Interesting, but there are several problems with the theory:
-- In order to double the diameter the Earth would have to gain enough mass to fill all that extra space. How much more? Eight times. Check it yourself -- Earth's diameter at present is 12,756,320 meters, and using the formula for the volume of a sphere: Volume = (4*3.1415926535*radius ^3) / 3, it's volume is 1.085923 10^21 cubic meters, and it's mass is 5.97219 × 10^24 kilogrammes, resulting in a mass of ~5500 kilogrammes per cubic meter. The smaller Earth (half it's present diameter) postulated would have a volume of 1.358579 x 10^20 cubic meters, and a mass of 7.472184 x 10^23 kilogrammes. Where did all this mass come from? Since the estimated mass of all the asteroids is only 3 x 10^21 kilogrammes, it becomes obvious that all that mass could not possibly be from debris from our solar system, so again, where did all that mass come from?
-- This theory does not account for the artifacts of plate techtonics such as subduction zones, the most famous example of which is the Mariana Trench, and the mid Atlantic Ridge.
-- Where did all of that water come from?
It is obvious that the theory was presented before plate techtonics was theorised and later proven.
There is the possibility that something large enough to increase the mass of the Earth sufficiently to confirm this theory collided with the Earth, ejecting enough mass to create the Moon (one theory on how it got there), but it would have had to happen several billion years ago when the proto earth was still largely molten, not "A few hundred million years ago" when the crust was largely solidified and would have been shattered into tiny pieces more or less evenly distributed across the surface.
On the other hand, logic is defined as "A perfect way to go wrong with complete confidence", ergo it could have happened but there just hasn't been enough interest in the theory to look into it. In other words, science's tunnel vision strikes again, which the "Scientific conspiracy" buffs love to shout about.
If it has already been done, it is safe to assume it is possible to do it.
On the other hand, if it has not been done never assume it is impossible to do it.
------- Rob --------
I just found it interesting and something I hadn't heard of before, though I'm quite sure there's a plethora of things I haven't heard of. And you had to spoil it all by bringing math into the picture;-)