The sea lanes are mainly a Canadian obsession, because the government believes the North-West Passage that weaves between Canada's Arctic islands will become a major commercial artery when the ice is gone. Canada is getting new Arctic patrol vessels and building a deep-water naval port and Arctic warfare training centre in the region, but it's all much ado about nothing. The Arctic Ocean will increasingly be used as a shortcut between the North Atlantic and the North Pacific, but ships will not use Canadian waters. Russia's "Northern Sea Route" will get the traffic because it's already open and much safer to navigate.
Then there's the hydrocarbon deposits under the Arctic seabed, which the US Geological Survey has forecast may contain almost one-fourth of the world's remaining oil and gas resources. But from a military point of view, there's only a problem if there is some disagreement about the seabed boundaries.
There are only four areas where the boundaries are disputed. Two are between Canada and its eastern and western neighbours in Alaska and Greenland, but there is zero likelihood of a war between Canada and the United States or Denmark (which is responsible for Greenland's defence).
In the Bering Strait a treaty defines the seabed boundary between the US and Russia, signed in the dying days of the Soviet Union, but the Russian Duma has refused to ratify it. However, the legal uncertainty caused by the dispute is more likely to deter future investment in drilling there than lead to war.
There was a seabed boundary dispute between Norway and Russia in the Barents Sea, which led Norway to double the size of its navy over the past decade. But last year the two countries signed an agreement dividing the disputed area right down the middle and providing for joint exploitation of its resources. So no war between Nato (of which Norway is a member) and the Russian Federation.
Which leaves the fish, and it's hard to have a war over fish. The danger is rather that the world's fishing fleets will crowd in and clean the fish out, as they are doing in the Southern Ocean around Antarctica.
If the countries with Arctic coastlines want to preserve this resource, they can only do so by creating an international body to regulate the fishing. And they will have to let other countries fish there too, with agreed catch limits, since it is mostly international waters. They will be driven to co-operate, in their own interests.
So no war over the Arctic. All we have to worry about is the fact the ice IS melting, which will speed global warming (open water absorbs more heat from the sun than highly reflective ice), and ultimately melt the Greenland icecap and raise world sea levels seven metres. But that's a problem for another day.
Gwynne Dyer is a London-based independent journalist whose articles are published in 45 countries.