[mechanical_fish]

I was quite confused by this statement, because it just looks wrong. Upon consulting the text you are citing, I figured out why: This is the author's summary of Einstein's position on the determinability of quantum systems, and Einstein was wrong, famously wrong. This statement is about how Einstein thought the world worked, not about how the world actually works.

This statement you quote has often been called by the jargon name "hidden variables theory". You're asking: What are these hidden variables? Well, Einstein could never find them, and later work has shown that this is because they don't exist. Read the end of the chapter first. ;)

Incidentally, at first glance this chapter doesn't look like light reading.

[othermaciej]

Technically, the only thing that is known not to exist is local hidden variables. There are non-local hidden variable theories which are consistent with all known experiments. Unfortunately, they are also not distinguishable by experiment from more mainstream interpretations of QM.

Here is an example of a non-local hidden variable theory: http://en.wikipedia.org/wiki/Bohm_interpretation