I'm not so convinced it's impossible. highly improbable, sure... but maybe not impossible.
various sources on the web put the number of particles in the universe somewhere between 1080 and 10120. giving the universe the benefit of the doubt and going with 10120, a little math will tell you that there are about 3.2 · 10496 more hashes in a 2048-bit space than there are (presumably) particles in the universe... so a perfect hashing algorithm that created 2048-bit digests could uniquely validate every possible bitstream of every possible length. it doesn't seem like such a leap to take a genuinely unique identifier and turn it back into that which it identifies.
ok I'm babbling, and I'm no mathematician, so I'm probably very astonishingly wrong. I just hate it when people assume something is impossible because it seems so unreasonable. at least, I haven't read a good reason yet... I'll keep reading. but if I don't find one soon, I'm going to tentatively chalk this one up on the list of impossible things to believe before breakfast.