I agree: in fact, I am looking forward to the completion of the Turin-Lyon high-speed line, so I can reach Paris with my back still healthy
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As far as I know, there is a proposal to ban short haul flights between cities linked by high-speed railways, but so far is only being discussed. Some member countries have already adopted national bans. Usually such bans involve links with cities having a hub airport and require that the airport is served by high-speed rail services, as many short-haul flights are the first part of a journey that continues once the traveller has reached a large airport.
Even without regulations, however, the mere existence of a high-speed rail link usually leads to a vertical drop in the number of connecting flights: this happened in France in 1981 when the first LGV (Ligne Grand Vitesse, High Speed Line) was opened between Paris and Lyon. The same also happened here in Italy when the high speed link from Milan to Rome (previously, the most busy internal air connection) was completed, linking the two major cities in Italy in less than 3 hours (non-stop trains take 2h 56m to travel 478 km). Flight time between the two cities is approximately 1 hour, but the need to travel to the airport and back makes the train very competitive. As a side note, this was the main reason for the fall of Alitalia, which focused on this route even knowing what happened in France some years before (a shiny example of brilliant management
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Going back to the original theme of the thread, the only place where I can see a high-speed railroad in the US is the North-East corridor, as distances and population densities (in other words, the number of likely passengers) are not too different from Europe or Japan. Outside this area (and in Australia) I think it would be very unlikely to succeed. Of course, this leaves aside the political will to build a fairly expensive infrastructure.