Sure, let's go over it together. Tlb is many things, but "rarely wrong" is probably near the top of the list. He certainly read those sections before making that comment, so there must be something here which made him as an engineering expert say that it doesn't properly address thermal expansion. I'll try to run an emulator of tlb's mind, but mine is far less sharp.

The tube will be supported by pillars which constrain the tube in the vertical
direction but allow longitudinal slip for thermal expansion as well as dampened
lateral slip to reduce the risk posed by earthquakes. In addition, the pillar to
tube connection nominal position will be adjustable vertically and laterally to
ensure proper alignment despite possible ground settling. These minimally
constrained pillars to tube joints will also allow a smoother ride. Specially
designed slip joints at stations will be able to take any tube length variance
due to thermal expansion. This is an ideal location for the thermal expansion
joints as the speed is much lower nearby the stations. It thus allows the tube to
be smooth and welded along the high speed gliding middle section.

This seems like the key sentence:

Specially designed slip joints at stations will be able to take any tube length variance
due to thermal expansion.

There are two stations, one in SF and one in LA: http://i.imgur.com/3TavjCY.png

(For simplicity, let's assume it's just the main route.)

That would mean each station needs to absorb 150 meters of thermal expansion. (Would anyone mind double-checking that tlb's calculation is correct?)

So it looks like the tube is resting on these things: http://i.imgur.com/srQjmps.png

and the plan is for the tube to expand due to heat, and the expansion will be absorbed at the two stations at the end.

Is that really feasible, especially given that different points along the route could have temperature differences? I drove along Highway 1 and saw how incredibly different the weather can get, and while that's south of where the route is planned, it's easy to imagine that part of the tube could be roasting in direct sunlight while the other is cooled by rain. Something like 90 degrees F at one part vs 70F at another part. That's a difference of 32.22C to 21.11C, or a total temperature difference of 11.11C.

The route from SF to LA is about 350 miles. If a tube of that length expands 300 meters, then we can divide 300 meters by 350 miles to get the total expansion over a single mile. So a variation of 40C would give an expansion of 0.85 meters within a single mile.

Since the variation in that scenario would be ~11C, multiplying the expansion by 11C/40C equals an expansion of 0.235 meters.

So I suppose the question is: Is it feasible for those things the tube is resting on to absorb a quarter meter of expansion without that expansion being pushed all the way up to the station? It's the temperature differential along the route that seems to matter, not necessarily the difference from summer to winter.

Judging by this screenshot: http://i.imgur.com/wgUJqWr.png

... it seems like an expansion of 0.25 meters might be a big deal.

But I don't know what I'm talking about. Is all of that about right so far?

I'd also be curious whether the thermal expansion results in the tube becoming bigger in the circular direction, like a bigger "O", or if it expands parallel to the tube, like becoming a longer tube. Or even both.

It seems like the plan addresses this with the first part of that paragraph:

The tube will be supported by pillars which constrain the tube in the vertical
direction but allow longitudinal slip for thermal expansion as well as dampened
lateral slip to reduce the risk posed by earthquakes. In addition, the pillar to
tube connection nominal position will be adjustable vertically and laterally to
ensure proper alignment despite possible ground settling.

But again, where precisely does 0.25m of steel go? I'm having trouble visualizing how the pillars could "allow for 0.25m of longitudinal slip over 1 mile."

I realize that a temperature variation of about 10C over 1 mile is a little extreme, but we should examine how the system handles extreme situations.