A rather weird question. Einstein once said that “God does not play with dice”. Nowdays one knows that QM is a strong reliable theory. What about Gödel's incompleteness theorems”. I should apologize if I did not grasp your question.

In quantum theory the set over which statistics is made exists in parallel universes that do not communicate with each other. This lifts any contradiction between the formally predictive quantum theory and "reality" that is split among many universes. This very profound (and correct) idea was introduced by the late Hugh Everett in the mid fifties

Let us take two fair dice. You throw the two dice one million times. Every time the total is 5, I give you $1. Every time the total is 7, you give me $1.

I bet all my belongings that I will end up richer than I was!

To answer your question, yes, statistical theories describe what really happens (in the above example, reality is that I win)!

The von Neumann entropy describes a microscopic system. However it is not possible to exactly describe coarse graining. It is an approximation, which does lead to satisfying results. The Complexity on the other hand is a new concept which is leading possibly to an infinite state which is not equal distributed but still continues infinitely with possible recurrences (Susskind: Three lecturers on Complexity and Black Holes

Take care Kay

Preprint The Universal Fractal Chirality of Riemann Zeta-Function: On...

You’re absolutely right to raise this question — it’s at the core of foundational physics. Statistical theories like quantum mechanics give us incredibly accurate predictions, but whether they describe reality itself or just our knowledge of outcomes is still deeply debated.

Some interpretations (like the Copenhagen or QBism approaches) say quantum theory reflects our knowledge or information — not reality itself. Others (like Bohmian mechanics or objective collapse models) propose that something real is evolving beneath the statistics. And decoherence offers yet another angle, explaining how probabilities arise from system–environment interactions without invoking a literal collapse.

If you’re interested in diving deeper, I recommend a recent comprehensive review:

“The Quantum Measurement Problem: Foundations, Interpretations, and Recent Developments”

You can read it here: https://www.researchgate.net/publication/390671023

It surveys all major theories and recent experiments, offering a complete picture of where the debate stands. It might be a strong foundation if you’re thinking of writing a paper on this topic.

Best wishes on your research journey!

The points raised by Dr.Adam Nasser are exactly what I have in my mind. All theories of physics are only representing our state of knowledge, nothing more.

Dear Prof. S. V. G. Menon , interesting question.

I can give an example: Low temperature properties of unconventional superconductors and the fits between theories and experimental data tell a lot about the physics, and they are based on a many body formalism and non equilibrium statistical physics.

Kind Regards.

The question is, if coarse graining is a deeply internal property of a statistical system. Von Neumann entropy is describing the fine grained system, but information which is sometimes called 'information loss' is some subtle 'mechanism.' Now is coarse graining a real effect or is it a result of the resolution problem? If we think about the idea that the second law of thermodynamics is resulting in the fact that there's non possibility to construct a perpetuum mobile and thus the fact: we cannot convert heat fully into work. So we can ask: Is the impossibility of constructing a perpetuum mobile a result of coarse graining or is it just a technological problem ?

Reformulating the question: Can we construct a system that is only showing von Neumann entropy?

This is a deep fundamental problem

Take care Kay