FrediFizzx wrote:I like this quote in the slides for Jaynes,
“But our present QM formalism is not purely epistemological; it is a peculiar
mixture describing in part realities of Nature, in part incomplete human information
about Nature — all scrambled up by Heisenberg and Bohr into an omelette that
nobody has seen how to unscramble. Yet we think that the unscrambling is a
prerequisite for any further advance in basic physical theory. For, if we cannot
separate the subjective and objective aspects of the formalism, we cannot know
what we are talking about; it is just that simple.”
We are working on the unscrambling.
As you like Jaynes, he is most known from the maximal entropy principle - from
https://en.wikipedia.org/wiki/Principle ... um_entropy :
The principle of maximum entropy states that the probability distribution which best represents the current state of knowledge is the one with largest entropy
To connect it with QM unscrambling, let's look at diffusion - for example for defected lattice like semiconductor, standard diffusion predicts nearly uniform stationary probability distribution of electrons - they would flow if applying electric field, making it conductor.
In contrast, in reality semiconductor often does not conduct electricity, what is explained by QM: predicting very strong (Anderson) localization - STM measurements (from
http://www.phy.bme.hu/~zarand/Lokalizac ... azdani.pdf ):
Where does this failure of standard diffusion comes from? Jaynes brings the answer.So turns out standard diffusion (GRW) is based on only approximating (Jaynes) principle of maximal entropy - maximizes entropy locally (for single steps), but not globally - for average over steps (
https://en.wikipedia.org/wiki/Entropy_rate ).
It is repaired in MERW (
https://en.wikipedia.org/wiki/Maximal_E ... andom_Walk ) finally maximizing entropy rate - thanks of that leading to the same localized stationary probability distribution as QM ground state ... and having Born rules, allowing not to satisfy Bell-like inequalities ...