What do I think about the collapses?
Each tower collapsed roughly in 10 seconds which is comparable to the time of free fall from the same height. Recall that in 9 seconds, you fall by 5 x 9 x 9 = 400+ meters which is a bit less than 417 meters of the full height of the WTC towers.
I don't see anything wrong with the nearly free-fall model. For example, the 93rd floor of WTC1 (or 77th floor of WTC2) suddenly broke because of the high temperature melting the metalic structure. The remaining 10+ floors of WTC1 (or 20+ floors of WTC2) above the critical point - whose mass was 50,000 tons for WTC1 (or 100,000 tons for WTC2) started to fall freely, and they were hitting the lower floors one by one and taking the other floors with them. The new floors slow down the avalanche a little but not much because the falling part of the tower is much heavier.
If the momentum of falling 20 floors is suddenly shared by 21 floors (because another floor joins the avalanche), the velocity decreases by 5 percent only, and this percentage is decreasing as the collapsing portion of the tower relatively grows.
P.S. (off-topic): There is a new contribution to the heavily overpopulated family of anti-physics shitheads. His name is Gregg Easterbrook. Oh no, he's been fighting against extra dimensions for years. Fortunately, Gene seems to be correct and some people are able to see that Easterbrook's text is nonsense: DovBear, Ezra Klein. Still, most people are morons, and I chose not to link to them because they have enough links to each other.
Update - elastic model
I have asked many people what they think about it. An interesting response came from Yevgeny Kats - during our long chat about more serious physics. He figured out that my model - that is totally plastic - is actually making things slower than necessary; intuitively it is because I am losing kinetic energy which slows things down. He proposed a different, completely elastic model, as a zeroth approximation, and I offer you my quantitative version of it.
In this picture, the floors never join into a single object. When the (F+1)st floor reaches the Fth floor, the upper floor stops completely while the lower floor picks all of its speed. Imagine that you look at the (F+1)st floor before the elastic collision but you choose the Fth floor after the elastic collision.
In this picture, you can visually follow a floor that is freely falling, and whenever it reaches another floor, it gives it a signal to fall freely (from zero initial velocity). If I exchange the identification of the 2 floors during each elastic collision, the floor whose initial height is "h" will thus reach the ground after time
- sqrt(2(H-h)/g) + sqrt(2h/g)
- h = H/2
- 2 sqrt(H/g)
- 2 sqrt(360 / 9.8) = 12 seconds,