Albert Einstein said he made his biggest blunder, while Stephen Hawking spoke of his "biggest mistake". One can read this in this interesting book review (The Nature of Space and Time by Stephen Hawking and Roger Penrose. Princeton, May 1996, 0 691 03791 4):
In Chapter 5 Hawking speaks of his own ‘greatest mistake’. Taking an expanding half-universe in which time’s arrow pointed in the direction familiar to us, he thought he could glue it to a contracting half-universe in which the arrow was reversed, so that ‘cups would mend themselves and jump back on the table.’ Unfortunately, this would work only in the cases of highly ‘unnatural’ universes: ones whose structures were chosen with fantastic care.
What was the Nature of these highly "Unnatural" universes? Which structures were chosen with "fantastic care"? Galaxies? Clusters of galaxies?
And how could this be related to the inversion of time? I short, to the fact that everything moves in a reversed way? All momenta of particles are reversed (quantum mechanically the situation might be more complicated, but not fundamentally).
What is so special about "the structures that were chosen with "fantastic care""? How could this reverse the momenta of all elementary particles when expansion was followed by a crunch? In the hypothetical case, that is.
To my knowledge, all laws of Nature are symmetric wrt a reversion of time. The weak interaction is an exception (see here): it's asymmetric wrt time as well as to the inversion of space, or, less generally, wrt interchanging left and right, above and below, or front and back).
What lays at the heart of his biggest mistake? How can the change from a state of expansion to a state of de-expansion cause all particles to change their momenta to the opposite value?