The universe is expanding in the 3 spatial dimensions, could it not also be expanding in time dimension. In other words, are we stuck in 3 dimensions because we are riding the "bow wave" of the big bang in the time dimension, stuck on a 3d plane perpendicular to our world lines in spacetime? Think of a 3d-printer, are we on the upper surface of the printed object with new time being added continuously.
Would this mean that the quantum foam is the moment when the universe comes into existence, that the collapse of wave functions is when probability becomes reality? In that way there would be no need for the many worlds interpretation of quantum physics. Ahead of now is "outside" the universe i.e. there is nothing so the extra quantum states never "existed" in any sense, they were only ever mathematical probabilities. The act of observation is simply being in the now and that's why quantum systems are different depending on where you measure them - it's a different locus of the 3 spatial dimensions and "now".
Update
I don't believe that this is a duplicate question. After some discussion elsewhere it turns out that what I am describing is the Evolving Block Universe. It is well (and more formally) described by South African cosmologist George Ellis in this paper:
http://arxiv.org/abs/gr-qc/0605049
There is also a YouTube presentation, recorded in 2012, here: