No, I think the lateral stability problem is far greater than the small annual growth in the width of the Atlantic. The solutions to the latter problem are much easier to come up with than for the stability issue. The anchorage of tether cables to the ocean floor may be stable, at least until there is a subocean earthquake or landslide which could be a problem. But the problem is that the tunnel itself would be swaying and twisting in the ocean some km above the ocean floor.
Take a kid's helium baloon outside and you will see it bob around dramatically in even a slight breeze. Now picture your trans-Atlantic tunnel also bobbing around, while trying to maintain a vacuum across tens of thousands of articulated connections and with a train weighing several thousand tons moving at several hundred/thousand kph. The Atlantic contains many different ocean currents moving in different directions and with different speeds. The weather and tides change the local behaviour of some of these currents. As a result the tunnel will adopt a series of continually moving curved paths. In current rail systems, the tracks are set and if they ever move it usually results in a crash. Although this Atlantic tunnel wouldn't have conventional tracks its path is going to be constantly changing and that presents some serious safety issues.
An analogy was made earlier in this thread to think of the train as being like a bullet in a barrel. I suggest you know think of that barrel as being wobbly, moving around and made of thin plastic. Would you feel safe using it now?
It might be just me, but i don't see much problem with that. According to the video, the anchors would be tight, but with enough room to wobble slightly. Think that the structure of both cables with the ground between them form a triangle, you can't deform it much.
Yes, there will be currents, but that's why it has a small room to wobble, to adapt to those changes. It's not going to be like a balloon that is sustained by a single thread. For example, take the helium balloon, tie it with 2 threads, and glue those threads to a table forming a triangle. Now, perpendicular to the plane of that triangle, place something in front and behind of the balloon, to account for the other segments of the tube. Now try blow some air against it, poke it softly, etc... it really won't move that much.
At least that's how i see it
