There is no timescale, no budget and it will compete with four existing intercity rail routes. But building a high speed line allowing 140mph trains to travel direct between Glasgow and Edinburgh is not as batty as it sounds.

Announced with great aplomb on Monday by Nicola Sturgeon in her relatively new role as Infrastructure Secretary, the proposed route will, she says, be complete by 2024 – ahead of the first phase of the high speed railway planned to open between London and Birmingham by 2026.

It sounds bold and, bluntly, unaffordable, especially considering that the latest route between the cities only opened two years ago, thanks to completion of the £300 million Airdrie-Bathgate link. There’s already a bulging list of expensive infrastructure projects in the transport portfolio, such as the £3bn earmarked for dualling the A9 by 2025, over the next decade and a half so adding a few extra billion’s worth of projects doesn’t sound wise.

In fact, the Glasgow-Edinburgh high speed rail plan is the relatively easy part. Bear with me here.

It picks up on an idea that has been floating around in policy circles in and around Transport Scotland for years. Namely that, if you are building a high speed rail route from England to Scotland, you can get a new line between Glasgow and Edinburgh thrown in for relatively little extra cost.

Let’s assume, as many in the rail industry do, that the mostly likely route for a cross-border line would be a Y-shape heading north from Manchester before splitting along separate branch lines to Glasgow and Edinburgh – pretty similar to the existing West Coast Main Line in fact. In order to get the new Glasgow-Edinburgh line, you simply need to construct a short section of track linking both branch lines. Ta da.

None of this takes away the eye-wateringly difficult task of getting that cross-border route. Where, for example, do you put the 400m-long trains when they reach Glasgow and Edinburgh? There isn’t space in either Glasgow Central or Waverley stations at present so either new terminuses or major reconstruction of the existing stations would be required.

Oh, and the last estimate of the cost of extending a network north of Preston to Scotland’s two biggest cities, by Network Rail in 2009, was £13bn.

The interesting aspect of Nicola Sturgeon’s announcement this week was the timing of what she is proposing. Rather than talking about completing the new Glasgow-Edinburgh route once agreement on the cross-border line is reached – something that is supposed to happen by 2015 – she is now talking about an up-front commitment to this aspect of the network.

Incidentally, this helps us make sense of the decision to slash investment in the Glasgow Edinburgh Improvement Programme in the summer by £350m. This electrification project would have cut journey times from 55 minutes to 37 between Scotland’s two biggest cities but will now only see it reduced to 42 minutes. When announcing the revised scope for EGIP in July, Transport Minister said one of the reasons was to ensure it was compatible with the Scottish Government’s high speed rail ambitions. Now we know why.

A positive view of Ms Sturgeon’s announcement this week is it puts pressure on Westminster to deliver the southern section of a cross-border high speed rail line by making clear Scotland’s commitment to the project. A more cynical view is that it is jam tomorrow, a political promise located so far in the future that there will be no comeback when it isn’t delivered.

In either case, there is no way it will happen in isolation. The prospect of Glasgow and Edinburgh getting yet another rail link depend entirely on how the wider UK high speed rail network develops.