Upon reading your two newer messages, I think I understand better what you're suggesting.
Is there a need? Grangemouth/Falkirk to Fife demand is not really catered for directly, but ultimately, there's not really a demand there. Falkirk isn't going to have strong economic ties (the government term for where people commute to work) to Fife.
Any passengers without cars will probably change at Edinburgh, which isn't a difficult or long change, and there are plenty of alternatives for driving. Most of the people going between Fife and the Forth Valley will drive over one of the bridges. I'm not sure you could make enough people add up to an hourly service, which is the minimum of what you need to justify to build a new railway.
Building a new rail bridge over the Forth isn't here or there; it would be possible but horrendously expensive. If you had a couple of billion burning a hole in your pocket, you wanted to spend some money to connect these two areas, and you were convinced rail was the way to do it, then there are other things that would help. Just extending the Alloa trains through to Dunfermline, and extending the Grahamston terminators to a new station at Grangemouth would probably tick all of the boxes.
This goes into the box of "in terms of pure engineering there is nothing that makes this impossible, but you'd never build it because the need isn't there"