Quantum mechanics via quantum tomography

[A. Neumaier]

If I understand you right before regarding your interpretation, one of your motivators was to question the physical justification of the statistical tools used, by an actual observer, to produce expectations for single outcome?

The statistical tools are impeccable. Instead I question the interpretation of the state.

Let me know if I understand you approximately right - your conceptual solution?
Seems to be to essentially consider the whole classical environment (with all the the macroscopic pointers etc) as an objective information sink, from which any quantum tomography is taking place.

No. I am not talking at all about information, except to contrast it with the subjective approach.

 

[Fra]

The statistical tools are impeccable. Instead I question the interpretation of the state.

Ok, I certainly don't mean that the mathematical tools was questioned withing the field of mathematics. In my phrasings the "justification of the tools", is the "interpretation" I guess, ie. to justify why those tools are the RIGHT tools, for the physical situation?

No. I am not talking at all about information, except to contrast it with the subjective approach.

In your terminolgoy, does reading off experimentally accessible macroscopic equipment (sources, detectors, filters, and instruments) not counts as gathering "information"? If we label it "objective, classical information", rather than "quantum information" does that make it better?

/Fredrik

 

[A. Neumaier]

Ok, I certainly mean that the mathematical tools was questioned withing the field of mathematics. In my phrasings the "justification of the tools", is the "interpretation" I guess, ie. to justify why those tools are the RIGHT tools, for the physical situation?

Statistics is indeed the right tool for handling aleatoric uncertainty in physics.

In your terminolgoy, does reading off experimentally accessible macroscopic equipment (sources, detectors, filters, and instruments) not counts as gathering "information"? If we label it "objective, classical information", rather than "quantum information" does that make it better?

It counts as gathering information in the colloquial sense, but not in the sense of information theory, which quantifies missing information rather than knowledge.

I don't know what 'quantum information' is. Quantum information theory is not about some mysterious 'quantum information' but about quantum state estimation and manipulation.

 

[Fra]

Statistics is indeed the right tool for handling aleatoric uncertainty in physics.

Here we may reach difficulties as I think we have taken on different tasks here. Which statistics? The task of general inference (including abducing the best laws) is much more than just "objective frequentist statistics" in my view. One has to ponder about things like information processing resource constraints. As no real observer/agent can simply or access store all raw data som some faithful form, from from that make "objective" inferences. The subjecitivty of inferences are not just due to having incomplete data, it may also be due to gaming elements, such as randomly trying certain rules. Also encoding data, may involve lossy compressions, and the lossy compressions have to be choosen from what is likely to be most beneficial for future predictions. In this soup, all things that I think you consider the model must evolve. I agree that fitting too many parameters at once as once will not work, this is part of the information contstrain considerations for me. It's also why I think neith the state space nor laws (such as hamiltoinans) can be trated as statics, with predtermined parameters. The hamiltonians is one of the things that begs explanation.

I do not have the answers, I just start raising questions that I think are important to foundations and the open questions.

It counts as gathering information in the colloquial sense, but not in the sense of information theory, which quantifies missing information rather than knowledge.

Ok, good, then I think I understand. I wasn't referring to just such "ignorance" that are from macro/micro levels. What counts for me is the agents real "predictive power" and fitness in a given environment, which is influenced both by knowledge and missing information.

/Fredrik

 

[A. Neumaier]

As no real observer/agent can simply store or access all raw data in some faithful form, from that make "objective" inferences.

The only agent that matters in an objective approach to physics is the scientific community as a whole. This community has access to all data (available at a given time) and makes decisions on what is true based on accepted statistical reasoning. This makes it objective to the extent that science can be objective.

 

[Fra]

The only agent that matters in an objective approach to physics is the scientific community as a whole. This community has access to all data (available at a given time) and makes decisions on what is true based on accepted statistical reasoning. This makes it objective to the extent that science can be objective

Ok, thanks for clarifying! Then I think I see your perspective and logic. I think its nice but It still leaves many questions in my perspective unanswererd though. My take on objectivity and inference seems different. And your view IS the more consesus one.

/Fredrik

 

[Fra]

The point of my paper is a proper conceptual foundation of quantum physics with the same characteristic features as classical physics - except that the density operator takes the place of the phase space coordinates.

Nice summary!

(This explains more your perspective. I have critique also against classical physics, and you import those problems. )

/Fredrik

 

[physika]

explain the electrical characteristics in terms of quantities like local densities of states...

Explain or describing ?

.

 

[Morbert]

Explain or describing ?

Definitely explaining. E.g. we might observe some undesired electrical characteristic like a poor subthreshold swing, or a high off-state current, or early onset of ambipolar current. We learn why this is happening by studying quantities and processes in the FET (Maybe electrons are tunnelling across the short-channel barrier, or into the valence band due to a poorly tuned band gap. Or maybe inelastic phonon scattering assists band-to-band tunnelling etc). And we anticipate which devices won't suffer from these problems based on these insights.

 

[PeterDonis]

Moderator's note: A subthread on Bayesian statistics in science has been moved to a separate thread:

https://www.physicsforums.com/threads/bayesian-statistics-in-science.1008801/

 

[A. Neumaier]

Is there a simplified version of your theory for "dummies"?

Not yet, but I'll try to create something. It will take some time since simplification is hard work...

The Christmas holidays helped a lot to finally get the task done...

What I'll add is a formula-free Ariadne's thread for dummies.

I just put a revised version (v3) of the paper on the arXiv, which will appear there tomorrow. In addition I created the requested/promised Ariadne's thread as an Insight article which is currently on Review. Unfortunately, to maintain understandability, I haven't managed to completely avoid formulas in the Ariadne's thread, but the text/formula ratio is very large, probably $>100$.

What would help a lot were a clear statement of what you call "first principles" and then a derivation of the POVM and the more conventional special case of projective measurements without too much philosophy in between.

Done. To make the paper a pleasure to read for philosophobists like you, the philosophical part has been completely separated from the physics and is placed in the revised v3 at the very end!

 

[A. Neumaier]

I just put a revised version (v3) of the paper on the arXiv, which will appear there tomorrow.

You can now find it here: https://arxiv.org/abs/2110.05294

 

[vanhees71]

Now it seems to be understandable for a physicist, at least the summary of the meaning of the statistical operator on p. 8 is now starting from the usual probabilistic notion of standard (minimally interpreted) QT. That's a big progress. Of course, I've to read more in detail to understand the full meaning.