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There is already an electric train between Paris and London that takes between 2:16 and 3 hours + 30 min checkin time: The Eurostar through the channel tunnel.

As a rule of thumb, any train journey faster than five hours is faster from city-centre to city-centre than getting on a plane.
That is because there is so much time overhead before and after the actual plane ride - most of all, the journey to and from the airports.
The only benefit for taking this plane would be if you would change to another plane at the airport or if your actual destination is not in the city proper but closer to the airport.

If the reason for the anomaly was that the clock in Geneva was 60 nanoseconds ahead of the clock in Italy, then measuring in both directions would show that that is the case.

For example. if you take this "measurement" of the times of trains between London and Paris
http://www.eurostar.com/pdf/timetables/UK_timetable.pdf
you will find from comparing departure and arrival times that trains from Paris to London typically take 1h 16m, whereas trains in the other direction take 3h 16m. This can be explained by the fact that the clock at Gare du Nord is 1 hour ahead of the clock at St Pancras, so the actual journey time is the average of the two - 2h 16m.

It takes longer, it takes 3 hours just to get to Brussels

Actually Brussels to London is only two hours (well 1h51 according to this). It can seem like three hours in one direction on the schedule though because of time zone differences (and the opposite direction looks to be only one hour for the same reason).

-- Pete.

In addition to the many helpful comments posted here about places in London (or there'bouts), don't forget you can travel to France quite easily by train.
For about £130 round-trip you can get from London to Paris on the Eurostar http://www.eurostar.com/ , it's about a 2 1/2 to 3hr train ride depending on what station you board.
So, my suggestion would be take a train at 6 AM and you'll be in Paris by 9 AM, enjoy this wonderful city (lots of walking) and ride back in the evening.
You have Notre Damme, Eifel Tower, Champs-Elysées and the Arche du Triomphe all within a reasoneable walk along the Sienne river.
And yes, if you are so inclined, you may bring your laptop also, although with all the walking I would not recommend it.
Enjoy your "use it or lose it" vacation

Train: 2hrs 25mins (plus check-in times: 30mins for regular punters, but can be as low as 10 mins)
Plane: 1hr 25mins (plus travel to the airport, plus a check-in delay of 2hrs, plus transfer time to centre of Paris (at least 40mins))
Car: 5hrs 17 mins plus traffic delays

It all depends on the trip you're making and the infrastructure that's in place to service that trip. The above is a moderately similar distance trip to yours.

...It's unlikely too many people would want to just ride the train and not need a car on the other end.

Then why not just make some (most?) of the carridges like they are on the Eurostar (see http://www.eurostar.com/ and http://en.wikipedia.org/wiki/Eurostar) and allow people to just drive straight onto the train? If it's only a 30 minute trip then people can stay in their cars. Just need to stick a couple of toilets in each carridge.

Erm, I think you're neglecting to consider a few factors in your unsupported hunchery.

Consider the forces at work. A train has to keep itself in motion, which requires pushing air out of the way. It also has some rolling resistance.

The airplane, on the other hand, also has to keep itself in forward motion, but there's also a lot of energy being spent keeping that fucker up in the air. The shape of a plane's wings generate lift, but they do so at the cost of creating drag. Lots of drag, compared to a train. There's just no possible way that the plane is ever going to be as efficient, because not only are you moving it horizontally across the earth, you're also putting it (and holding it) some 30,000 feet off the ground. That's much more energy-intensive than overcoming the rolling resistance of a few wheels and bearings, particularly when the wheels are running on steel rail and you can optimize the hell out of the rest of the system. (As a civilization, we're pretty good at making things rotate with minimal resistance. Ironically, it's jet aircraft that have really brought the engineering of high-speed turbobearings to near-perfection.)

It would be pretty easy to run the numbers if you wanted to: just look at the fuel consumption in gallons per hour for a modern locomotive and a jet aircraft, multiply by the energy density of the fuel (aviation kerosene and diesel), and divide by the number of passengers in each. With trains that aren't in fixed trainsets, it would get a little difficult to figure out how many "passengers" to include, but you could get some ballpark numbers.

Anyway, other people have already run the numbers. Here's a comparison done by Eurostar comparing London to Paris by plane and train, in terms of CO2 emissions:
link. "The research shows that each passenger on a return flight between London Heathrow and Paris Charles de Gaulle generates 122 kilograms of CO2, compared with just 11 kilograms for a traveller on a London-Paris return journey by train."

Now, that's CO2 emissions, not energy consumption (although the two are basically directly proportional when you're getting your power via the combustion of petroleum products), and it's probably made somewhat artificially low because the French generate a lot of electricity from fission, which is CO2-neutral, but that's not enough to explain a tenfold decrease.

Physics just isn't on the side of the airplane in terms of energy efficiency. Anything that stays on the ground is going to have a huge advantage.

The service speed of the TGV (and derivatives, like Eurostar) is 300 kph. This is far from standing still. It's totally smooth like all modern train travel. The only way you can tell how fast you're going is by looking out the window or by noting the generally higher pitch of what few mechanical noises you hear.

My favourite TGV story involves the A1 autoroute north of Paris. The TGV Nord line is parallel to the highway for a ways out of Paris. The speed limit is 130 kph, but les flics tolerate 160 if the traffic and weather are favourable (and don't seem to mind lots more if you drive a 911).

You're driving along at a speed that would get you thrown in jail in the U.S., and the TGVs pass you like you're standing still. It's almost cruel.

...laura

Yeah, what ever. Does this mean Europe is more united than the Uncooperative States of America?

To add a little more perspective, the cheapest fare now for that journey is $455 US dollars (249 pounds sterling).

Err, I don't know where you got that. I just looked it up, the cheapest price is 223.50 EUR.

Don't know how much it is by plane, but I suppose some low-fair company like Ryanair is cheaper.

The pictures on the California highspeed rail site are actually of a EuroStar.

In Europe (as in the USA from what I read in other comments) the railway system has had a lot of problems: not being on time, bad management, bad equipment, bad products, ...

But in the last few years Railway operators have discovered the business market and are offering new (high speed) products towards that market.

Thalys and Eurostar are two great examples. They interconnect a few major cities in differnt European countries. Especially THALYS (connecting Brussels (B), Amsterdam (NL) and Colone (D) amongst others) is a big success. It's not much faster or cheaper than flying, but it's much more luxurious and they drive you right to the city centre.
Eurostar (connecting Brussels, Paris and London)is not yet very successful, but that's because can't yet benifit from high speeds on the English tracks.

Looks like California High Speed Rail have decided to use the same blue-prints for the trains as used by the Eurostar. At least thats from looking at the photos.

Loosing my memory again, it is The Eurostar anyway.