Don't burn your phd yet. They are embedding the Hilbert space that represents (is?) the current universe in a larger Hilbert space that represents (is?) the universe in the future. They change the "size"[1], but they don't change the L2 norm.
[1] The dimension of both is probably infinite, but one is a proper subspace the other.
L2 is also known as Euclidean space. It says the length of a vector is the square root of the sum of the squares of its components. There are other ways of defining vector length (or distance). E.g., in L1 is the sum of the absolute value of the components. The way distance is measured changes the properties of a space. E.g., in L2, Pythagoras is trivially true, but in L1 the hypotenuse would be as long as the sum of both other sides. That has far reaching consequences. E.g., in L1, you can't take a shortcut.
Wikipedia is not your friend, it seems. It's just terse definitions. Perhaps other math sites are more helpful.
And my original "joke" is that the Schrodinger operator is unitary on L2 spaces (which is like a mathematical statement of conservation of "energy"), so if we're throwing out unitarity then I may as well throw out my phd.
I actually studied dispersive pdes (Schodinger, KdV, etc.), though not with a computer. In that study, the properties of the Fourier transform on L2-based spaces are very important.
The other joke is a that I do software now, so of course the phd was useless, haha!
