I've been thinking about this recently:
Here in Germany we only have a couple of high speed rail lines, in most other cases the high speed trains will run on existing track at moderate speeds, since the tracks don't allow higher speeds that 160 kph in most places.
Now the real problem is that they stop so damn often. For example the ICE from Basel to Franfurt will stop in places like Offenburg or Baden-Baden, even the super duper HSR from Frankfurt Airport to Cologne will stop at villages (sorry) like Limburg or Siegburg and what's that other place's name. So moments after reaching it's top speed it has to brake again, stop, let about 2 passengers get off and then accelerate again, losing a good 10 minutes on the way. Multiply that by the number of stops in between.
So here's my idea. A train that runs without stopping between, let's say, Rome and London, or Paris and Madrid, or Stockholm and Lisbon. Whenever the train passes a city on the way, passengers who want to get off would proceed to the last car, which will then uncouple and come to a stop. At the same time, another similar car will have boarded the passengers at that station who want to get on, then that car would accelerate and catch up with the rest of the train. So unless you want to get off, the train will never stop, and you save lots of time on the way.
The result would be that HSR speed could be reached on lines that aren't even that fast, just by eliminating the time consuming stops.
Would this be possible?