toy models of QM

12:00 AM

But how does QM achieve this? The many world interpretation seems to go exactly into the opposite direction, and Bohmian mechanics is even worse than many worlds with respect to the amount of information required for its ontology.

But the temptation to "create an ontology" for QM is probably already part of the problem, i.e. it might be what you are hinting at with "I feel it's only difficult if you fix your philosophical postition from the start, or if that position is too restrictive".

The pioneers of QM stressed that it is an epistemological theory, which I can confirm now. But for me, the density matrix formulation was important for seeing this. However, the various ways to come back from a density matrix to a wave function are not well described in the textbooks available to me.

I have the impression that most people (here at physics.se) are not aware that there are many different ways back from a density matrix to a wave function, and that the church of the bigger Hilbert space is neither the only nor always the best way back.

vzn

1:34 AM

the pioneers of QM disagreed on its meaning. it more the bohrian copenhagen interpretation that its necessarily an "epistemological theory". the minority faction which incl many major physicists went along with this lacking experimental evidence to the contrary, but not without disagreement.

vzn

1:50 AM

its actually bohr who, decades ago, originally seemed to "fix his philosophical position from the start"...

NikolajK

8:44 AM

@ThomasKlimpel: Which German textbook are you referring to? (I'm German speaking as well). Regarding QM philosophy: afaik we're not really able to bridge e.g. the standard model to semiconducor-phyiscs, say. We can't integrate out all degrees of freedom and get from the microscopic theory to the exact less-microscopic one. Hence, I don't know why I should view people doing QM as anything more than using a tool-box. I'm no realist by any means, so again, that's my pragmatic perspective.

This also reminds me of

web2.ph.utexas.edu/~wktse/Welcome_files/…

by

Philip Warren Anderson

Philip Warren Anderson (born December 13, 1923) is an American physicist and Nobel laureate. Anderson has made contributions to the theories of localization, antiferromagnetism, symmetry breaking, high-temperature superconductivity and to the philosophy of science through his writings on emergent phenomena. == Biography == Anderson was born in Indianapolis, Indiana and grew up in Urbana, Illinois. He graduated from University Laboratory High School in Urbana in 1940. Afterwards, he went to Harvard University for undergraduate and graduate work, with a wartime stint at the U.S. Naval Resea...

Besides, real numbers don't contain infinite information.

Take

$user image$

It has some finite Kolmogorov complexity. Any computable reals do.

And the non-computable ones, such as

ncatlab.org/nlab/show/Specker+sequence

And the undefinable ones, such as

oh shap, you can't talk about them

they are just tokens in the game of math

NikolajK

9:03 AM

---My point being the numbers which you think might be infinitely complex and where anyone could extract any information from are not object which you can talk about case by case. They are artifcats of human comprehension of the power set.

We have a language with countably many sentences and can express our idea of uncountably sets, and by comprehension specify the set of U=R\{every real we can specify}, U being a set of undefinable numbers. But this "set" does not in any good sense "contain" any members - after all, by definition, you can't even specify them. Coming back to physics, I'm not a fan of the idea that anything we talk about when we set up models of the world does correspond to "actual things".

For example, we have Newtons laws, F=ma. And it works. But there is no force in QM, just hamiltonians and correlation functions. You can, in principle, integrate out stuff form the detailed QM theory and end up with Newtons theory. But yo don't have to.

A being, some alien, that lives on a scale of 10^{-16}m^3, which quantum effects are daily business the see ever time...they would never think of forces. Well, for them, the theory of Newton would be soemthing like our cosmology.

the idea of Mass m, which is relevant to us, might be an obscure large scale thingy. For them the Einstein equations is where it's at, and everything above this is inaccurate. Nothing in history suggest that this "finding a finer theory" progress should ever end.

All our words and signs are tools to make sense of causation we experience. But there "is" no mass, or energy, or whatever.

I'm mostly arguing against your "So nature has to use QM"

nature doesn't do something which is written down in a language we use.

There are no photons and electrons - just because we say an electron wiggles in our eye when an electron wiggles in your mothers face, and you hence see it, ...we descibe the correlation be introducing photons, optics, but that's a tool that works - there is no need for photons to "exist"

Thomas Klimpel

9:46 AM

A significant difference between QM and classical mechanics is that classical mechanics is a physical theory, while QM is a framework for physical theories.

Before I finally managed to become more familiar with QM, I sometimes asked physicists who said they understood QM to explain me the Compton effect in detail. The reply was often that this is not QM, but quantum field theory. And this is indeed the correct answer. But this means that understanding QM is not really related to electrons of photons.

But quantum field theory, the standard model and even string theory are all physical theories within the framework of QM. So trying to understand QM in order to better understand electrons and light is not a bad idea after all.

NikolajK

@ThomasKlimpel: Yeah, I agree with everything you said. Well, except I'd also say that quantum field theory and string theory are frameworks, not individual theories.

Thomas Klimpel

Cool, so quantum field theory and string theory are frameworks within the framework of QM :)

@NikolajK This "So nature has to use QM" is an argument for making it clear why it is difficult to "create an ontology" for QM. You nicely summarize this by 'I'm not a fan of the idea that anything we talk about when we set up models of the world does correspond to "actual things"'.

NikolajK

@ThomasKlimpel: to the first point: Just like the romance genre is a framework within books in the entertainment framework. Maybe in the 40's people meant QED when they said QFT and in the 80's they meant the string theory emerging from QFT research.

Also, if at one point some Newton/Bernulli/Euler figure would have introduced the quantitiy temperature squared E=T^2, or inverse velocity b=1/v,...our theories, now expressed in terms of E and b, would try to describe the same things with all quantities removed by completely different ones. Trying to understand the role of the wave function in the theory of QM is usefull, but to discuss about it's philosphical meaning for 100 years and mystifying people...

I like the examples because T is actually a bad thingy, \beta=1/T is more natural in many context

The small scale aliens (or, imagine some alien which has non-local peception - it feels things 3km apart from each other), they would have some theory and T^2 might be crucial and intuitive. What matters is that we do physics (and math) and take pleasure in it, not the reality of our symbols.

I disregard here, to so extent, the good "why" question, "why do these things work, and not other". My favorite is "why does it turn out that theories with a notion of 'conserved energy' always come back and seem to work again". One of my thinkings is that many things would work, but we use the ones which are easiest and approachable.

I often like Neumaiers ways of thinking (although he surely isn't an anti-realist in my way) (and not because he's also Viennese :). It seems he tries to clarify the role of formal algebra a lot (he has this book on the arXiv, on Lie-algebras in physics). I'm also on a personal question to formulate physics in a clear way, or clear for me at least. At the moment I'm trying to "factor out" combinatorics from physics. To me combinatorics is, essentially, a theory of physics.

I don't like the math/physics dicotomy, it seems just to say that math people work in this department and have this way of thinking and physics people work over there and have had a somewhat different education - not more.

You could say mathematicians are theoretical physicists who fell in love with the formalities of their theories too much. (and I don't mean to say this in a negative tone of any kind)

Thomas Klimpel

10:12 AM

Regarding mathematicians as some sort of physicists might not really be a good idea.

And believing that all mathematical parts of physics are necessarily tasks for mathematicians is an even worse idea.

@NikolajK Thinking more about this "quantum field theory is also a framework", I should have written "The reply was often that this is not QM, but quantum electro dynamics". I think both QED and the standard model are complete physical theories and not just frameworks. I just mixed up these things, because I'm still not too familiar with QM and quantum field theories.

NikolajK

10:39 AM

Why not? Mathematicans and theoetical physicists build frameworks to solve some problems, and often (when the theories are sketched out), the inverstigate them more.

The difference is just emphasis and different interest, coming from different education and seperated buildings. There is an evolutionary difference due to seperation, but I think they do the same thing - then again, I have an easier time to view it like that because I don't think theoretical physics is more than model building. I argue against "truth", if you will.

Yeah, QED and (more generally) the standard model are most specific than just quantum field theory - they are essentially defined by a fixed Lagrangian.

Though I think in practice, working with those theories has still a lot of ad hoc elements, as opposed to doing finite arithmetic say, where the axioms and possible tools/math, are really fixed.

Maybe you want to divide mathematicans and physicists in this way: the mathematicans work, more often than the physicists, with accurately fixed theories.

@ThomasKlimpel: But I feel it's again easy to argue that this is just because the math uni is there and the physics uni is there.

For example, if you read the introductory section to F_{un}, you find that doing math, Grothendieck-style, is just like fishing for the right physical theory

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Similarly

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In algebraic geometry, a motive (or sometimes motif, following French usage) denotes 'some essential part of an algebraic variety'. To date, pure motives have been defined, while conjectural mixed motives have not. Pure motives are triples (X, p, m), where X is a smooth projective variety, p : X ⊢ X is an idempotent correspondence, and m an integer. A morphism from (X, p, m) to (Y, q, n) is given by a correspondence of degree n – m. As far as mixed motives, following Alexander Grothendieck, mathematicians are working to find a suitable definition which will then provide a "universal" cohomology...

If the theory we search for is bound by predicting the right corrections to the hydrogen spectral line, or if it's bounded by proving that the fundamental group of the circle is Z...it's both just abstractly formulated "facts" that we use as guidelines in our research.

vzn

4:15 PM

7 hours ago, by NikolajK

I'm mostly arguing against your "So nature has to use QM"

who said that?

your cite of andersons writing reminds me of an essay on mesoscale physics, talking about nonreductionism & emergence, cant remember who wrote it.....

7 hours ago, by NikolajK

the idea of Mass m, which is relevant to us, might be an obscure large scale thingy. For them the Einstein equations is where it's at, and everything above this is inaccurate. Nothing in history suggest that this "finding a finer theory" progress should ever end.

so then what is a/ the "finer theory" of QM? the copenhagen interpretation does seem to be an emphatic insistence that the end is now found with QM, that there is no deeper story...

oh see TKs quote "nature has to use QM...." above but that is something of a truncation of his statement.

agree somewhat with TKs earlier statement. QM can be seen as a sort of "blurred lens" for reality.

my example/ thought experiment with the acoustic digitizer LSB gives a conceptual model for this "blurring". suspect that it is not far from khrennikov detector dynamics derivations.

"realism" is now a term with a lot of baggage and supposedly the only philosophical alternative to copenhagen interpretation. maybe we should invent a new one. (term/ interpretation)

for you philosophers, the digitizer LSB has some rough similarities to plato's cave allegory....

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