I think all the quantum puzzles can be easily understood by examining some certain shared a priori-assumptions that make it possible for ourselves to comprehend nature.
But before i come to my point, i must explain first what i mean with my first sentence here. This first sentence would be somewhat circular if one ignores a crucial fact about the very nature of quantum physics. It would be circular because starting that some of our a priori-assumptions in understanding nature could explain exactly this nature we are wondering about would be itself an a priori-assumption. And that because a priori-assumptions are at suspicion to not be able to contain more information (together with a theorem) that one can plug in to them. But in spite of this, our best scientific conclusions and hence theories (at first admittedly including quantum mechanics and its physical effects - for whatever reasons they might occur) - if they are true (even maybe though not under all circumstances) - afford and imply their (at least partial) self-understanding at some point in spacetime. this would be valid both in a strictly deterministic world as well as in a "randomly evoluting" world because of the fact that we can do effectivly physics and would be in my opinion a reason to be strongly perplexed.
On the grounds of this wonderment i assume the a priori-essence of all reality to be of logical and hence "intelligent" (but not necessarily consciousness in the sense of a human beeing) structure. Why? Because the glue that sticks together the (quantum) world is in my opinion a (let it be continous or discrete) field of more or less evolved and yet evolveable and evolving "truths" out of other "truths".
I will now come to the point: The structure of reality is governed by logical relations and some of them can be "more real" than others due to Gödel's and Löb's theorems. For example Gödel's famous 1931 implies - for the aim of my discussion! - that undecidable statements (at least in maths) are consistent but incomplete and not vice versa. My assumption here is that indeed we live in a consistent world that is incomplete concerning its final information content.
For me it turns out that self-governed logical relations evolve due to negative selection effects thereby conserving continously their main axioms from the start. For example Löb's theorem can be formulated in the way
"if this sentence is true, then the moon consists of cheese"
which is a tautology because it conserves its consequence into its antecedent (and vice versa!). It can be therefore written as
"if the moon consists of cheese, then the moon consists of cheese"
which is obviously as true as any other statement of the form "if x exists, then x exists" and selects out the self-referential antecedent above. Because tautologies are true under - most if not all - circumstances, i assume that these forms of logical propositions form the majority of our macrocosmical matter.
In our microcosmos i would apply a simple logical rule of proportion (rule of three) to gain insight into 3-dimensionality of space and time like following example shows:
"If Bruce is ill, he coughs" (Conditional statement)
"Bruce is ill" (Antecedent)
"Bruce coughs" (consequence wich is valued TRUE)
Now what about if we measure not the "antecedent" first, but the "consequence"? This would look like the following:
"If Bruce is ill, he coughs" (Conditional statement)
"Bruce coughs" (Antecedent)
"Bruce is ill" (consequence wich is valued UNDECIDABLE)
So if Bruce coughs, this will not necessarily mean, that he's indead ill (but it could mean exactly this!). The same appears if we swap antecedent and consequence in the conditional statement. So we have two true values and two fuzzy values. The latter sums up to one value because it is not distinguishable from each other. At the end we have approximately the proportion of 1/3 (two truth values and one fuzzy value) to wich the Bell's inequalities are violated in the experiment of Alan Aspect.
My opinion on the discussion of the nature of reality is that
1. reality is somewhat intelligent out of itself
2. "Truth" in the common and traditional sense is not only
an affair of existence/non-existence but can and will
be constructed continously (--> probabilities in QM).
3. Time is one of many constructive creations out of the
fundamental level of more or less "true" relationships.
4. Space is one of many constructive creations of the
fundamental level of more or less "true" relationships.
5. With the fact that human intelligence can divide
something into two parts (for example
into "inconsistency" and "incompleteness") one can
deduce that all reality flows out of an undivided,
consistent and unchangeable - yet unknown - ground.
6. I think that the notion of "information" in QM is the
best path to gain more insights into a "valid"
interpretation of QM.