That's pretty doggone fast!

Fascinating concept!!!

Mixed with magnets, I guess they will go fast:

There have been concepts about putting these trains under the ocean too. I worry that if there is an accident it would be catastrophic, and probably destroy the entire rail line.

Take a nice deep hit from that bong, and out with it. Train disintegrates.

Crosstown commutes are a series of tubes...

or at many manufacturing facilities where they have to get samples to the lab for analysis quickly before they use the product that makes the parts that they are about to make. I know Iron foundries use them for that reason as do some plastic manufacturers.
I've worked on these systems at the foundry where i worked for several years back during the raygun years and there really isn't much to go wrong other than something bending the tube or the vacuum quits working. Other than that they're pretty fail safe and quick as all get outs. At the foundry they'd have samples back at the lab a couple hundred feet away for analysis way faster than they could by any other means, like right fucking now.

It always seemed too obvious not to have been thought of by someone else...

One thing I wonder is how much energy goes into maintaining the vacuum vs. the energy saved by virtually eliminating air resistance.

It's not just maintaining the vacuum, but it's starting and stopping the vacuum at each station.

Especially compared to the engineering challenges of tunneling through the N.A./Eurasian plate boundary (and for thousands of miles).

An airlock would be comparatively simple to set up. Since the (pressurized) train itself would fill up the bulk of the lock, there wouldn't be all that much air to evacuate/fill each time. Probably easier than the Panama locks.

Without a sea-change in the US, passenger rail will be nothing but a small-time novelty in many areas.

It really doesn't have much to do with passenger rail in the US. That might not pick up at all.

But such a transatlantic option (very high speed combined with very low cost) would be a game-changer.

For how much of the trip, at what kind of G-forces for the passengers on starting and stopping, and at what kind of pressure change in the cabin? There are reasons that elevators don't make it to the top of skyscrapers in seconds, even though there are ways to make that happen. Plus there's that whole Mid-Atlantic Ridge and laying tube over an expanding magma field.

A slower version on land might be plausible, but I don't think many people would like to experience astronaut-on-takeoff, or life as chunky salsa, to see Europe or space.

4000 km/hr is around 1100 m/s - let's round down to 1000 m/s and take g=10 m/s^2. Then at 1 g it takes 100 seconds - less than 2 minutes - to reach such a speed. I'm not sure what the best choice for a propulsion system would be in that case - you're then talking about accelerating over a distance of tens of km.

I think reaching modern jetliner speeds would be a more reasonable and still-useful goal.

Cabin pressure changes don't have to be an issue at all - I presume you would seal the compartments at whatever pressure you like; making it 1 atmosphere is just a matter of building a sturdy enough compartment.

Laying the tubes could be a real showstopper, though. Magma isn't going to be a congenial environment for this!

All those people in a confined space have to have some way of obtaining fresh oxygen and removing carbon dioxide. Even if you have stored oxygen in tanks, the CO2 builds up and poisons everyone. That's why jets pressurize the cabin constantly and vent the used air, which means an inevitable pressure change for the passengers. Not to mention someone's BO or the air around the required toilet...

1G in a car is more than enough to throw you back into the seat. That's about 0-60 in 2.7 seconds. More comfortable speeds for unbelted passengers or those not wanting a thrill-ride experience would be something like 0.1 g, which means your train takes 20 minutes to get up to speed, and 20 minutes to slow down. That one-hour travel time isn't so realistic now.

You just need more sophisticated air handling than airliners use. We keep people in space for months on end; air quality is a minor technical issue. Depending on the use of the tunnel and pumping speed one could even imagine venting gases out the rear if there were a need to do so.

Concerning acceleration, why assume unbelted passengers? On an airliner you are belted for substantial periods of time that do not exceed those required for accelerating and decelerating one of these trains. Airliners might be a good benchmark for realistic readily-tolerated accelerations - they're well short of 1 g, but I'd say closer to 1/4 than 1/10 of a g.

I'm not obsessed with the hypervelocity claims and 1-hour travel times; I do think there could be substantial benefits to this approach for shorter trips and slower speeds.

would pass from the North American tectonic plate to the Eurasian tectonic plate. Hard to imagine what could go wrong there.

Something goes wrong on a plane and you could always hope to glide to Iceland or wherever. If it goes really wrong, you could hope to die quickly.

On a train you might be sitting there for a long, long, long time.

in fragments, through the mouth of a volcano