The old KGB headquarters in the Lithuanian capital, Vilnius, is a sinister place, full of ghosts. It is a solid 19th-century neoclassical building with walls thick enough to have muffled the screams of those under interrogation. The cells in the basement are as cold and damp as they were in Soviet times and there are stone steps down to an airless, claustrophobic chamber where prisoners were executed, a thousand of them, the wall still pock-marked with bullet holes. You can imagine people hurrying by on the other side of the road in the old days, not daring to look up at the pale grey façade, knowing what took place behind it.

The building now houses Lithuania’s Museum of Genocide Victims, a monument to the one third of the country’s population killed or deported to Siberia during the-Soviet occupation. Lithuanian army recruits are taken there just as Israeli conscripts make a ritual visit to the Holocaust-museum near Jerusalem. ‘We feel the same,’ said my friend, a senior officer in the Lithuanian army, who was showing me round. ‘Never again… We will not repeat the mistakes we made when we allowed Lithuania to be occupied by the Soviet Union without one shot fired. It took an enormous effort for the freedom fighters after the second world war to resist and take that shame away.’

Russian tanks rolling into the Baltic states — Estonia, Latvia, and Lithuania — once again? It seems a mad idea, but Lithuania thinks it real enough to have reinstated conscription. This is more than just Baltic alarm: Sweden signed a defence pact with the United States in June, and Finland is-trying to do the same. A recent Norwegian television drama imagined the country under Russian occupation. Meanwhile, in real life, Russia has formed three new motorised rifle divisions, with more than 30,000 troops, many of them to be sent close to the Baltics. And short-range missiles that can carry nuclear bombs have been delivered to Kaliningrad, the neighbouring Russian enclave.

Lithuania’s President, Dalia Grybaus-kaite, called the missiles’ deployment an ‘open demonstration of power and aggression against not [just] the Baltic states but against European capitals.’ The Russian military said it was only an exercise. My friend, the Lithuanian army officer, said: ‘We constantly see Russian forces on exercises close to the border. Most of these activities are offensive in nature: paratroopers conducting airborne assaults, marines in landing operations. When it’s combined with aggressive political rhetoric, we take this threat very seriously.’

A retired British general, Richard Shir-reff, believes that the Russians might well be coming. A former Nato deputy commander, he has written a future history novel called 2017: War with Russia. In it, Russia invades the Baltics then paralyses Nato by threatening to use nuclear weapons. The general’s view, shared by many serving-officers, is that complacent politicians have cut too much from defence and Nato countries need to rearm in order to deter Russia. ‘At all costs, we must avoid a miscalculation that could lead to the sort of scenario I outline in the book,’ he said. ‘Unless the risk of doing so is sufficiently high, the Russians might do it. They could bite off the Baltic states in pretty short order.’

A Russian invasion of Estonia and-Latvia would be complete in as little as 36 hours, according to a study by the Rand Corporation for the Pentagon. Russian tanks would be rumbling through Tallinn and Riga before Nato could so much as convene an emergency meeting to invoke Article 5 of its charter for mutual defence. The Rand study showed that it would take more than a week for Nato to get its tanks to the Baltics from Germany in response. By then it would all be over.So Nato has decided to send four battalions of troops to the Baltics, including one from Britain — exactly the kind of reinforcement that General Shirreff wants. The Baltic states have welcomed this.

One of the saddest exhibits in the KGB museum in Vilnius shows the long and ultimately doomed war ‘in the forest’ against the Soviet occupation. The partisans managed to smuggle a messenger through the Iron Curtain to the West, a difficult and dangerous journey, only for him to return two years later with the devastating news that no help would be coming. General Shirreff thinks that history might repeat itself.

Listen to Ben Judah and Dmitri Linnik on Putin's information war

‘If Putin did move into the Baltic states, that is probably the end of Nato,’ he said. ‘How certain are we that the alliance-really would invoke Article 5? The defence of Europe has depended on the certainty that America would come to the aid of a Nato member if attacked. But Germany? France? Italy? The UK? To recapture the Baltics would take massive military force, the like of which we haven’t seen since Overlord or Desert Storm. It’s difficult to see how Nato could summon the will or the capability.’

James Carden, a former adviser to a US presidential commission on Russia, agrees. ‘We have a habit of leading on these people who are along the periphery of Russia. Do the Baltics really think that we’ll get into a nuclear exchange if Russia runs over their borders? We won’t. We’re not going to go to war for them. De Gaulle knew this as far back as the 1960s, that the US would not trade New York for Paris in a-nuclear war.’ But he doubted that Russia really-wanted the Baltics back: it was just sending a-message to the West.

Certainly, the Russian military described the new motorised rifle divisions and the missiles in Kaliningrad as a response to Nato exercises on the border. To the West, Russia illegally annexed Crimea and tried to do the same to eastern Ukraine. But to-Russia, the West has recklessly ignored understandings about Ukraine’s neutrality by trying to bring it into Nato and the EU. Nato is already — symbolically — as close to the Russian-motherland as the Wehrmacht got in the second world war. Things look very different from Moscow. ‘We look the aggressors to Russia. Maybe their paranoia is understandable.’

If an invasion of the Baltics came, it would probably not start with tanks but with well-trained thugs stirring up trouble in Estonia’s Russian-speaking northeast.

This is all-shadow boxing, so far, a phoney war. So much depends on the personality of Vladimir Putin. ‘He’s a great tactician,’ said Professor Karen Dawisha, author of a book on Putin. ‘He’s a terrible strategist, as we can see from where Russia has fallen… He has been a huge failure in promoting Russia’s long-term interests but he has the capability to take us from one crisis to another.’

Putin knows perfectly well that going to war with the West — in Syria or the-Baltics — would be a disaster. ‘So he’ll want to-prevent that and one of the ways he prevents it is by convincing us all — and we are all convinced — that he’s slightly crazy.’

Putin, then, may have adopted Richard Nixon’s ‘madman theory’ — the attempt to scare a potential enemy into thinking you might just go to war, might even drop the big one, if pushed. Others in the Russian federation are playing their part — it sometimes seems as if the whole country has been gripped by world war three hysteria. The state-controlled TV channel NTV took its cameras into a nuclear bunker, telling-viewers: ‘Everyone should know where the nearest bomb shelter is.’ The chairman of the Duma’s defence committee even appeared on television in his old uniform as commander of the country’s airborne troops and promised to fly to the US on a military-transport plane if ordered to by President Putin. ‘We need to stop apologising to the Westerners,’ he said.

The very fact that people are talking seriously about an invasion of the Baltics may be evidence that Putin’s tactics are working. But it is a terrifying gamble. ‘Russia can win big but it can also lose big,’ said the Russian newspaper Moskovskij Komsomolets, speaking of the looming confrontation between the West and Russia in Syria.

Actual madman or just a convincing impression? We may not be able to tell the difference until it’s too late.

It sometimes seems as if the whole of Russia has been gripped by world war three hysteria