The difference in ticket prices between low-cost airlines and high speed trains is so large that it is impossible to achieve a significant modal shift from planes to trains. Nevertheless, both the European Union and the International Union of Railways have published many reports showing that people are switching from planes to trains, saving energy and carbon emissions. How can that be? Because these reports are flawed.
Picture: The TEE Rheingold Amsterdam-Geneva (1965-1987). Source: Wikipedia Commons.
Granted, on many routes where high speed trains have been introduced, air traffic has diminished significantly. In general, when high speed rail offers a journey time of three hours or less, it attracts at least 60% of the combined air and rail market. On some routes, such as the Brussels-Paris and Cologne-Frankfurt, air traffic has disappeared completely. 
Based on these figures, the advocates of sustainable high speed trains conclude that the reduction in energy use and carbon emissions equals the flights that have been "avoided", minus the (lower) energy consumption and emissions generated by high speed trains. This is a tempting conclusion, but once you start looking who is on those trains and why, things start to look very different.
First of all, passengers who switch from planes to high speed rail are not switching from low-cost airlines to high speed trains -- as you would suspect by comparing the fares. The most important substitution effects are those by passengers travelling with traditional air companies, which have similar fares as high speed trains.  However, low-cost airlines are responsible for the growth of air traffic and the increase of energy use and emissions.
High Speed Trains Fuel Air Traffic
Secondly, the studies that claim an ecological advantage for high speed trains ignore the extra traffic being generated by such trains. On one hand, high speed trains induce new demand for train travel. Between 30 and 50% of the trips on a high speed train are due to new demand.  These are all trips that would not have been undertaken if the high speed train did not exist. These travels do not replace a plane or car trip and consequently don't save energy and emissions.
A EuroCity train in Austria. Source: Wikipedia Commons.
Not surprisingly, this new demand is largely coming from affluent customers. While part of the demand is from tourists, a much larger part is business related. A study of the high speed line between Rome and Naples in Italy shows that on weekdays almost 60% of new demand is due to business trips.  Another 6% corresponds to people that have moved their residence from Rome to Naples and started to commute every day -- and that was only one year after the line was opened.
On the other hand, high speed trains also generate more air traffic. A study of 56 airports and 28 cities in the UK, France, Spain, Italy and Germany between 1990 and 2010 shows that in most of these airports and cities air traffic has kept growing despite the presence of extensive high speed train lines.  A significant part of this extra traffic is prompted by high speed trains. The study observes that short haul flights have indeed decreased. However, at the same time, medium and long-haul flights (within Europe) have increased. This is because high speed rail allows airports to run more long-distance flights, which are more profitable for airlines.
Two-thirds of passengers on the high speed train between Cologne and Frankfurt are either coming from or going to the airport
In other words, by alleviating the congestion at airports, the high-speed train helps to pave the way for the growth of low-cost airlines.  Air traffic between Paris and Brussels, and between Cologne and Frankfurt has disappeared completely because airlines have agreed to use trains instead of planes to serve main airport hubs. According to Deutsche Bahn, the German national railway operator, two-thirds of passengers on the high speed train between Cologne and Frankfurt are either coming from or going to the airport.  However, their longer flight might not have been possible without the high speed train.
Towards a Truly Sustainable Transportation System
In conclusion, affluent customers switch from (expensive) planes to (expensive) trains, at least for medium distances where the train is faster, or as fast, as a plane. All other people choose low-cost airlines for longer distances, and cars or busses for medium distances where affordable train travel isn't an option anymore. They generally only travel on high speed trains when they are on their way to an airport to catch a long-distance flight, or when they can get hold of a cheap fare. Lastly, almost nobody chooses high speed rail when the travel time is over five hours, not even those who can afford the ticket.
A Pullman train from the 1920s. Picture: B. Zsolt (Wikipedia Commons)
If Europe wants to make its long-distance transportation more sustainable, it has no other choice than to limit the growth of air traffic in a direct way. Such a measure should accompany a more affordable railway system, like the one that is now being dismantled, or long-distance travel will become a privilege of the rich. The tracks are still there, so this could be done in no time.
It's enlightening to look at the present European focus on high speed trains in the context of railway history. It's not the first time that smooth international railway traffic has been reserved for the elite. The high speed train is the latest in a long history of European luxury trains aimed at business travellers, which seem to appear whenever the economy is booming, and disappear when good times are over.
The high speed train is the latest in a long history of European luxury trains aimed at business travellers, which seem to appear whenever the economy is booming, and disappear when good times are over
Only the rich could afford the luxurious Pullman trains that appeared on European railways in the 1920s.  These trains only carried first class cars. The original Étoile du Nord, the first direct connection between Paris and Amsterdam, was one of these trains.
High Speed Rail in the 1950s
Pullman trains started taking second class coaches during the economic downturn in the 1930s, after which the Pullman heritage withered. The economic crisis of that time tipped the balance to more affordable international train travel, and it would stay like that for almost thirty years.
At the end of the 1950s, elite trains made a comeback. In 1957, the direct train connection between Paris and Amsterdam was modernized in the context of the Trans Europ Express (TEE) project, which was aimed at travellers on business. TEE trains only took first class cars and the fares were higher than the kilometre charges for first class travel on normal trains.
TEE was an answer to the growing competition from airplanes, which were at that time exclusively used by rich people. The similarities with today's high speed trains are striking -- TEE was marketed as a "plane on wheels". Faster trains were introduced (with top speeds over 140 km/h) and travel distances were mostly under 500 km. At its peak in 1974-1975, the TEE network consisted of 31 routes, stretching from Copenhagen to Barcelona and from Amsterdam to Sicily. (See the illustration above, from Wikipedia Commons). 
High Speed Trains for Everybody: EuroCity
At the end of the 1970s, air travel had become faster and more comfortable with the introduction of the jet engine. Business people switched to planes again. Losing their affluent customers, the railways reverted to affordable international trains -- planes were still too expensive for the masses. There was, however, strong competition from road transport. Thousands of kilometres of motorways had been built and the car had become the main long-distance transport means for the majority of Europeans.
EuroCity and EuroNight formed a sustainable, efficient and cheap long-distance transport system that was the best that Europe ever had.
TEE trains were equipped with second class carriages, a trend which eventually culminated in the EuroCity project, which was launched in 1987. EuroCity trains were as fast as TEE trains, but they carried mostly second-class coaches and the price of a ticket was again based on the regular kilometre fares. From the start, EuroCity offered 64 pairs of international trains with 50,000 daily seats, connecting 200 cities in 13 countries. 
The EuroCity train between Geneva and Venice. Picture: Wikipedia Commons.
EuroCity accompanied an extensive network of night trains (EuroNight), and together they formed a sustainable and efficient transport system that was probably the best that Europe ever had. The Étoile du Nord that connected Paris and Amsterdam until 1995 and covered the route in just 4h20 was a EuroCity train, and the night train that covered the trajectory was a EuroNight. The Catalan Talgo was a EuroCity train, and the Trenhotels fitted the EuroNight class.
The 1996/97 version of the Thomas Cook Guide to European Night Trains  lists a total of more than one hundred international night trains in Europe, and another one hundred domestic night trains. Western Europe has axed most of them in recent years. Some examples: From the 21 night trains leaving from Belgium in 1997, heading as far as Moscow, not one remains. From the 36 domestic overnight trains in Spain, only eight remain. Understandably, the yearly Guide to European Night Trains has ceased publication.
What makes a train affordable?
EuroCity and EuroNight trains still run in Central and Eastern Europe, with the result that fast international trains are still available for fixed, affordable prices. The great advantage of EuroCity and EuroNight trains is that they do not require a unique railway infrastructure, which makes them far less costly to initiate. Furthermore, they are cheaper to operate than high speed trains. This allows for more affordable ticket prices, and it also means that the network can be extended at a faster pace.
The EuroCity network in 1987 (left) and in 2010 (right). Western Europe now opts for high-speed trains. Maps from Wikipedia Commons.
Of course, if more people travel by low speed train, the infrastructure will have to be extended. But building low speed rail is much cheaper than building high speed rail, which costs an average of 18 million euro per km, excluding planning and land acquisition costs.  High speed trains often run on newly built dedicated high speed tracks that allow higher speeds through the use of wider curves, less steep grades, more powerful electrification systems and different branching systems. Logically, these high investment costs, combined with higher operating costs, lead to higher ticket prices, and to the abolishment of alternative routes that might compromise the economic viability of a new high speed line. 
The local and regional rail infrastructure, which carries many more passengers than high speed rail, is greatly underfunded in many European countries with high speed trains.
Much more (public) money will be needed to complete the European high speed rail system: of the 30,750 km of high speed lines planned for 2030, only 10,000 km has been built.  Naturally, the high investment costs also have a negative effect on the maintenance of the domestic low speed network. The local and regional rail infrastructure, which carries many more passengers than high speed rail, is greatly underfunded in many European countries with high speed trains. Rolling stock is outdated, services are reduced, delays are frequent and accidents are on the rise. 
What makes a train fast?
Obviously, limiting the growth of low-cost airlines would decrease the ability for affordable air travel -- that's the price we need to pay for sustainability. But, as we have seen, a network of "low speed trains" would not be significantly slower than a continental network of high speed trains.
A TEE train in the Transport Museum in Nürnberg, Germany. Source: Wikipedia Commons.
The top speed of a train is only one of many factors that influences travel time. European high speed trains reach top speeds of 250 to 350 km/h, but their average speed is much lower. For example, the average speed of the Thalys between Paris and Amsterdam is below 170 km/h. This is well within reach of "slow" EuroCity and EuroNight trains, which can reach speeds of 200 km/h.
The top speed of a train is only one of many factors that influences travel time. European high speed trains reach top speeds of 250 to 350 km/h, but their average speed is well within reach of "low speed" trains
The speed of many high speed trains is limited due to, for example, their proximity to densely urbanised areas (to ease the impact of noise and minimise the risk of accidents), the existence of viaducts or tunnels (where speed must be reduced to 160-180 km/h for safety reasons), or the need to climb steeper grades (and when steeper grades are avoided, this often results in considerably longer routes, which is the case for the whole corridor Barcelona-Paris-Brussels). 
In many European countries, high speed trains are combined with normal rail traffic on some sections of their route: only 6,000 km of the 10,000 km of high speed lines is dedicated high speed track. Sharing infrastructure with slower trains decreases capital costs, but also brings down speed. 
The Eurocity train between Milan and Zürich. Source: Wikipedia Commons.
On the other hand, EuroCity trains have to meet several criteria to shorten travel time, and many of these are also applicable to high speed trains. For example, the trains only stop in important cities, turnover time in stations is less than five minutes, border control happens on-board, and the trains are given priority over other trains in order to comply with timetables. These are all factors that influence travel time as much as the speed of the train.
High Speed Night Trains
Even on routes where high speed trains are significantly faster than normal trains -- such as between Barcelona and Paris -- they are still slower than the night trains that covered the same distance, at least when we look at perceived travel time. Because time flies when you are under the covers, the night train is the ultimate low-tech alternative for the high speed train.
Of course, high speed trains could also introduce night services. A few months ago, the International Union of Railways -- who has a clear bias towards high speed trains -- published a study about high speed night trains, investigating the potential for operating night train service on high speed lines using high speed rolling stock.  One such a train already exists in China. "Very Long Distance Trains" could provide night train service on corridors over 2,000 km long. For example, you could board a train in Barcelona and wake up in Hamburg the next morning.
Because time flies when you are under the covers, the night train is the ultimate low-tech alternative for the high speed train
However, in Europe, with its fragmented railspace, operating such night trains would be a costly affair. On most routes, the fare would be about €700 for a single ticket just to cover the operating costs of the trip, as calculated by the International Union of Railways. A single ticket for a low-cost flight from Barcelona to Hamburg costs €75 (ordered up to 3 weeks in advance) to €130 (ordered one day before departure).  Using a combination of low speed trains, the trip previously could have been done in a night and a day for less than €200.
On the night train Madrid-Portbou. Picture by Low-tech Magazine.
Of course, the high speed train is a very comfortable way to travel. The question, however, is not whether we like the idea of a high speed train network, but whether or not we can afford it. Spending billions of tax money on a transportation network that excludes the majority of the population from using it might not be a sound investment.
A 2009 study by Spanish researchers analysing the economic impact of high speed rail in Europe  puts it this way:
"Building, maintaining and operating high speed rail may substantially compromise both the transport policy of a country and the development of its transport sector for decades... An exhaustive revision of the specific economic literature shows that the research effort devoted to the economic analysis of investing in high speed railways is almost insignificant... It deserves a closer look, well beyond the technological hype and the demand figures... Deciding to reject the construction of a high speed rail line is not necessarily a position against progress."
In less than 10 years, Spain has built the most extensive high speed rail network in Europe. Today, the country is virtually broke and can hardly afford to keep its trains running.
Kris De Decker (edited by Deva Lee)
 Present and historical timetables and itineraries cited in this article come from a variety of sources. For present timetables starting December 2013, I have consulted the online database of the German Railways (the link goes to the Austrian version which I find more user-friendly), as well as the online timetables from RENFE (Spain), SNCF (France), NMBS (Belgium), NS (The Netherlands), SBB (Switzerland) and TrenItalia (Italy). For recent timetables pre-dating December 2013 (rail operators traditionally change timetables and trains routes in December), I have relied on the Thomas Cook European Rail Timetable and my own collection of train tickets. Information about train routes was found in a variety of rail maps and atlasses. The historical timetables for the Étoile du Nord and other trains were found in the Dutch Magazine "Het Spoor".
 All prices: winter 2013. See TGV-europe and the national railway operators listed above . Fares from before December 2013 are based on my own collection of train tickets. The Man in Seat 61 provided missing information.
 Applying Low Cost Airline Pricing Strategies on European Railroads, Thomas Sauter-Servaes, 2006
 In 2012, a joint venture between Belgian and Dutch railways introduced a competing high speed train on the section between Brussels and Amsterdam: the Fyra. Its introduction went together with the abolishment of a slightly slower but much cheaper alternative, the Benelux train -- which is also operated by the Belgian and Dutch railways. If everything would have gone according to plan, the route between Amsterdam and Brussels would now be a copy of the route between Paris and Brussels. Travellers would be forced to use the more expensive fast train, or take a combination of regional trains that would be ridiculously slow. However, the Fyra trains were plagued by technical problems and had to be retired after two months. An alternative route has been established -- slower than the Benelux train, but faster than the combination of regional trains. It is still unclear how things will evolve in the future. For the calculations of travel times in this article, I assume that the Benelux train is still running.
 Prices: Vueling, December 2013.
 Can't afford London's sky-high rent? Try commuting from Barcelona, The Atlantic Cities, November 2013.
 Challenges of Growth 2013 (PDF), Eurocontrol, 2013
 High-speed Europe, a sustainable link between cities, European Commission, 2010
 Economic analysis of high speed rail in Europe (PDF), Ginés de Rus et al., 2009
 Forecasting Demand for High Speed Rail (PDF), Maria Börjesson, 2012
 High speed rail demand: empirical and modelling evidences from Italy (PDF), Ennio Cascetta, 2011.
 Impacts of high-speed rail and low-cost carriers on European Air Traffic (PDF), Regina R. Clewlow, 2013
 Histoire des Trains de Luxes: de l'Orient-Express au TEE, George Behrend, 1977
 It should be noted that there is not one high speed line that can recover infrastructure costs. However, high speed trains in France and Spain are able to recover their operating costs. Source: see 
 News reporting in Le Monde and El País, following the spectacular train accidents in France and Spain last summer (Note: the crashed train near Santiago de Compostela was not a high speed train). News reporting in La Vanguardia, following a cascade of smaller accidents involving local trains in Barcelona. News reporting in De Standaard, following train accidents in Belgium.
 Germany is the only country with a "fully mixed model", which means that both high speed and conventional services can run on each type of infrastructure. High speed trains can use upgraded tracks while freight services use the spare capacity of high speed lines during the night. Germany has relatively few dedicated high speed tracks, and trains are comparatively slow. These factors make HSR more affordable in Germany than in France or Spain. [Edited]
 Night Trains 2.0. (PDF), International Union of Railways, 2013