It is these subliminal Trump-Putin linkages – whatever the realities of any formal collusion – that will make it so fascinating to travel to Moscow. Trump clearly still yearns to hold a summit with Putin, which he recently proposed. Last week, despite the chemical attack in Syria, he twitter-blamed "much of the bad blood with Russia" on the "Fake & Corrupt Russia Investigation."

So long as Trump refuses to confront Putinism and the Gerasimov doctrine he will undercut any hope of a coherent U.S. pushback against cyberwar – or chemical attacks by the Russia-backed regime in Syria. This blinkered outlook, says McFaul, would also make any Putin-Trump summit extremely risky.

On the other hand, it will be fascinating to hear how Trumpism – and Putinism — appear to Russian analysts and journalists in Moscow.  And whether the U.S. strike on Syria has dragged Trump into a tit-for-tat confrontation with the Russian leader, opening a new chapter in Cold War 2.0.