I wonder if it's possible to ever find out what our reality is even if we will eventually reach the intellectual and technology necessary because we are part of it and it's probably impossible to have an objective view of the matter.
And I felt that the Planck-scale was somehow a proof for this.
We, as clever little beings found similarities and analogies between the universe and mathematics and leverage those to make conjecture regarding the form and nature of the universe. However, having a "complete" knowledge of either mathematics or the physical universe does not confer complete knowledge of the other.
I wish the word "reality" would stop being thrown around without justification. "Fundamental" might be a more appropriate term.
Only among high-energy physicists. Perhaps not coincidentally there's also a belief among high-energy physicists that only they count as physicists.
In reality, they're a small minority of physicists. The largest specialty in physics, accounting for about half of all research, is condensed matter physics. Then in no particular order you've got AMO (atomic/molecular/optical), astrophysics, geophysics, biophysics, and a bunch of other stuff sitting between or outside those categories. With the exception of just a few corners of astrophysics, none of these fields needs, or can make sure of, the stuff being done on fundamental interactions; regular old quantum mechanics plus relativity is good enough for describing everything we can actually measure.
Any physical system that can be described by a set of mathematical laws is bound to have some axioms that simply cannot be proven within its context. Godel's incompleteness theorems prove that.
Hence, we will never get to the bottom of the reality of our universe.
Gödel's incompleteness theorems are about mathematical theories, not about physical theories. It may well be that for physical understanding a very limited arithmetic is sufficient. Also, there may be statements that are unprovable, but these might turn out to be irrelevant to sufficiently understanding the universe.
Also, an axiom, by definition, can not be proven. The things that are proven are theorems, statements, etc. An axiom is an assumption.
Eventually, it all depends on what level of understanding you want. But Gödel's theorems have little to do with that.
In fact, the theorem showing how to do so (Bayes' Theorem) is so utterly elementary we teach it in the first probability course everyone takes.
This means that at some point, existence must have been started by something non-existent. Because we only comprehend cause-and-effect, we can't possibly find the origin in a provable way while researching from within existence.
Where Gödel comes into the picture is that he gives us no right to believe that only those axioms are all there is.
If the reality is mathematics, Gödel justifies the Multiverse hypothesis: just because we are objects within some theory doesn't mean there don't exist other theories (perhaps superset of this one).
"Unable to prove" in the Gödel sense can be then equated with "unable to peer into another universe".
Gödel's sentence becomes analogous to some phenomenon or artifact of another universe which cannot exist in ours because it cannot be derived from its axioms.
I often use this line of thought to talk about God with open-minded believers. If there is a God that created our reality and acts on it, then the effects of these actions are real in our sense and thus measurable. It then follows that God isn't separate from the natural world and can be observed like many other natural phenomena we don't look at directly. Without a chain of interactions this wouldn't be possible.
What I mean is our reality is one of interactions. What is real to us, and what can be called "existing" is what interacts directly or indirectly with our senses and our minds. What we mean by "nature" on a large scale is ultimately internal structure. Once we hit a level where internal structure doesn't make sense anymore, I'm not sure what we are looking at and what the word "nature" can be made to encompass.
On the other hand, due to the nature of HN, one has to choose between either spending a few days researching the comment and posting it with a very slim chance of being read or answered, or blurting out something not very polished.
In this case it's the latter. (How you define “objective”? “reality”? A rough example of how could the answer to the question “what reality is” roughly look like? Any links to existing research—people certainly attempted to ask a question of this nature before?) The resulting discussion may be worth it, though.