This week's hard to understand physics

Another week, another arXiv paper that seems important, if only I could follow it properly.

This one is about how to understand the quantum "delayed choice" experiments, which on one interpretation can be thought to show "backwards time influence".

This, according to the paper, is not the right way to think about collapsing wave functions. The crucial section of the paper seems to be this:

Although the above expressions are all very simple, the result is, upon second thought, very non-trivial. It shows that in general, the relative time ordering of measurements on separated (but possible entangled) particles A and B doesn’t matter at all....

This makes explicit that a measurement on one particle does not at all influence the other one. (I.e. the operator 1 acts trivially.) The only effect a measurement has, is changing probabilities of other measurements into conditional probabilities, as explained just above. More important, these conditional probabilities hold regardless of the moment at which you perform the measurement on the other particle. Whether it occurs later, earlier or at the same time - that doesn’t matter at all. This forces us to abandon the (popular, but incorrect) view on the wave function collapse as an event stretching out along a space-like slice. Even though this view is appealing, it creates a wrong intuition about the physics involved.

I understand the idea that he says is wrong; I don't understand the alternative way of looking at it that he is suggesting.

By the way, whatever happened to John Cramer's "backward causation" experiment? It's taking a long time for any results to come out.