Quantum analog of Boltzmann entropy?

[Fra]

Detectors are usually all there is relevant in the sense of measuring a particle. They are indeed big enough to be treated classically. There is nothing more subjective in the quantum description of Nature than in the classical description.

Yes, I agree. And the subjectivity of the macroscopic domain is neglectable when it comes to small subsystems.

But problems appear when the "quantum part" contains parts that are treated both as quantum, and as part of the classical part (ie. part of the observer). And even worse when one considers gravity.

The question, which symmetries (or regularities, describable by mathematics) are manifested in Nature has to be found out by observation and model building in close interdepency. It's at the deepest level what the entire endeavor of the natural sciences is about.

The problem I see is this: Unless we find a more coherent theory that connects or relates the effective theories (much better than today that is), then - in principle - the scientific findings and the inference for any given experimental setup, has to be done independently for each observation or energy scale. This is not "wrong" but it leaves us with a patchwork of effective theories, with a bunch of experimentally tuned parameters, without the slightest clue how they are related.

Can we improve this situation? How?

/Fredrik

 

[vanhees71]

That's the question indeed!

 

[Demystifier]

By observer do not mean humans, which I think I declared many times. It's thinking it's "humans" that are the root of the confusion.

I mean the observer=agent = the part of the universe in which the inference of the remainder takes place - ie the part that distinguishes, counts and records events at the input that interface to the rest of the world.

Can a dog be an agent?

 

[Fra]

Can a dog be an agent?

What I meant is that I that a agent/observer doesn't need to be human - not that can't be human, or a dog for that matter. I only want to get away from those associating "epistemology" as a human phenomena.

The generalized physical concept I imagine is more how one part of the universe can "learn" via interactions, about other parts of the universe. The parts does not need to have brains. As I see it, an agent needs at least a structure for encoding information, and a way to process this information and respond to input. This processing in my vision does not imply brains, or computers, it can be "natural processes". Ultimaltey, the instruction set would somehow be related to the laws of physics, but at the same time these laws are subject to constant evolution.

So, sure a dog can be an agent, or a a molecule can also be an agent in the general sense. In the ordinary sense of observer a la Bohr, where it's essential the macroscopic(or "classical") environment that is the observer, then the role of the human is that it can _control_ the laboratory and the procedure of preparation and detectors, electronics etc. In this sense the physicist at least in principle have control, and access to the whole macroscopic environment, at least to the extent technology and economy allows. The exeprimental uncertainty there is, is IMO a manifestation of the ambigousness of the macroscopic observer still. This uncertainty would be larger if the negineers at LHC were dogs, but the principles are the same.

Surely a dog can't do this, and dogs would not produce QED or QCD. Those "theories" are certainly human inventions.

So what I entertain at this point are "toy models" of primordal observers, which is like the simplest possible "agents" one can imagine. It's nowhere near a dog or a molecule in complexity, it's imaginary things that I envision would perhaps been dominating in some TOE era in early big bang. One idea is similar to string theory, where my "interpretation" of string theory, would be this: the "string" is the mathematical description of a primordal observer or a living "measure". The modes of the string represents it's way of encoding information. But the problem is that the strings also lives in a background spacetime, whose dynamics is poorly understood still it seems. The various dualities in string theory in my mind, corresponds to agents different "internal recodings" or alternative representations, which also gives different dynamics. But one would need to understand the interaction between strings, and systems of strings, to understand how the background is selected. Then one can imagine largers objects constructed by strings interacting and consider the evolutionary pressure of making transition to other bakgrounds (via dualities). But I have realise this is not how string theorists think, i can't recall ahving seen one paper in this direction. So I have chosen another path.

/Fredrik

 

[romsofia]

So, I'm hesitant to post this because I get a somewhat crack potty feeling to the book (however, he actually does reference some of your papers in the more "normal" section [i.e section 1.5.2 he references https://arxiv.org/abs/quant-ph/0305131]), but I'm not sure if that's because my Bohmian mechanics principles are weak (I only know the basic of how they apply the Hamilton-Jacobi equations), but with that being said...

I stumbled upon this book https://www.amazon.com/dp/9813227974/?tag=pfamazon01-20 in my search for a book to learn this theory.

At the start of chapter 2, he states:
"$S_Q=-\frac{1}{2} \ln \rho$
where $\rho$ is the probability density (describing the space-temporal distribution of an ensemble of particles, namely the density of particles in the element of volume $d^3 x$ around a point $\vec{x}$ at time $t$ )associated with the wave function $\psi(\vec{x}, t)$ of an individual physical system. In the entropic version of Bohmian quantum mechanics, the space-temporal distribution of the ensemble of particles describing the individual physical system under consideration is assumed to generate a modification, a sort of deformation of the background space characterized by the quantity given by equation (2.1). On the basis of equation (2.1), it is plausible to make a parallelism with the standard definition of entropy given by the Boltzmann law, in other words equation (2.1) may be considered indeed as the quantum counterpart of a Boltzmann-type law. In the light of its relation with the wave function, the quantity given by equation (2.1) can be appropriately defined as "quantum entropy". The quantum entropy (2.1) can be interpreted as the physical parameter that, in the quantum domain, measures the degree of order and chaos of the vacuum - a storage of virtual trajectories supplying optimal ones for particle movement - which supports the density $\rho$ describing the space-temporal distribution of the ensemble of particles associated with the wave function under consideration."

So, the issues I have is that everything he references in this part is... his own articles, which IMO isn't THAT big of an issue, it just gets more suspicious because I can't find the journals/papers. But, I'll post this for you, and let you be the judge.

[BTW, in case anyone is interested, I ended up going with https://www.amazon.com/dp/0521485436/?tag=pfamazon01-20 but just need to actual take time and study the chapters in depth, but it is a nicely written book so far IMO.]

 

[dextercioby]

@romsofia Holland is a classic, pretty sure anyone working in BM read it. While for the 1st book you quoted, you need to check the table of references (bibliography). Does it contain only known books and articles in peer-reviewed journals? Does it include references published by the book's author? Making sure of these does not, however, exclude the possibility that the book is full of crackpot ideas, or simply wrong statements. Today, anyone can publish a book. WS, Springer, and others will not ensure that the board of editors accepts only correct manuscripts.

 

[romsofia]

Does it contain onltly known books and articles in the peer-reviewed journals? Does it include references published by the book's author?

Exactly the issue I ran into. One of his own papers (that he references a lot to justify the relation in the boltzmann entropy) comes from "D. Fiscaletti, “Perspectives of Bohm’s quantum potential towards a geometrodynamic interpretation of quantum physics. A critical survey”, Reviews in Theoretical Science 1, 2, 103–144 (2013)". However, this journal seems to be gone (and predatory?).

In fact, the only reason I decided to go ahead and post is because the book's author heavily uses OP's work, and even goes as far to dub his work as "Nikolic's approach" throughout the book. So, if anyone could be a proper judge, I'd guess it'd be from somehow who wrote the papers that influenced a lot of this book.

 

[dextercioby]

Sorry, for me publishing in a predatory journal is akin to uploading to vixra, because you can't get an endorsement to upload it to arxiv. @Demystifier Is this book by a certain Fiscaletti author known to you? Care to make some comments on it? Thanks!

 

[Demystifier]

and even goes as far to dub his work as "Nikolic's approach" throughout the book.

It refers to my older works, but my approach has significantly changed in the meantime. My current view of Bohmian mechanics is best represented by the article in my signature, and more recently by https://arxiv.org/abs/2205.05986 where the last section describes how my views changed over time.